Details

Time bar (total: 5.9s)

sample399.0ms

Algorithm
intervals
Results
45.0ms106×body1280valid
24.0ms67×body80valid
12.0ms51×body640valid
3.0ms17×body320valid
2.0ms15×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2205
3215
4215

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*r*
10×add-exp-log add-cbrt-cube
5×pow1
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
3 → 73
Calls
3 calls:
17.0ms
(* r (/ (sin b) (cos (+ a b))))
9.0ms
(/ (sin b) (cos (+ a b)))
11.0ms
(cos (+ a b))

series151.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(* r (/ (sin b) (cos (+ a b))))
34.0ms
(/ (sin b) (cos (+ a b)))
29.0ms
(cos (+ a b))

simplify41.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0263560
11093504
25002504

prune214.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

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 a) (cos b))
26.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
70.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms
(* (sin a) (sin b))

series374.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (cos a) (cos b))
102.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
194.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
43.0ms
(* (sin a) (sin b))

simplify57.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04451273
119101154
250011152

prune398.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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))

rewrite61.0ms

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:
12.0ms
(* (cos a) (cos b))
9.0ms
(* r (sin b))
27.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms
(* (sin a) (sin b))

series308.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (cos a) (cos b))
38.0ms
(* r (sin b))
194.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
40.0ms
(* (sin a) (sin b))

simplify48.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0382724
11662634
25001633

prune319.0ms

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)))))

rewrite128.0ms

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))
34.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms
(* (sin a) (sin b))
69.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series368.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* r (sin b))
89.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
45.0ms
(* (sin a) (sin b))
199.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04901317
124611134
250011106

prune347.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes148.0ms

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
439.0ms1837×body640valid
119.0ms738×body320valid
116.0ms2180×body80valid
41.0ms349×body160valid