Details

Time bar (total: 5.5s)

sample77.0ms

Algorithm
intervals
Results
43.0ms101×body1280valid
13.0ms52×body640valid
5.0ms31×body320valid
3.0ms57×body80valid
2.0ms15×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2195
3205
4205

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
4.1b
(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×times-frac associate-*r* associate-*l* associate-/r* 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 → 47
Calls
3 calls:
4.0ms
(* r (sin b))
5.0ms
(/ (* r (sin b)) (cos (+ a b)))
12.0ms
(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
56 → 56
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0198305
1861257
25001256

prune139.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin 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))))

rewrite24.0ms

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×associate-/r/ cos-mult
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 diff-log clear-num div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
5.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms
(* r (sin b))
5.0ms
(* (sin a) (sin b))
9.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
37.0ms
(* r (sin b))
46.0ms
(* (sin a) (sin b))
212.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify52.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0344770
11513673
25002663

prune288.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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
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 diff-log associate-*r/ clear-num
Counts
4 → 100
Calls
4 calls:
5.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
12.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
7.0ms
(* (sin a) (sin b))
8.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
213.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
43.0ms
(* (sin a) (sin b))
110.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify60.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04011307
117331182
250011178

prune366.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))
0.2b
(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
0.3b
(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
32×add-sqr-sqrt
24×*-un-lft-identity
23×add-cube-cbrt
22×add-cbrt-cube
21×associate-*r*
20×times-frac
14×pow1 prod-exp
9×associate-*l*
8×associate-/r/ cbrt-unprod
6×div-exp
5×pow-prod-down sin-mult
4×associate-*r/ cos-mult add-log-exp unswap-sqr
3×cbrt-undiv rec-exp 1-exp associate-/r* *-commutative associate-/l*
2×flip3-- un-div-inv frac-sub flip-- div-inv sub-div
1×pow-flip frac-2neg clear-num inv-pow
Counts
4 → 118
Calls
4 calls:
12.0ms
(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
8.0ms
(* (sin a) (sin b))
7.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
12.0ms
(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
46.0ms
(* (sin a) (sin b))
96.0ms
(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
112.0ms
(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04561487
119771272
250021240

prune334.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes140.0ms

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
02011
12011

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.3s2950×body1280valid
458.0ms1794×body640valid
132.0ms756×body320valid
125.0ms2132×body80valid
47.0ms370×body160valid