Details

Time bar (total: 5.8s)

sample330.0ms

Algorithm
intervals
Results
45.0ms99×body1280valid
15.0ms62×body640valid
4.0ms23×body320valid
4.0ms64×body80valid
1.0ms8×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2205
3215
4215

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

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)))
3.7b
(cos (+ a b))

rewrite34.0ms

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:
7.0ms
(* r (/ (sin b) (cos (+ a b))))
4.0ms
(/ (sin b) (cos (+ a b)))
6.0ms
(cos (+ a b))

series160.0ms

Counts
3 → 9
Calls
3 calls:
97.0ms
(* r (/ (sin b) (cos (+ a b))))
39.0ms
(/ (sin b) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify40.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0263560
11093504
25002504

prune215.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos a) (cos b))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(/ (sin b) (- (* (cos a) (cos b)) (* (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:
4.0ms
(* (cos a) (cos b))
11.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms
(* (sin a) (sin b))

series411.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (cos a) (cos b))
218.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
111.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms
(* (sin a) (sin b))

simplify57.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04451273
119101154
250021152

prune411.0ms

Filtered
125 candidates to 95 candidates (76.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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))))

rewrite24.0ms

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))))

series352.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (cos a) (cos b))
37.0ms
(* r (sin b))
48.0ms
(* (sin a) (sin b))
221.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0382724
11662634
25001633

prune305.0ms

Filtered
101 candidates to 72 candidates (71.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
62×add-sqr-sqrt
58×add-cube-cbrt *-un-lft-identity
16×associate-/r*
15×add-exp-log add-cbrt-cube
8×pow1
6×associate-*r* associate-*l* div-inv associate-/l*
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u associate-/l/ add-log-exp
3×cos-mult sin-mult
2×frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
1×flip3-- div-sub associate-/r/ frac-sub flip-- sub-div
Counts
4 → 148
Calls
4 calls:
8.0ms
(* (cos a) (cos b))
7.0ms
(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
8.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
5.0ms
(* (sin a) (sin b))

series427.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (cos a) (cos b))
229.0ms
(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
114.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
45.0ms
(* (sin a) (sin b))

simplify78.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
05892127
125381985
250021965

prune498.0ms

Filtered
160 candidates to 130 candidates (81.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes137.0ms

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

sample2.2s

Algorithm
intervals
Results
1.2s2895×body1280valid
466.0ms1889×body640valid
138.0ms798×body320valid
107.0ms2084×body80valid
44.0ms336×body160valid