Details

Time bar (total: 5.6s)

sample81.0ms

Algorithm
intervals
Results
44.0ms101×body1280valid
15.0ms58×body640valid
3.0ms19×body320valid
3.0ms64×body80valid
2.0ms14×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: 14.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
4.3b
(cos (+ a b))

rewrite35.0ms

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:
9.0ms
(* r (sin b))
12.0ms
(/ (* r (sin b)) (cos (+ a b)))
12.0ms
(cos (+ a b))

series155.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(* r (sin b))
92.0ms
(/ (* 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

prune157.0ms

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

rewrite69.0ms

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:
9.0ms
(* r (sin b))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms
(* (sin a) (sin b))
27.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series366.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* r (sin b))
76.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms
(* (sin a) (sin b))
206.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify48.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0369835
11591735
25002730

prune330.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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

rewrite34.0ms

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:
9.0ms
(* r (sin b))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
12.0ms
(* (sin a) (sin b))
11.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series370.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* r (sin b))
80.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
43.0ms
(* (sin a) (sin b))
211.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify36.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0273680
11161578
25002578

prune301.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
58×add-sqr-sqrt
56×add-cube-cbrt *-un-lft-identity
16×associate-/r*
13×add-exp-log add-cbrt-cube
6×pow1 div-inv associate-/l* add-log-exp
5×sin-mult
4×cbrt-undiv expm1-log1p-u div-exp cos-mult log1p-expm1-u associate-/l/
3×associate-*r* associate-*l*
2×flip3-- frac-2neg clear-num frac-sub flip-- sub-div
1×sub-neg fma-neg diff-log div-sub prod-diff pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod unswap-sqr
Counts
4 → 145
Calls
4 calls:
19.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
27.0ms
(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))
15.0ms
(/ r (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))
12.0ms
(* (sin a) (sin b))

series429.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
100.0ms
(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))
211.0ms
(/ r (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))
43.0ms
(* (sin a) (sin b))

simplify77.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05922221
125262082
250022064

prune513.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes168.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01612
11612

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2926×body1280valid
437.0ms1822×body640valid
144.0ms765×body320valid
116.0ms2145×body80valid
42.0ms345×body160valid