sin(x)/cos(x)

Time bar (total: 1.9s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze152.0ms (8.1%)

Memory
34.1MiB live, 34.1MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
50%50%50%0%0%0%0%3
50%50%50%0%0%0%0%4
50%50%50%0%0%0%0%5
50%50%50%0%0%0%0%6
50%50%50%0%0%0%0%7
50%50%50%0%0%0%0%8
50%50%50%0%0%0%0%9
50%50%50%0%0%0%0%10
50%50%50%0%0%0%0%11
50%50%50%0%0%0%0%12
Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.1s (60.6%)

Memory
86.9MiB live, 440.8MiB allocated
Samples
874.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 600.0ms
ival-sin: 273.0ms (45.5% of total)
ival-cos: 188.0ms (31.3% of total)
ival-div: 60.0ms (10% of total)
ival-<=: 49.0ms (8.2% of total)
ival-and: 14.0ms (2.3% of total)
exact: 13.0ms (2.2% of total)
ival-assert: 4.0ms (0.7% of total)
Bogosity

explain94.0ms (5%)

Memory
-47.7MiB live, 26.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(/.f64 (sin.f64 x) (cos.f64 x))
00-0-(cos.f64 x)
00-0-(sin.f64 x)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
40.0ms512×0valid
Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 28.0ms
ival-cos: 12.0ms (42.6% of total)
ival-sin: 12.0ms (42.6% of total)
ival-div: 4.0ms (14.2% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess18.0ms (1%)

Memory
5.4MiB live, 5.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0613
11911
23411
37711
415311
528411
637411
737611
839011
940311
045
075
075
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/.f64 (sin.f64 x) (cos.f64 x))
Outputs
(/.f64 (sin.f64 x) (cos.f64 x))
Symmetry

(negabs x)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.7%
(/.f64 (sin.f64 x) (cos.f64 x))
Compiler

Compiled 5 to 4 computations (20% saved)

simplify2.0ms (0.1%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(cos.f64 x)
cost-diff0
(sin.f64 x)
cost-diff0
(/.f64 (sin.f64 x) (cos.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0410
0710
0710
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(/.f64 (sin.f64 x) (cos.f64 x))
(sin.f64 x)
x
(cos.f64 x)
Outputs
(/.f64 (sin.f64 x) (cos.f64 x))
(sin.f64 x)
x
(cos.f64 x)

localize25.0ms (1.3%)

Memory
6.9MiB live, 6.9MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(cos.f64 x)
accuracy0.00390625
(sin.f64 x)
accuracy0.174160009768442
(/.f64 (sin.f64 x) (cos.f64 x))
Samples
20.0ms256×0valid
Compiler

Compiled 12 to 6 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-sin: 6.0ms (43.9% of total)
ival-cos: 5.0ms (36.6% of total)
ival-div: 2.0ms (14.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory
0.6MiB live, 0.6MiB allocated
Counts
3 → 14
Calls
Call 1
Inputs
(/.f64 (sin.f64 x) (cos.f64 x))
(sin.f64 x)
(cos.f64 x)
Outputs
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(/ (sin x) (cos x))
(sin x)
(cos x)
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
((/ (sin x) (cos x)) (sin x) (cos x))
0.0ms
x
@-inf
((/ (sin x) (cos x)) (sin x) (cos x))
0.0ms
x
@inf
((/ (sin x) (cos x)) (sin x) (cos x))

simplify170.0ms (9.1%)

Memory
36.4MiB live, 36.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
060140
1158140
2405128
31185128
42025128
53334128
63628128
73925128
84372128
96319128
08127110
Stop Event
1×iter limit
1×node limit
Counts
14 → 13
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(/ (sin x) (cos x))
(sin x)
(cos x)
Outputs
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(sin x)
(sin.f64 x)
(cos x)
(cos.f64 x)

rewrite85.0ms (4.6%)

Memory
-70.4MiB live, 10.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049
076
1166
2516
32206
012316
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
3 → 119
Calls
Call 1
Inputs
(/.f64 (sin.f64 x) (cos.f64 x))
(sin.f64 x)
(cos.f64 x)
Outputs
(*.f64 (/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))
(*.f64 (/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1/2 binary64))) (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64))))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (pow.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x)))
(*.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (sin.f64 x))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(*.f64 (tan.f64 x) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (neg.f64 (log.f64 (tan.f64 x)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (cos.f64 x))) (sin.f64 x))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (cos.f64 x))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 x)))) (neg.f64 (tan.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 (tan.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 x)) (*.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 x))))))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (*.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 x)))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (*.f64 (sin.f64 x) (cos.f64 x)))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (sin.f64 x) (neg.f64 (cos.f64 x))))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 x)))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (neg.f64 (cos.f64 x))) (*.f64 (neg.f64 (cos.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 x)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 (sin.f64 x) (cos.f64 x))
(neg.f64 (neg.f64 (tan.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal 0 binary64) (tan.f64 x))
(tan.f64 x)
(-.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 x)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64)))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal 0 binary64)) (tan.f64 x))
(+.f64 #s(literal 0 binary64) (tan.f64 x))
(*.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x)))
(*.f64 #s(literal 1 binary64) (sin.f64 x))
(*.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64))
(*.f64 (sin.f64 x) #s(literal 1 binary64))
(pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (sin.f64 x)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (*.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64))
(/.f64 (sin.f64 x) #s(literal 1 binary64))
(neg.f64 (neg.f64 (sin.f64 x)))
(fma.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (sin.f64 x) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (sin.f64 x) #s(literal 1 binary64) #s(literal 0 binary64))
(sin.f64 x)
(-.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 #s(literal 0 binary64) (sin.f64 x))
(+.f64 (sin.f64 x) #s(literal 0 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x)))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(*.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal -1/2 binary64))) (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64))
(/.f64 (cos.f64 x) #s(literal 1 binary64))
(neg.f64 (neg.f64 (cos.f64 x)))
(fma.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) #s(literal 0 binary64))
(fma.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (cos.f64 x) #s(literal 1 binary64) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 x)))
(cos.f64 x)
(exp.f64 (neg.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal -1 binary64))))
(+.f64 #s(literal 0 binary64) (cos.f64 x))
(+.f64 (cos.f64 x) #s(literal 0 binary64))

