sin(PI*x)

Time bar (total: 40.4s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%25%75%0%0%0%0
100%25%0%75%0%0%0%1
Compiler

Compiled 12 to 8 computations (33.3% saved)

sample609.0ms (1.5%)

Memory
47.7MiB live, 265.8MiB allocated
Samples
321.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 171.0ms
ival-sinu: 103.0ms (60.2% of total)
ival-<=: 43.0ms (25.1% of total)
ival-and: 12.0ms (7% of total)
exact: 11.0ms (6.4% of total)
ival-assert: 3.0ms (1.8% of total)
Bogosity

explain100.0ms (0.2%)

Memory
42.0MiB live, 94.9MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(sin.f64 (*.f64 (PI.f64) x))
00-0-(*.f64 (PI.f64) x)
00-0-(PI.f64)
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
71.0ms512×0valid
Compiler

Compiled 26 to 16 computations (38.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-sinu: 7.0ms (54.2% of total)
ival-mult: 4.0ms (31% of total)
ival-pi: 2.0ms (15.5% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess46.0ms (0.1%)

Memory
-67.1MiB live, 5.5MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
11511
2309
3499
4749
5939
61079
71129
81189
91189
044
074
184
084
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sin.f64 (*.f64 (PI.f64) x))
Outputs
(sin.f64 (*.f64 (PI.f64) x))
(sin.f64 (*.f64 x (PI.f64)))
Symmetry

(negabs x)

Compiler

Compiled 4 to 4 computations (0% 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%
(sin.f64 (*.f64 (PI.f64) x))
Compiler

Compiled 4 to 4 computations (0% saved)

simplify3.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(PI.f64)
cost-diff0
(*.f64 (PI.f64) x)
cost-diff0
(sin.f64 (*.f64 (PI.f64) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049
079
189
089
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(sin.f64 (*.f64 (PI.f64) x))
(*.f64 (PI.f64) x)
(PI.f64)
x
Outputs
(sin.f64 (*.f64 (PI.f64) x))
(sin.f64 (*.f64 x (PI.f64)))
(*.f64 (PI.f64) x)
(*.f64 x (PI.f64))
(PI.f64)
x

localize16.0ms (0%)

Memory
5.9MiB live, 5.9MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(PI.f64)
accuracy0.01171875
(sin.f64 (*.f64 (PI.f64) x))
accuracy0.2109375
(*.f64 (PI.f64) x)
Samples
12.0ms256×0valid
Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-sinu: 3.0ms (51.1% of total)
ival-mult: 2.0ms (34% of total)
ival-pi: 1.0ms (17% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Counts
3 → 5
Calls
Call 1
Inputs
(sin.f64 (*.f64 (PI.f64) x))
(*.f64 (PI.f64) x)
(PI.f64)
Outputs
(* x (PI))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
(sin (* x (PI)))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
((sin (* (PI) x)) (* (PI) x) (PI))
0.0ms
x
@inf
((sin (* (PI) x)) (* (PI) x) (PI))
0.0ms
x
@-inf
((sin (* (PI) x)) (* (PI) x) (PI))

simplify80.0ms (0.2%)

Memory
8.5MiB live, 8.5MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03576
19776
231576
387270
4113970
5144770
6168270
7183570
8185570
9261070
10266670
11266670
12266670
13274770
14274970
0274964
Stop Event
1×iter limit
1×saturated
Counts
5 → 5
Calls
Call 1
Inputs
(* x (PI))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
(sin (* x (PI)))
Outputs
(* x (PI))
(*.f64 (PI.f64) x)
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 3 binary64)) #s(literal -1/6 binary64) (*.f64 (PI.f64) x))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) #s(literal 1/120 binary64)) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 3 binary64)) #s(literal -1/6 binary64) (*.f64 (PI.f64) x)))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
(fma.f64 (pow.f64 x #s(literal 7 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 7 binary64)) #s(literal -1/5040 binary64)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) #s(literal 1/120 binary64)) (fma.f64 (pow.f64 (*.f64 (PI.f64) x) #s(literal 3 binary64)) #s(literal -1/6 binary64) (*.f64 (PI.f64) x))))
(sin (* x (PI)))
(sin.f64 (*.f64 (PI.f64) x))

rewrite61.0ms (0.2%)

