Details

Time bar (total: 5.7s)

sample78.0ms

Algorithm
intervals
Results
43.0ms99×body1280valid
15.0ms62×body640valid
4.0ms23×body320valid
3.0ms64×body80valid
1.0ms8×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2195
3205
4205

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
3.7b
(cos (+ a b))

rewrite25.0ms

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:
11.0ms
(* r (sin b))
5.0ms
(/ (* r (sin b)) (cos (+ a b)))
7.0ms
(cos (+ a b))

series160.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(* r (sin b))
98.0ms
(/ (* r (sin b)) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify34.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0207327
1884279
25001279

prune170.0ms

Filtered
62 candidates to 46 candidates (74.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

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))))

rewrite25.0ms

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))
5.0ms
(* (sin a) (sin b))
9.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series346.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (cos a) (cos b))
40.0ms
(* r (sin b))
44.0ms
(* (sin a) (sin b))
221.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0382724
11662634
25001633

prune334.0ms

Filtered
101 candidates to 73 candidates (72.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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:
5.0ms
(* (cos b) (cos a))
12.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
8.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
5.0ms
(* (sin a) (sin b))

series419.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (cos b) (cos a))
219.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
112.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
48.0ms
(* (sin a) (sin b))

simplify56.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04441273
118911154
250011152

prune418.0ms

Filtered
125 candidates to 94 candidates (75.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(expm1 (* (sin a) (sin b)))
0.2b
(* r (/ (sin b) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin a) (sin b)))))))
0.2b
(/ (sin b) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
19×times-frac
18×associate-*r*
13×add-exp-log add-cbrt-cube
8×pow1
6×associate-*l*
5×log1p-expm1-u
4×expm1-log1p-u associate-/r/ add-log-exp
3×prod-exp associate-/r* cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative flip-- div-inv
1×expm1-log1p frac-2neg associate-*r/ clear-num sin-mult expm1-udef
Counts
4 → 99
Calls
4 calls:
1.0ms
(expm1 (* (sin a) (sin b)))
14.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin a) (sin b)))))))
8.0ms
(/ (sin b) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin a) (sin b))))))
5.0ms
(* (sin a) (sin b))

series535.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(expm1 (* (sin a) (sin b)))
258.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin a) (sin b)))))))
155.0ms
(/ (sin b) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin a) (sin b))))))
46.0ms
(* (sin a) (sin b))

simplify53.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04061336
117491177
250011173

prune393.0ms

Filtered
111 candidates to 88 candidates (79.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes153.0ms

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
01410
11410

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s2895×body1280valid
486.0ms1889×body640valid
147.0ms798×body320valid
129.0ms2084×body80valid
42.0ms336×body160valid