Details

Time bar (total: 5.3s)

sample77.0ms

Algorithm
intervals
Results
39.0ms87×body1280valid
17.0ms65×body640valid
4.0ms72×body80valid
4.0ms22×body320valid
1.0ms10×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2195
3205
4205

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
3.7b
(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×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)))
6.0ms
(cos (+ a b))

series166.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(* r (sin b))
100.0ms
(/ (* r (sin b)) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify32.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0198305
1861257
25001256

prune151.0ms

Filtered
56 candidates to 40 candidates (71.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

series398.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
38.0ms
(* r (sin b))
50.0ms
(* (sin a) (sin b))
223.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0344770
11513673
25002663

prune303.0ms

Filtered
88 candidates to 64 candidates (72.7%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* (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))))

rewrite35.0ms

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:
8.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
11.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
5.0ms
(* (sin a) (sin b))
8.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
226.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
44.0ms
(* (sin a) (sin b))
114.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04011307
117331182
250011178

prune395.0ms

Filtered
112 candidates to 84 candidates (75.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin a) (sin b))
0.2b
(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.3b
(pow (* (sin a) (sin b)) 3)
25.7b
(cbrt (pow (* (sin a) (sin b)) 3))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
9×pow1 times-frac
8×cbrt-prod
4×sin-mult add-log-exp
3×cube-div pow-unpow associate-*r* associate-*l* associate-/r* associate-/r/ associate-/l*
2×cube-mult unpow-prod-down cbrt-div pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod rem-cube-cbrt sqr-pow
1×cbrt-undiv pow-to-exp flip3-- frac-2neg pow1/3 div-exp clear-num cos-mult *-commutative frac-sub flip-- rem-cbrt-cube div-inv unswap-sqr
Counts
4 → 90
Calls
4 calls:
5.0ms
(* (sin a) (sin b))
14.0ms
(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3))))
5.0ms
(pow (* (sin a) (sin b)) 3)
3.0ms
(cbrt (pow (* (sin a) (sin b)) 3))

series281.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin a) (sin b))
116.0ms
(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3))))
69.0ms
(pow (* (sin a) (sin b)) 3)
47.0ms
(cbrt (pow (* (sin a) (sin b)) 3))

simplify46.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0343902
11433826
25001813

prune328.0ms

Filtered
102 candidates to 72 candidates (70.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes174.0ms

Accuracy

0% (0.3b 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
01712
11712

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2935×body1280valid
468.0ms1835×body640valid
139.0ms748×body320valid
120.0ms2144×body80valid
45.0ms342×body160valid