Details

Time bar (total: 7.8s)

sample114.0ms

Algorithm
intervals
Results
51.0ms43×body2560valid
34.0ms86×body1280valid
15.0ms69×body640valid
4.0ms24×body320valid
2.0ms19×body160valid
1.0ms15×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.8b
(- 1.0 (cos x))

rewrite15.0ms

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))

series60.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(/ (- 1.0 (cos x)) (sin x))
25.0ms
(- 1.0 (cos x))

simplify36.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0292569
1965460
25002460

prune190.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
0.4b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
2.5b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
233×add-sqr-sqrt
165×*-un-lft-identity
144×prod-diff
138×unpow-prod-down cube-prod
113×add-cube-cbrt
80×difference-of-squares
75×times-frac
66×sqr-pow
26×cube-mult unpow3
25×associate-/l* distribute-lft-out--
12×fma-neg
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-def associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative pow-to-exp sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub div-exp pow-exp clear-num sum-log flip-+ div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 354
Calls
4 calls:
59.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
21.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series213.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
28.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
54.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify149.0ms

Algorithm
egg-herbie
Counts
366 → 366
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
08284951
132444033
250023940

prune557.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
2.5b
(- (pow 1.0 3) (pow (cos x) 3))
2.7b
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
288×prod-diff
205×add-sqr-sqrt
179×*-un-lft-identity
174×unpow-prod-down cube-prod
157×add-cube-cbrt
149×log-prod
146×exp-sum
66×sqr-pow
50×cube-mult unpow3
32×difference-of-squares
26×log-pow
25×exp-prod
12×fma-neg
10×distribute-lft-out--
8×add-log-exp
6×pow1
5×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-def
2×difference-cubes sub-neg
1×+-commutative pow-to-exp log-div flip3-- pow-pow flip3-+ exp-diff diff-log rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 420
Calls
4 calls:
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
21.0ms
(- (pow 1.0 3) (pow (cos x) 3))
68.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series152.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
65.0ms
(- (pow 1.0 3) (pow (cos x) 3))
49.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify128.0ms

Algorithm
egg-herbie
Counts
432 → 432
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07985039
122923291
250021806

prune483.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
2.5b
(- (pow 1.0 3) (pow (cos x) 3))
2.7b
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))
2.8b
(- (cos x) 1.0)

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
297×prod-diff
213×add-sqr-sqrt
185×*-un-lft-identity
174×unpow-prod-down cube-prod
163×add-cube-cbrt
149×log-prod
146×exp-sum
66×sqr-pow
50×cube-mult unpow3
33×difference-of-squares
26×log-pow
25×exp-prod
15×fma-neg
11×distribute-lft-out--
8×add-log-exp
6×pow1
5×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×sub-neg pow-unpow
2×difference-cubes flip3-- diff-log flip--
1×pow-to-exp log-div pow-pow exp-diff rem-log-exp pow-exp rem-cube-cbrt
Counts
4 → 431
Calls
4 calls:
1.0ms
(pow (cos x) 3)
23.0ms
(- (pow 1.0 3) (pow (cos x) 3))
68.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))
4.0ms
(- (cos x) 1.0)

series155.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (cos x) 3)
53.0ms
(- (pow 1.0 3) (pow (cos x) 3))
47.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))
26.0ms
(- (cos x) 1.0)

simplify144.0ms

Algorithm
egg-herbie
Counts
443 → 443
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
08375119
124473326
250011857

prune510.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

regimes211.0ms

Accuracy

98.3% (0.5b remaining)

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

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03636
13636

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.0s1537×body2560valid
1.4s2824×body1280valid
453.0ms1931×body640valid
178.0ms923×body320valid
48.0ms451×body160valid
21.0ms329×body80valid
21.0ms5×body5120valid