Details

Time bar (total: 11.5s)

sample70.0ms

Algorithm
intervals
Results
20.0ms61×body1280valid
14.0ms64×body640valid
13.0ms270×body80valid
5.0ms35×body320valid
2.0ms18×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

prune12.0ms

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:

0.1b
(* (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))

series323.0ms

Counts
2 → 6
Calls
2 calls:
108.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
215.0ms
(/ (* (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

prune160.0ms

Filtered
57 candidates to 39 candidates (68.4%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
9×add-exp-log add-cbrt-cube
6×associate-/r*
4×pow1
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
2 → 85
Calls
2 calls:
11.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
3.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series319.0ms

Counts
2 → 6
Calls
2 calls:
216.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
102.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0253776
11117684
25001659

prune230.0ms

Filtered
91 candidates to 57 candidates (62.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.3b
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (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))))

rewrite31.0ms

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)))
15.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
7.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series1.1s

Counts
3 → 9
Calls
3 calls:
112.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
222.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
805.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify75.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
04882207
125281901
250011864

prune421.0ms

Filtered
136 candidates to 94 candidates (69.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
0.3b
(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))
0.3b
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
0.7b
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

rewrite429.0ms

Algorithm
rewrite-expression-head
Rules
1848×times-frac
1647×cbrt-prod
1173×add-sqr-sqrt
812×add-cube-cbrt *-un-lft-identity
510×sqrt-prod
376×associate-*r*
92×add-exp-log
85×unswap-sqr
65×associate-/l*
49×add-cbrt-cube
43×cbrt-undiv div-exp
35×associate-*l*
33×div-inv
23×prod-exp cbrt-unprod
22×associate-/r*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×associate-/l/
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 1109
Calls
4 calls:
19.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
4.0ms
(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))
278.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
19.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
431.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
307.0ms
(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))
253.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
375.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify244.0ms

Algorithm
egg-herbie
Counts
1121 → 1121
Iterations

Useful iterations: 1 (56.0ms)

IterNodesCost
0363726959
1500226339

prune4.0s

Filtered
1121 candidates to 735 candidates (65.6%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes175.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02125
12125

end0.0ms

sample2.3s

Algorithm
intervals
Results
842.0ms2520×body1280valid
473.0ms2093×body640valid
416.0ms8081×body80valid
160.0ms973×body320valid
62.0ms574×body160valid