Details

Time bar (total: 1.2m)

sample151.0ms

Algorithm
intervals
Results
92.0ms62×body2560valid
32.0ms78×body1280valid
12.0ms55×body640valid
4.0ms26×body320valid
2.0ms18×body160valid
1.0ms17×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.9b
(- 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:
34.0ms
(/ (- 1.0 (cos x)) (sin x))
26.0ms
(- 1.0 (cos x))

simplify38.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0292569
1965460
25002460

prune184.0ms

Filtered
74 candidates to 51 candidates (68.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

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)))
0.6b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
0.9b
(- 1.0 (cos x))

rewrite45.0ms

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)))
13.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms
(- 1.0 (cos x))

series141.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ (- 1.0 (cos x)) (sin x))
41.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
40.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms
(- 1.0 (cos x))

simplify43.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03681009
11099873
25002871

prune348.0ms

Filtered
144 candidates to 101 candidates (70.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
0.6b
(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))))
0.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
491×add-sqr-sqrt
462×times-frac
353×*-un-lft-identity
251×add-cube-cbrt
242×log-pow
241×exp-prod
198×unpow-prod-down cube-prod
160×difference-of-squares
144×prod-diff
106×sqr-pow
50×distribute-lft-out--
26×cube-mult unpow3
12×fma-neg
10×difference-cubes
8×add-log-exp
6×pow1
5×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u div-inv
3×pow-unpow log-prod fma-def
2×div-sub
1×+-commutative pow-to-exp sub-neg 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 → 490
Calls
4 calls:
2.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
124.0ms
(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))))
22.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series252.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
161.0ms
(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))))
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify177.0ms

Algorithm
egg-herbie
Counts
502 → 502
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
014086419
147885472
250015472

prune999.0ms

Filtered
502 candidates to 210 candidates (41.8%)
Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
0.4b
(+ 1.0 (cos x))
0.4b
(+ 1.0 (cos x))
0.9b
(- (/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)) (/ (/ (pow (cos x) 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)))

rewrite4.1s

Algorithm
rewrite-expression-head
Rules
57336×times-frac
27010×add-sqr-sqrt
26944×*-un-lft-identity
26842×add-cube-cbrt
15376×prod-diff
6807×unpow-prod-down cube-prod
2265×sqr-pow
2253×cube-mult unpow3
1009×div-inv
124×fma-neg
49×distribute-lft-out--
40×associate-/l*
36×difference-of-squares
14×add-exp-log
10×add-log-exp
9×add-cbrt-cube
7×div-exp
6×fma-def
4×pow1 expm1-log1p-u distribute-rgt-out-- log1p-expm1-u
3×cbrt-undiv associate-/r*
2×+-commutative flip3-+ sum-log flip-+ distribute-lft-out
1×pow-to-exp sub-neg flip3-- frac-2neg diff-log pow-exp clear-num frac-sub flip-- associate-/l/ sub-div
Counts
4 → 15821
Calls
4 calls:
14.0ms
(/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
3.0ms
(+ 1.0 (cos x))
3.0ms
(+ 1.0 (cos x))
944.0ms
(- (/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)) (/ (/ (pow (cos x) 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)))

series512.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
10.0ms
(+ 1.0 (cos x))
10.0ms
(+ 1.0 (cos x))
370.0ms
(- (/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)) (/ (/ (pow (cos x) 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)))

simplify12.5s

Algorithm
egg-herbie
Counts
15833 → 15833
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0104471584440

prune47.5s

Filtered
15833 candidates to 7389 candidates (46.7%)
Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.0b

regimes212.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 30.2b

bsearch3.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06582
16982
26982

end0.0ms

sample3.9s

Algorithm
intervals
Results
2.0s1605×body2560valid
1.1s2781×body1280valid
407.0ms1894×body640valid
127.0ms900×body320valid
46.0ms455×body160valid
36.0ms7×body5120valid
22.0ms358×body80valid