Details

Time bar (total: 9.2s)

sample72.0ms

Algorithm
intervals
Results
25.0ms79×body1280valid
13.0ms257×body80valid
12.0ms57×body640valid
5.0ms36×body320valid
1.0ms14×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

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:
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series324.0ms

Counts
2 → 6
Calls
2 calls:
106.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
217.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0202424
1995365
25001359

prune153.0ms

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)))

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 fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 127
Calls
3 calls:
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
7.0ms
(/ (* (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)))

series976.0ms

Counts
3 → 9
Calls
3 calls:
112.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
645.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
218.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify76.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
04882207
125281901
250011871

prune389.0ms

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
60×add-exp-log
28×add-cbrt-cube
23×div-exp prod-exp
14×cbrt-undiv cbrt-unprod
13×add-sqr-sqrt
12×cbrt-prod
11×add-cube-cbrt *-un-lft-identity
10×times-frac associate-/r*
6×sqrt-prod
5×pow1 1-exp
3×expm1-log1p-u associate-*r* associate-*l* log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef div-inv associate-/l*
1×distribute-rgt-in distribute-lft-in associate-*r/ pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 94
Calls
3 calls:
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
7.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
19.0ms
(/ (* 1 (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (cbrt (sqrt 2.0)))

series991.0ms

Counts
3 → 9
Calls
3 calls:
112.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
653.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
226.0ms
(/ (* 1 (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (cbrt (sqrt 2.0)))

simplify68.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04821367
125991005
25002955

prune252.0ms

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

rewrite129.0ms

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 fma-udef
1×distribute-rgt-in frac-times distribute-lft-in associate-*r/ associate-*l/ associate-/l/
Counts
4 → 305
Calls
4 calls:
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
7.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
15.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (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))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

series2.1s

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
874.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
832.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
239.0ms
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

simplify92.0ms

Algorithm
egg-herbie
Counts
317 → 317
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
013317346
150016415

prune982.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes187.0ms

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
01914
12114
22114

end0.0ms

sample2.2s

Algorithm
intervals
Results
810.0ms2545×body1280valid
455.0ms2103×body640valid
394.0ms8016×body80valid
168.0ms1036×body320valid
56.0ms520×body160valid