Details

Time bar (total: 5.2s)

sample72.0ms

Algorithm
intervals
Results
37.0ms89×body1280valid
16.0ms57×body640valid
5.0ms84×body80valid
3.0ms18×body320valid
1.0ms8×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2195
3205
4205

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
3.2b
(cos (+ a b))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
5×pow1
3×expm1-log1p-u times-frac associate-*r* associate-*l* associate-/r* log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×cos-sum frac-2neg pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 53
Calls
3 calls:
4.0ms
(* r (sin b))
5.0ms
(/ (* r (sin b)) (cos (+ a b)))
12.0ms
(cos (+ a b))

series158.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(* r (sin b))
96.0ms
(/ (* r (sin b)) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify34.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0207327
1884279
25001279

prune162.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* r (sin b))
0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b
(* (sin a) (sin b))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult log1p-expm1-u
3×times-frac prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×sub-neg frac-2neg fma-neg diff-log prod-diff clear-num div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
4.0ms
(* r (sin b))
5.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms
(* (sin a) (sin b))

series380.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* r (sin b))
82.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
214.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms
(* (sin a) (sin b))

simplify50.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0369835
11591735
25002730

prune334.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* r (sin b))
0.1b
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
0.2b
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
0.2b
(* (sin a) (sin b))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative unswap-sqr
1×frac-2neg clear-num fma-udef div-inv sin-mult associate-/l*
Counts
4 → 74
Calls
4 calls:
4.0ms
(* r (sin b))
1.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
5.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
5.0ms
(* (sin a) (sin b))

series383.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* r (sin b))
82.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
219.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
45.0ms
(* (sin a) (sin b))

simplify39.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0273680
11161578
25001578

prune286.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (* (sin a) (sin b)))
0.1b
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
0.2b
(/ (* r (sin b)) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
0.2b
(* (sin a) (sin b))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
3×times-frac associate-*r* associate-*l* associate-/r*
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×log1p-udef frac-2neg log1p-expm1 pow-prod-down clear-num *-commutative fma-udef div-inv sin-mult associate-/l* unswap-sqr
Counts
4 → 65
Calls
4 calls:
1.0ms
(log1p (* (sin a) (sin b)))
1.0ms
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
5.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
5.0ms
(* (sin a) (sin b))

series491.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(log1p (* (sin a) (sin b)))
113.0ms
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
257.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
44.0ms
(* (sin a) (sin b))

simplify35.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0287769
11130631
25001624

prune263.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes153.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01410
11410

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2870×body1280valid
489.0ms1886×body640valid
136.0ms749×body320valid
119.0ms2149×body80valid
50.0ms349×body160valid