Details

Time bar (total: 5.3s)

sample74.0ms

Algorithm
intervals
Results
40.0ms93×body1280valid
11.0ms46×body640valid
6.0ms32×body320valid
4.0ms74×body80valid
1.0ms11×body160valid

simplify9.0ms

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: 14.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
3.7b
(cos (+ a b))

rewrite22.0ms

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:
3.0ms
(* r (sin b))
4.0ms
(/ (* r (sin b)) (cos (+ a b)))
7.0ms
(cos (+ a b))

series155.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* r (sin b))
94.0ms
(/ (* r (sin b)) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify35.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0207327
1884279
25001279

prune160.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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:
3.0ms
(* r (sin b))
5.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms
(* (sin a) (sin b))
9.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series370.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* r (sin b))
80.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms
(* (sin a) (sin b))
208.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify51.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0369835
11591735
25002730

prune320.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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:
3.0ms
(* r (sin b))
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
4.0ms
(* (sin a) (sin b))
4.0ms
(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series387.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* r (sin b))
84.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
49.0ms
(* (sin a) (sin b))
217.0ms
(/ (* 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

prune292.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
20×associate-*r*
19×times-frac
13×add-exp-log add-cbrt-cube
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×flip3-- prod-exp associate-/r* frac-sub flip-- cbrt-unprod associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×sub-neg frac-2neg fma-neg diff-log associate-*r/ prod-diff clear-num
Counts
4 → 110
Calls
4 calls:
5.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
4.0ms
(* (sin a) (sin b))
8.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
27.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
43.0ms
(* (sin a) (sin b))
115.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
216.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify57.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04271385
118191256
250011254

prune370.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes149.0ms

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
01712
11712

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2893×body1280valid
480.0ms1890×body640valid
135.0ms764×body320valid
121.0ms2088×body80valid
58.0ms365×body160valid