Details

Time bar (total: 13.6s)

sample128.0ms

Algorithm
intervals
Results
54.0ms41×body2560valid
43.0ms98×body1280valid
16.0ms60×body640valid
4.0ms27×body320valid
2.0ms22×body160valid
1.0ms8×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
1117
2147
3167
done167

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.1b
(- 1.0 (cos x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
9.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

series58.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ (- 1.0 (cos x)) (sin x))
18.0ms
(- 1.0 (cos x))

simplify1.5s

Counts
74 → 74
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0134964
1295831
2730731
32616719
done5000718

prune179.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.3b
(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.1b
(- 1.0 (cos x))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt *-un-lft-identity
45×times-frac
40×add-cube-cbrt
38×exp-prod
20×log-pow
11×distribute-lft-out-- difference-of-squares
9×prod-diff
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×log-prod fma-neg div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 132
Calls
4 calls:
9.0ms
(/ (- 1.0 (cos x)) (sin x))
11.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms
(- 1.0 (cos x))

series134.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (- 1.0 (cos x)) (sin x))
41.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
38.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms
(- 1.0 (cos x))

simplify1.7s

Counts
144 → 144
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01951743
13711509
28491372
328831333
done50001332

prune348.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (sin x))
0.3b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
1.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
591×add-sqr-sqrt
537×times-frac
411×*-un-lft-identity
279×add-cube-cbrt
234×unpow-prod-down cube-prod
208×difference-of-squares
144×prod-diff
130×sqr-pow
79×associate-/l*
65×distribute-lft-out--
26×cube-mult unpow3
13×difference-cubes
12×fma-neg
10×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv pow-unpow fma-def div-exp associate-/r*
2×div-sub
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow frac-2neg flip3-+ diff-log pow-exp clear-num sum-log flip-- flip-+ associate-/l/ distribute-lft-out rem-cube-cbrt
Counts
4 → 571
Calls
4 calls:
58.0ms
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (sin x))
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
21.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series256.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (sin x))
29.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
54.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify1.9s

Counts
583 → 583
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
069521873
1156417698
2473416508
done500016508

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
1.0b
(log (exp (pow (cos x) 3)))
1.9b
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
192×prod-diff
170×log-pow
156×exp-prod
119×add-sqr-sqrt
117×*-un-lft-identity
112×add-cube-cbrt
94×unpow-prod-down cube-prod
32×sqr-pow
31×cube-mult unpow3
19×pow1
12×fma-neg
7×add-log-exp
6×log-prod
5×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×pow-unpow fma-def associate--r+
2×distribute-lft-out--
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ diff-log rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 295
Calls
4 calls:
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
4.0ms
(log (exp (pow (cos x) 3)))
34.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series118.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
28.0ms
(log (exp (pow (cos x) 3)))
51.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify919.0ms

Counts
307 → 307
Iterations

Useful iterations: 2 (289.0ms)

IterNodesCost
030910650
15975142
214853447
done50013447

prune341.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes166.0ms

Accuracy

98.2% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 29.8b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04188
14588
done4588

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.1s1553×body2560valid
1.2s2752×body1280valid
454.0ms1875×body640valid
350.0ms930×body320valid
55.0ms497×body160valid
25.0ms388×body80valid
14.0ms5×body5120valid