Details

Time bar (total: 9.0s)

sample77.0ms

Algorithm
intervals
Results
25.0ms79×body1280valid
15.0ms57×body640valid
13.0ms257×body80valid
6.0ms36×body320valid
2.0ms14×body160valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
4×pow1
3×associate-*r* associate-*l*
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod fma-udef log1p-expm1-u add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
2 → 51
Calls
2 calls:
4.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series338.0ms

Counts
2 → 6
Calls
2 calls:
111.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
227.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0202424
1995365
25001359

prune354.0ms

Filtered
57 candidates to 39 candidates (68.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
36×cbrt-prod
35×add-exp-log add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
22×add-cbrt-cube
18×sqrt-prod
13×cbrt-undiv div-exp
12×div-inv
10×associate-/r*
9×prod-exp cbrt-unprod
6×associate-/l*
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 127
Calls
3 calls:
4.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
8.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
12.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series998.0ms

Counts
3 → 9
Calls
3 calls:
116.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
661.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
221.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify73.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04882207
125281901
250011871

prune391.0ms

Filtered
136 candidates to 93 candidates (68.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (fma a1 a1 (* a2 a2)) (cos th))
0.2b
(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b
(/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
36×cbrt-prod
35×add-exp-log add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
22×add-cbrt-cube
18×sqrt-prod
13×cbrt-undiv div-exp
12×div-inv
10×associate-/r*
9×prod-exp cbrt-unprod
6×associate-/l*
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 125
Calls
3 calls:
3.0ms
(* (fma a1 a1 (* a2 a2)) (cos th))
7.0ms
(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
12.0ms
(/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series857.0ms

Counts
3 → 9
Calls
3 calls:
98.0ms
(* (fma a1 a1 (* a2 a2)) (cos th))
574.0ms
(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
185.0ms
(/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify71.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04762193
122931883
250011852

prune387.0ms

Filtered
134 candidates to 93 candidates (69.4%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fma a1 a1 (* a2 a2)) (cos th))
0.2b
(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.2b
(/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
0.2b
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
241×add-exp-log
180×cbrt-prod
171×times-frac
117×add-sqr-sqrt
100×div-exp
97×prod-exp
83×*-un-lft-identity
78×add-cube-cbrt
77×add-cbrt-cube
67×associate-*r*
52×cbrt-undiv
45×cbrt-unprod
36×sqrt-prod
29×div-inv
16×unswap-sqr
13×associate-/r*
12×rec-exp 1-exp
10×associate-*l*
8×pow1
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative
1×frac-times associate-*r/ associate-*l/ associate-/l/
Counts
4 → 303
Calls
4 calls:
3.0ms
(* (fma a1 a1 (* a2 a2)) (cos th))
7.0ms
(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
13.0ms
(/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
85.0ms
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (fma a1 a1 (* a2 a2)) (cos th))
570.0ms
(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
726.0ms
(/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
197.0ms
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

simplify85.0ms

Algorithm
egg-herbie
Counts
315 → 315
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013197344
150016403

prune995.0ms

Filtered
315 candidates to 199 candidates (63.2%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes170.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01413
11413

end0.0ms

sample2.3s

Algorithm
intervals
Results
853.0ms2545×body1280valid
468.0ms2103×body640valid
414.0ms8016×body80valid
161.0ms1036×body320valid
56.0ms520×body160valid