Details

Time bar (total: 5.3s)

sample86.0ms

Algorithm
intervals
Results
46.0ms101×body1280valid
16.0ms59×body640valid
7.0ms21×body320valid
4.0ms67×body80valid
1.0ms8×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2195
3205
4205

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.6b

Counts
2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
2.9b
(cos (+ a b))

rewrite18.0ms

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

series164.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(* r (sin b))
102.0ms
(/ (* 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

prune156.0ms

Filtered
62 candidates to 46 candidates (74.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New521062
Fresh000
Picked101
Done000
Total531063

Merged error: 0.2b

Counts
63 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult log1p-expm1-u
3×times-frac prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×sub-neg frac-2neg fma-neg diff-log prod-diff clear-num div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
5.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin 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))))

series379.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
36.0ms
(* r (sin b))
46.0ms
(* (sin a) (sin b))
216.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0369835
11591735
25002730

prune305.0ms

Filtered
98 candidates to 74 candidates (75.5%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New851398
Fresh819
Picked101
Done000
Total9414108

Merged error: 0.0b

Counts
108 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative unswap-sqr
1×frac-2neg clear-num fma-udef div-inv sin-mult associate-/l*
Counts
4 → 74
Calls
4 calls:
1.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
7.0ms
(* r (sin b))
5.0ms
(* (sin a) (sin b))
5.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
40.0ms
(* r (sin b))
43.0ms
(* (sin a) (sin b))
216.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify39.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0273680
11161578
25002578

prune241.0ms

Filtered
86 candidates to 61 candidates (70.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New85186
Fresh11213
Picked101
Done000
Total8713100

Merged error: 0.0b

Counts
100 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
11×add-cube-cbrt *-un-lft-identity
8×pow1
7×add-log-exp
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u
3×times-frac prod-diff prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv flip3-- diff-log div-exp pow-prod-down associate-/r/ *-commutative flip-- unswap-sqr
1×sub-neg log1p-udef frac-2neg fma-neg clear-num div-inv sin-mult associate-/l*
Counts
4 → 85
Calls
4 calls:
5.0ms
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
4.0ms
(* r (sin b))
5.0ms
(* (sin a) (sin b))
8.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))

series455.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
36.0ms
(* r (sin b))
47.0ms
(* (sin a) (sin b))
259.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0373982
11631775
25001769

prune238.0ms

Filtered
97 candidates to 68 candidates (70.1%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New97097
Fresh01212
Picked011
Done000
Total9713110

Merged error: 0.0b

Counts
110 → 13

regimes170.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01712
11712

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.3s2897×body1280valid
502.0ms1829×body640valid
162.0ms819×body320valid
136.0ms2077×body80valid
58.0ms382×body160valid

Profiling

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