eval14.0ms (0.7%)

Memory
11.3MiB live, 11.3MiB allocated
Compiler

Compiled 1 393 to 332 computations (76.2% saved)

prune2.0ms (0.1%)

Memory
5.0MiB live, 5.0MiB allocated
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New1311132
Fresh000
Picked101
Done000
Total1321133
Accuracy
100.0%
Counts
133 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(tan.f64 x)
Compiler

Compiled 2 to 2 computations (0% saved)

simplify3.0ms (0.1%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
cost-diff0
(tan.f64 x)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
023
033
033
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(tan.f64 x)
x
Outputs
(tan.f64 x)
x

localize15.0ms (0.8%)

Memory
4.4MiB live, 4.4MiB allocated
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(tan.f64 x)
Samples
12.0ms256×0valid
Compiler

Compiled 5 to 4 computations (20% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-tan: 6.0ms (93.9% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Counts
1 → 5
Calls
Call 1
Inputs
(tan.f64 x)
Outputs
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
((tan x))
0.0ms
x
@inf
((tan x))
0.0ms
x
@0
((tan x))

simplify26.0ms (1.4%)

Memory
4.0MiB live, 4.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02551
17251
219445
355945
490045
599445
699745
799745
8100645
0100639
Stop Event
1×iter limit
1×saturated
Counts
5 → 4
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
Outputs
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 17/315 binary64) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

rewrite45.0ms (2.4%)

Memory
4.7MiB live, 4.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022
032
162
2142
3492
42202
012322
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
1 → 59
Calls
Call 1
Inputs
(tan.f64 x)
Outputs
(*.f64 (/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))
(*.f64 (/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1/2 binary64))) (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64))))
(*.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (pow.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x)))
(*.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (sin.f64 x))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(*.f64 (tan.f64 x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (neg.f64 (log.f64 (tan.f64 x)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (cos.f64 x))) (sin.f64 x))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (cos.f64 x))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 x)))) (neg.f64 (tan.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 (tan.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 x)) (*.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 x))))))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (*.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 x)))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (*.f64 (sin.f64 x) (cos.f64 x)))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (sin.f64 x) (neg.f64 (cos.f64 x))))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (neg.f64 (cos.f64 x))) (*.f64 (neg.f64 (cos.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 x)))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 x)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (tan.f64 x) #s(literal 1 binary64))
(neg.f64 (neg.f64 (tan.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal 0 binary64) (tan.f64 x))
(tan.f64 x)
(-.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 x)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64)))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal 0 binary64)) (tan.f64 x))
(+.f64 #s(literal 0 binary64) (tan.f64 x))

eval7.0ms (0.4%)

Memory
5.4MiB live, 5.4MiB allocated
Compiler

Compiled 647 to 154 computations (76.2% saved)

prune2.0ms (0.1%)

Memory
2.8MiB live, 2.8MiB allocated
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New63063
Fresh000
Picked011
Done000
Total63164
Accuracy
100.0%
Counts
64 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(tan.f64 x)
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes3.0ms (0.1%)

Memory
3.2MiB live, 3.2MiB allocated
Accuracy

Total -0.2b remaining (-∞%)

Threshold costs -0.2b (-∞%)

Counts
2 → 1
Calls
Call 1
Inputs
(tan.f64 x)
(/.f64 (sin.f64 x) (cos.f64 x))
Outputs
(tan.f64 x)
Calls

2 calls:

1.0ms
(/.f64 (sin.f64 x) (cos.f64 x))
1.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 (sin.f64 x) (cos.f64 x))
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify9.0ms (0.5%)

Memory
5.0MiB live, 5.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022
Stop Event
1×saturated
Calls
Call 1
Inputs
(tan.f64 x)
Outputs
(tan.f64 x)

soundness49.0ms (2.6%)

Memory
0.7MiB live, 0.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049
076
1166
2516
32206
012316
Stop Event
1×done
1×iter limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 9 to 7 computations (22.2% saved)

preprocess17.0ms (0.9%)

Memory
9.4MiB live, 9.4MiB allocated
Remove

(negabs x)

Compiler

Compiled 18 to 16 computations (11.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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