Memory
12.8MiB live, 12.8MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
048
078
1238
21218
38134
460114
560784
663644
777274
080564
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
3 → 6
Calls
Call 1
Inputs
(sin.f64 (*.f64 (PI.f64) x))
(*.f64 (PI.f64) x)
(PI.f64)
Outputs
(sin.f64 x)
(*.f64 x (PI.f64))
(*.f64 (PI.f64) x)
x
(PI.f64)
#s(literal 1 binary64)

eval1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Compiler

Compiled 109 to 34 computations (68.8% saved)

prune1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New9211
Fresh000
Picked011
Done000
Total9312
Accuracy
99.7%
Counts
12 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.7%
(sin.f64 (*.f64 (PI.f64) x))
▶17.6%
(sin.f64 x)
▶98.0%
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify3.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 x)
cost-diff0
(PI.f64)
cost-diff0
(*.f64 (PI.f64) x)
cost-diff0
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0816
01116
11216
01216
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
(*.f64 (PI.f64) x)
(PI.f64)
x
(sin.f64 x)
x
Outputs
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
(*.f64 (PI.f64) x)
(PI.f64)
x
(sin.f64 x)
x

localize19.0ms (0%)

Memory
7.1MiB live, 7.1MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(sin.f64 x)
accuracy0.0
(PI.f64)
accuracy0.2109375
(*.f64 (PI.f64) x)
accuracy1.0601052760903882
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
Samples
14.0ms256×0valid
Compiler

Compiled 14 to 7 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-sinu: 3.0ms (38.5% of total)
ival-mult: 2.0ms (25.7% of total)
ival-sin: 2.0ms (25.7% of total)
ival-pi: 1.0ms (12.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Counts
4 → 10
Calls
Call 1
Inputs
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
(*.f64 (PI.f64) x)
(PI.f64)
(sin.f64 x)
Outputs
(* x (PI))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
x
(* 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))))
(sin (* x (PI)))
(sin x)
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
((sin (* (PI) x)) (* (PI) x) (PI) (sin x))
0.0ms
x
@-inf
((sin (* (PI) x)) (* (PI) x) (PI) (sin x))
0.0ms
x
@inf
((sin (* (PI) x)) (* (PI) x) (PI) (sin x))

simplify172.0ms (0.4%)

Memory
38.8MiB live, 38.8MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053124
1149124
2423118
31352112
42096112
53160112
63853112
74093112
84368112
96359112
08224100
Stop Event
1×iter limit
1×node limit
Counts
10 → 9
Calls
Call 1
Inputs
(* x (PI))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
x
(* 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))))
(sin (* x (PI)))
(sin x)
Outputs
(* x (PI))
(*.f64 x (PI.f64))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(fma.f64 (pow.f64 (*.f64 x (PI.f64)) #s(literal 3 binary64)) #s(literal -1/6 binary64) (*.f64 x (PI.f64)))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) #s(literal 1/120 binary64)) (PI.f64)) x (*.f64 (pow.f64 (*.f64 x (PI.f64)) #s(literal 3 binary64)) #s(literal -1/6 binary64)))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 (*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 7 binary64)) #s(literal -1/5040 binary64)) x) x (*.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) #s(literal 1/120 binary64))) (fma.f64 (pow.f64 (*.f64 x (PI.f64)) #s(literal 3 binary64)) #s(literal -1/6 binary64) (*.f64 x (PI.f64))))
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)
(sin (* x (PI)))
(sin.f64 (*.f64 x (PI.f64)))
(sin x)
(sin.f64 x)

rewrite103.0ms (0.3%)

Memory
-71.9MiB live, 10.2MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0814
01114
12714
212514
38068
459808
560478
663368
777028
084198
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 7
Calls
Call 1
Inputs
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
(*.f64 (PI.f64) x)
(PI.f64)
(sin.f64 x)
Outputs
#s(approx (sin (* (PI) x)) x)
(*.f64 x (PI.f64))
(*.f64 (PI.f64) x)
x
(PI.f64)
#s(literal 1 binary64)
(sin.f64 x)

eval2.0ms (0%)

