Details

Time bar (total: 6.7s)

sample76.0ms

Algorithm
intervals
Results
41.0ms99×body1280valid
15.0ms54×body640valid
4.0ms75×body80valid
3.0ms17×body320valid
1.0ms11×body160valid

simplify9.0ms

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

localize12.0ms

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))

rewrite22.0ms

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))

series158.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(* r (sin b))
96.0ms
(/ (* r (sin b)) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify35.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0207327
1884279
25001279

prune162.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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))))

rewrite22.0ms

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))
4.0ms
(* r (sin b))
4.0ms
(* (sin a) (sin b))
9.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series334.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (cos a) (cos b))
40.0ms
(* r (sin b))
42.0ms
(* (sin a) (sin b))
213.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0382724
11662634
25001633

prune311.0ms

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)))))

rewrite45.0ms

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))))
4.0ms
(* (sin a) (sin b))
24.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series393.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* r (sin b))
98.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms
(* (sin a) (sin b))
213.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04901317
124611134
250011106

prune364.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
38×add-exp-log add-cbrt-cube
31×times-frac
29×add-cube-cbrt *-un-lft-identity
23×associate-*r*
17×associate-*l*
14×frac-times prod-exp cbrt-unprod
13×pow1
9×cbrt-undiv div-exp sin-mult
8×associate-*r/ associate-*l/ associate-/r/ cos-mult
5×pow-prod-down unswap-sqr
4×expm1-log1p-u flip3-+ frac-add flip-+ log1p-expm1-u add-log-exp
3×associate-/r* *-commutative div-inv associate-/l*
2×flip3-- frac-sub flip-- sub-div
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 153
Calls
4 calls:
4.0ms
(* (sin a) (sin b))
11.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
31.0ms
(* (/ r (fma (cos b) (cos a) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms
(* (* (/ r (fma (cos b) (cos a) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.3s

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin a) (sin b))
112.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
485.0ms
(* (/ r (fma (cos b) (cos a) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
647.0ms
(* (* (/ r (fma (cos b) (cos a) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09633544
150013008

prune619.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes205.0ms

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
02024
12024

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s2911×body1280valid
488.0ms1901×body640valid
139.0ms760×body320valid
120.0ms2097×body80valid
47.0ms335×body160valid