Details

Time bar (total: 13.9s)

sample111.0ms

Algorithm
intervals
Results
36.0ms67×body1280valid
27.0ms263×body80valid
21.0ms62×body640valid
9.0ms34×body320valid
3.0ms18×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

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))

series526.0ms

Counts
2 → 6
Calls
2 calls:
306.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
221.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0202424
1995365
25001359

prune147.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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

rewrite28.0ms

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)))
12.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
8.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series964.0ms

Counts
3 → 9
Calls
3 calls:
107.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
217.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
640.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify80.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
04882207
125281901
250011864

prune379.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

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)))
0.4b
(* (/ (/ (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)))))

rewrite420.0ms

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)))
270.0ms
(* (/ (/ (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)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
428.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
289.0ms
(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))
230.0ms
(* (/ (/ (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)))))
351.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify258.0ms

Algorithm
egg-herbie
Counts
1121 → 1121
Iterations

Useful iterations: 1 (60.0ms)

IterNodesCost
0363726959
1500226339

prune4.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (* (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt 1)) (/ (/ (sqrt (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)))))
6.1b
(sqrt (fma a1 a1 (* a2 a2)))
6.1b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
217×add-exp-log
143×times-frac
124×add-cbrt-cube
93×cbrt-undiv div-exp
81×prod-exp cbrt-unprod
66×add-sqr-sqrt
64×add-cube-cbrt *-un-lft-identity
54×cbrt-prod
35×associate-*l*
33×sqrt-prod
31×associate-/l*
11×pow1
5×frac-times associate-*r/ div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down associate-*l/
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef hypot-def
1×frac-2neg associate-*r* clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 241
Calls
4 calls:
195.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (* (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt 1)) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))))
15.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series678.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (* (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt 1)) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))))
354.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
49.0ms
(sqrt (fma a1 a1 (* a2 a2)))
44.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify63.0ms

Algorithm
egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010986145
150014383

prune1.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes161.0ms

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

sample3.4s

Algorithm
intervals
Results
1.2s2515×body1280valid
807.0ms7891×body80valid
705.0ms2051×body640valid
263.0ms1016×body320valid
99.0ms513×body160valid