Memory
1.4MiB live, 1.4MiB allocated
Compiler

Compiled 182 to 53 computations (70.9% saved)

prune3.0ms (0%)

Memory
2.5MiB live, 2.5MiB allocated
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New14216
Fresh000
Picked022
Done011
Total14519
Accuracy
99.7%
Counts
19 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.7%
(sin.f64 (*.f64 (PI.f64) x))
✓17.6%
(sin.f64 x)
99.2%
#s(approx (sin (* (PI) x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 (*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 7 binary64)) #s(literal -1/5040 binary64)) x) x (*.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) #s(literal 1/120 binary64))) (fma.f64 (pow.f64 (*.f64 x (PI.f64)) #s(literal 3 binary64)) #s(literal -1/6 binary64) (*.f64 x (PI.f64)))))
✓98.0%
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
17.6%
#s(approx (sin (* (PI) x)) x)
Compiler

Compiled 106 to 69 computations (34.9% saved)

regimes5.0ms (0%)

Memory
5.6MiB live, 5.6MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (sin (* (PI) x)) x)
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
(sin.f64 x)
(sin.f64 (*.f64 (PI.f64) x))
#s(approx (sin (* (PI) x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 (*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 7 binary64)) #s(literal -1/5040 binary64)) x) x (*.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) #s(literal 1/120 binary64))) (fma.f64 (pow.f64 (*.f64 x (PI.f64)) #s(literal 3 binary64)) #s(literal -1/6 binary64) (*.f64 x (PI.f64)))))
Outputs
(sin.f64 (*.f64 (PI.f64) x))
Calls

3 calls:

2.0ms
(*.f64 (PI.f64) x)
2.0ms
(sin.f64 (*.f64 (PI.f64) x))
2.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
99.7%1(sin.f64 (*.f64 (PI.f64) x))
99.7%1(*.f64 (PI.f64) x)
Compiler

Compiled 8 to 8 computations (0% saved)

regimes4.0ms (0%)

Memory
5.1MiB live, 5.1MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (sin (* (PI) x)) x)
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
(sin.f64 x)
Outputs
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
Calls

3 calls:

1.0ms
(sin.f64 (*.f64 (PI.f64) x))
1.0ms
(*.f64 (PI.f64) x)
1.0ms
x
Results
AccuracySegmentsBranch
98.0%1x
98.0%1(sin.f64 (*.f64 (PI.f64) x))
98.0%1(*.f64 (PI.f64) x)
Compiler

Compiled 8 to 8 computations (0% saved)

regimes3.0ms (0%)

Memory
4.5MiB live, 4.5MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (sin (* (PI) x)) x)
Outputs
#s(approx (sin (* (PI) x)) x)
Calls

3 calls:

1.0ms
(sin.f64 (*.f64 (PI.f64) x))
1.0ms
(*.f64 (PI.f64) x)
1.0ms
x
Results
AccuracySegmentsBranch
17.6%1x
17.6%1(*.f64 (PI.f64) x)
17.6%1(sin.f64 (*.f64 (PI.f64) x))
Compiler

Compiled 8 to 8 computations (0% saved)

simplify11.0ms (0%)

Memory
5.1MiB live, 5.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0918
11018
Stop Event
1×saturated
Calls
Call 1
Inputs
(sin.f64 (*.f64 (PI.f64) x))
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
#s(approx (sin (* (PI) x)) x)
Outputs
(sin.f64 (*.f64 (PI.f64) x))
#s(approx (sin (* (PI) x)) (*.f64 (PI.f64) x))
#s(approx (sin (* (PI) x)) x)

soundness39.2s (96.9%)

Memory
138.6MiB live, 212.8MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03576
19776
231576
387270
4113970
5144770
6168270
7183570
8185570
9261070
10266670
11266670
12266670
13274770
14274970
0274964
0814
01114
12714
212514
38068
459808
560478
663368
777028
084198
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×saturated
Compiler

Compiled 24 to 15 computations (37.5% saved)

preprocess22.0ms (0.1%)

Memory
14.4MiB live, 14.4MiB allocated
Remove

(negabs x)

Compiler

Compiled 60 to 42 computations (30% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

Loading profile data...