Details

Time bar (total: 17.3s)

sample84.0ms

Algorithm
intervals
Results
25.0ms77×body1280valid
18.0ms84×body640valid
15.0ms245×body80valid
7.0ms40×body320valid
2.0ms22×body160valid

simplify20.0ms

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

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
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
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* fma-udef log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 61
Calls
3 calls:
0.0ms
(fma a1 a1 (* a2 a2))
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series365.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(fma a1 a1 (* a2 a2))
109.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
221.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0205467
11002399
25001393

prune191.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
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))))
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×add-exp-log cbrt-prod add-sqr-sqrt
34×add-cube-cbrt *-un-lft-identity
23×add-cbrt-cube
18×sqrt-prod
13×cbrt-undiv div-exp
12×div-inv
10×associate-/r*
9×prod-exp cbrt-unprod
6×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* fma-udef
2×frac-2neg clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
4 → 137
Calls
4 calls:
0.0ms
(fma a1 a1 (* a2 a2))
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)))

series1.0s

Counts
4 → 12
Calls
4 calls:
39.0ms
(fma a1 a1 (* a2 a2))
111.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
654.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
222.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify78.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
04912250
125351935
250011905

prune437.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite427.0ms

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)))))
16.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
437.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
294.0ms
(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))
234.0ms
(* (/ (/ (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)))))
358.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify261.0ms

Algorithm
egg-herbie
Counts
1121 → 1121
Iterations

Useful iterations: 1 (62.0ms)

IterNodesCost
0363726959
1500226339

prune4.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite394.0ms

Algorithm
rewrite-expression-head
Rules
1637×times-frac
1583×cbrt-prod
1072×add-sqr-sqrt
773×add-cube-cbrt *-un-lft-identity
484×sqrt-prod
376×associate-*r*
97×add-exp-log
68×unswap-sqr
52×add-cbrt-cube
45×cbrt-undiv div-exp
35×associate-/l*
31×associate-*l*
30×div-inv
25×prod-exp cbrt-unprod
22×associate-/r*
6×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/
1×pow-prod-down *-commutative
Counts
4 → 1032
Calls
4 calls:
22.0ms
(/ (/ (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)))
231.0ms
(* (/ (cos th) (cbrt (sqrt 2.0))) (/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
41.0ms
(/ (* (/ (cos th) (cbrt (sqrt 2.0))) (/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
447.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
297.0ms
(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))
851.0ms
(* (/ (cos th) (cbrt (sqrt 2.0))) (/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
242.0ms
(/ (* (/ (cos th) (cbrt (sqrt 2.0))) (/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify222.0ms

Algorithm
egg-herbie
Counts
1044 → 1044
Iterations

Useful iterations: 1 (54.0ms)

IterNodesCost
0340821466
1500120941

prune3.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes192.0ms

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
01815
11815

end0.0ms

sample2.3s

Algorithm
intervals
Results
821.0ms2502×body1280valid
469.0ms2132×body640valid
408.0ms8008×body80valid
171.0ms1094×body320valid
54.0ms504×body160valid