Details

Time bar (total: 5.5s)

sample76.0ms

Algorithm
intervals
Results
43.0ms106×body1280valid
12.0ms51×body640valid
4.0ms67×body80valid
3.0ms17×body320valid
2.0ms15×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: 15.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
3.5b
(cos (+ a b))

rewrite40.0ms

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))
18.0ms
(/ (* r (sin b)) (cos (+ a b)))
11.0ms
(cos (+ a b))

series145.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(* r (sin b))
88.0ms
(/ (* 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

prune163.0ms

Pruning

10 alts after pruning (10 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
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.3b
(* (sin a) (sin b))

rewrite62.0ms

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:
10.0ms
(* (cos a) (cos b))
9.0ms
(* r (sin b))
27.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms
(* (sin a) (sin b))

series307.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (cos a) (cos b))
33.0ms
(* r (sin b))
192.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
43.0ms
(* (sin a) (sin b))

simplify48.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0382724
11662634
25001633

prune333.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
23×associate-*r*
19×times-frac
15×add-exp-log add-cbrt-cube
10×pow1
9×associate-*l*
8×associate-/r/
5×cos-mult sin-mult
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp frac-sub flip-- div-inv sub-div
1×frac-2neg associate-*r/ clear-num
Counts
4 → 113
Calls
4 calls:
10.0ms
(* (cos b) (cos a))
27.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
72.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
12.0ms
(* (sin a) (sin b))

series376.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (cos b) (cos a))
105.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
196.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
41.0ms
(* (sin a) (sin b))

simplify56.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04441273
118911154
250021152

prune414.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 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))))
0.3b
(* (sin a) (sin b))
0.3b
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite129.0ms

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:
9.0ms
(* r (sin b))
32.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms
(* (sin a) (sin b))
71.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series360.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* r (sin b))
88.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
40.0ms
(* (sin a) (sin b))
198.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04901317
124611134
250011106

prune341.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes133.0ms

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
1.2s2898×body1280valid
455.0ms1837×body640valid
128.0ms738×body320valid
114.0ms2180×body80valid
44.0ms349×body160valid