Details

Time bar (total: 6.4s)

sample74.0ms

Algorithm
intervals
Results
40.0ms99×body1280valid
14.0ms54×body640valid
4.0ms75×body80valid
3.0ms17×body320valid
1.0ms11×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: 16.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
4.3b
(cos (+ a b))

rewrite17.0ms

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))
4.0ms
(/ (* r (sin b)) (cos (+ a b)))
7.0ms
(cos (+ a b))

series157.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(* r (sin b))
96.0ms
(/ (* r (sin b)) (cos (+ a b)))
23.0ms
(cos (+ a b))

simplify36.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0207327
1884279
25001279

prune157.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos a) (cos b))
0.1b
(* r (sin b))
0.2b
(* (sin a) (sin b))
0.3b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
10×pow1
9×associate-*r* associate-*l*
4×expm1-log1p-u prod-exp associate-/r/ cbrt-unprod log1p-expm1-u add-log-exp
3×times-frac pow-prod-down associate-/r* cos-mult *-commutative sin-mult unswap-sqr
2×cbrt-undiv div-exp
1×flip3-- frac-2neg clear-num frac-sub flip-- div-inv associate-/l* sub-div
Counts
4 → 89
Calls
4 calls:
4.0ms
(* (cos a) (cos b))
3.0ms
(* r (sin b))
4.0ms
(* (sin a) (sin b))
12.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series328.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (cos a) (cos b))
36.0ms
(* r (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
101 → 101
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0382724
11662634
25001633

prune304.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b
(* (sin a) (sin b))
0.2b
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
27×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity associate-*r*
22×add-cbrt-cube
18×times-frac
14×pow1 prod-exp
8×associate-/r/ cbrt-unprod
7×associate-*l*
6×div-exp
5×pow-prod-down sin-mult
4×expm1-log1p-u cos-mult log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp 1-exp associate-/r* *-commutative associate-/l*
2×flip3-- frac-sub flip-- div-inv sub-div unswap-sqr
1×pow-flip frac-2neg associate-*r/ clear-num un-div-inv inv-pow
Counts
4 → 122
Calls
4 calls:
3.0ms
(* r (sin b))
10.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
6.0ms
(* (sin a) (sin b))
25.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series385.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* r (sin b))
95.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
46.0ms
(* (sin a) (sin b))
206.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04901317
124611134
250011106

prune366.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×add-exp-log add-cbrt-cube
26×associate-*r*
23×add-cube-cbrt *-un-lft-identity
22×times-frac
20×associate-*l*
15×pow1 prod-exp cbrt-unprod
14×frac-times
8×cbrt-undiv associate-*r/ div-exp associate-*l/ sin-mult
6×pow-prod-down cos-mult unswap-sqr
4×expm1-log1p-u flip3-+ frac-add associate-/r/ *-commutative flip-+ log1p-expm1-u add-log-exp
2×div-inv
1×distribute-rgt-in flip3-- distribute-lft-in frac-sub flip-- sub-div
Counts
4 → 141
Calls
4 calls:
4.0ms
(* (sin a) (sin b))
4.0ms
(* (sin a) (sin b))
34.0ms
(* (/ r (fma (cos b) (cos a) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
47.0ms
(* (* (/ r (fma (cos b) (cos a) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.2s

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin a) (sin b))
46.0ms
(* (sin a) (sin b))
464.0ms
(* (/ r (fma (cos b) (cos a) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
626.0ms
(* (* (/ r (fma (cos b) (cos a) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09523129
150012623

prune542.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes192.0ms

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
02024
12024

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2911×body1280valid
493.0ms1901×body640valid
136.0ms760×body320valid
112.0ms2097×body80valid
47.0ms335×body160valid