Details

Time bar (total: 6.1s)

sample76.0ms

Algorithm
intervals
Results
39.0ms93×body1280valid
16.0ms61×body640valid
5.0ms68×body80valid
4.0ms25×body320valid
1.0ms9×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: 15.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
5.2b
(cos (+ a b))

rewrite21.0ms

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:
3.0ms
(* r (sin b))
4.0ms
(/ (* r (sin b)) (cos (+ a b)))
12.0ms
(cos (+ a b))

series159.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(* r (sin b))
98.0ms
(/ (* r (sin b)) (cos (+ a b)))
23.0ms
(cos (+ a b))

simplify33.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0207327
1884279
25001279

prune159.0ms

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
(* (sin a) (sin b))
0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b
(* r (sin b))
0.3b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite26.0ms

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
(* (sin a) (sin b))
7.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
3.0ms
(* r (sin b))
9.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series379.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin a) (sin b))
83.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
37.0ms
(* r (sin b))
212.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0369835
11591735
25002730

prune337.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
20×associate-*r*
19×times-frac
13×add-exp-log add-cbrt-cube
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×flip3-- prod-exp associate-/r* frac-sub flip-- cbrt-unprod associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×sub-neg frac-2neg fma-neg diff-log associate-*r/ prod-diff clear-num
Counts
4 → 110
Calls
4 calls:
4.0ms
(* (sin a) (sin b))
5.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
25.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
9.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series458.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin a) (sin b))
82.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
219.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
113.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify61.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04271384
118191255
250011254

prune419.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* r (/ (sin b) (/ (* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (fma (cos b) (cos a) (* (sin a) (sin b))))))
0.2b
(/ (sin b) (/ (* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (fma (cos b) (cos a) (* (sin a) (sin b)))))
0.3b
(* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
0.3b
(/ (* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (fma (cos b) (cos a) (* (sin a) (sin b))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
46×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
34×add-exp-log add-cbrt-cube
29×associate-*r*
12×cbrt-undiv div-exp
10×associate-/r* div-inv
9×associate-*r/
8×pow1 prod-exp cbrt-unprod
6×associate-*l*
4×expm1-log1p-u cos-mult log1p-expm1-u associate-/l/ sin-mult associate-/l* add-log-exp
3×distribute-rgt-in distribute-lft-in unswap-sqr
2×sub-neg flip3-- frac-2neg prod-diff pow-prod-down clear-num associate-/r/ *-commutative frac-sub flip-- sub-div
Counts
4 → 158
Calls
4 calls:
22.0ms
(* r (/ (sin b) (/ (* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (fma (cos b) (cos a) (* (sin a) (sin b))))))
7.0ms
(/ (sin b) (/ (* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (fma (cos b) (cos a) (* (sin a) (sin b)))))
17.0ms
(* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
13.0ms
(/ (* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (fma (cos b) (cos a) (* (sin a) (sin b))))

series586.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(* r (/ (sin b) (/ (* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (fma (cos b) (cos a) (* (sin a) (sin b))))))
117.0ms
(/ (sin b) (/ (* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (fma (cos b) (cos a) (* (sin a) (sin b)))))
166.0ms
(* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
85.0ms
(/ (* (fma (cos b) (cos a) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (fma (cos b) (cos a) (* (sin a) (sin b))))

simplify132.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
07074545
140873810
250023682

prune601.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes155.0ms

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
01824
11824

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s2903×body1280valid
500.0ms1879×body640valid
141.0ms727×body320valid
134.0ms2148×body80valid
46.0ms348×body160valid