Details

Time bar (total: 27.2s)

sample198.0ms

Algorithm
intervals
Results
94.0ms59×body2560valid
49.0ms44×body1280valid
21.0ms126×body80valid
12.0ms16×body640valid
4.0msbody320valid
1.0msbody160valid

simplify9.4s

Counts
1 → 1
Iterations
IterNodes
136997
121431
11496
10235
9143
8106
788
680
576
469
356
231
117
08

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (sin x) x)
1.1b
(- 1 (/ (sin x) x))
16.2b
(/ (- 1 (/ (sin x) x)) (* x x))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
25×*-un-lft-identity
23×times-frac
13×add-cube-cbrt
12×difference-of-squares
11×associate-/l*
10×add-cbrt-cube add-exp-log
add-log-exp
associate-/r*
pow1 cbrt-undiv div-exp insert-posit16 distribute-lft-out--
clear-num frac-2neg flip3-- div-inv flip-- associate-/l/
sub-neg diff-log div-sub prod-exp cbrt-unprod
Counts
3 → 81
Calls
3 calls:
19.0ms
(/ (sin x) x)
21.0ms
(- 1 (/ (sin x) x))
78.0ms
(/ (- 1 (/ (sin x) x)) (* x x))

series335.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(/ (sin x) x)
96.0ms
(- 1 (/ (sin x) x))
171.0ms
(/ (- 1 (/ (sin x) x)) (* x x))

simplify3.3s

Counts
90 → 90
Iterations
IterNodes
33690
21053
1342
0148

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* 1/5040 (* x x)) 1/120)
0.0b
(+ 1/6 (* (* x x) (- (* 1/5040 (* x x)) 1/120)))
0.1b
(* (* x x) (- (* 1/5040 (* x x)) 1/120))
0.1b
(* 1/5040 (* x x))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-cbrt-cube add-exp-log
add-sqr-sqrt add-log-exp
*-un-lft-identity pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
sub-neg
distribute-rgt-in associate-+r+ distribute-lft-in associate-*r* associate-*l* insert-posit16
flip3-- associate-*r/ *-commutative flip-- unswap-sqr
+-commutative sum-log flip3-+ diff-log flip-+
Counts
4 → 75
Calls
4 calls:
39.0ms
(- (* 1/5040 (* x x)) 1/120)
26.0ms
(+ 1/6 (* (* x x) (- (* 1/5040 (* x x)) 1/120)))
170.0ms
(* (* x x) (- (* 1/5040 (* x x)) 1/120))
37.0ms
(* 1/5040 (* x x))

series484.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (* 1/5040 (* x x)) 1/120)
95.0ms
(+ 1/6 (* (* x x) (- (* 1/5040 (* x x)) 1/120)))
210.0ms
(* (* x x) (- (* 1/5040 (* x x)) 1/120))
55.0ms
(* 1/5040 (* x x))

simplify2.7s

Counts
87 → 87
Iterations
IterNodes
33793
2985
1346
0114

prune926.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes83.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.6b

bsearch255.0ms

Steps
ItersRangePoint
11
6.39684937763006e-15
11427567992489.943
0.009462403866380574
9
-170.1724623506855
-7.250512869097592e-05
-0.009272911760413088

simplify39.0ms

Iterations
IterNodes
231
131
027

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.6s1586×body2560valid
2.4s1261×body1280valid
756.0ms4089×body80valid
618.0ms593×body640valid
221.0ms309×body320valid
57.0ms162×body160valid