Details

Time bar (total: 13.8s)

sample78.0ms

Algorithm
intervals
Results
31.0ms86×body1280valid
13.0ms267×body80valid
12.0ms56×body640valid
4.0ms30×body320valid
2.0ms21×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: 0.4b

localize10.0ms

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))

series364.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(fma a1 a1 (* a2 a2))
114.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
216.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0205467
11002399
25001393

prune181.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.1b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b
(/ (* (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)))

rewrite30.0ms

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))
4.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
7.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
14.0ms
(/ (/ (* (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:
41.0ms
(fma a1 a1 (* a2 a2))
109.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
667.0ms
(/ (* (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)))

simplify75.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
04912250
125351935
250011905

prune425.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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 (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
0.2b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.4b
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
194×times-frac
150×cbrt-prod
112×add-exp-log
76×add-sqr-sqrt
74×add-cube-cbrt *-un-lft-identity
61×add-cbrt-cube
51×cbrt-undiv div-exp
31×prod-exp cbrt-unprod div-inv
30×sqrt-prod
15×associate-/l*
14×associate-/r*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* associate-*l* clear-num
2×fma-udef associate-/l/
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 253
Calls
4 calls:
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
25.0ms
(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
7.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
13.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
235.0ms
(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
667.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
807.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify150.0ms

Algorithm
egg-herbie
Counts
265 → 265
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
09217187
146366299
250016220

prune920.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (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)))))

rewrite407.0ms

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:
21.0ms
(/ (/ (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)))
260.0ms
(* (/ (/ (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)))))
15.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
440.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
287.0ms
(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))
221.0ms
(* (/ (/ (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)))))
580.0ms
(/ (/ (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 (62.0ms)

IterNodesCost
0363726959
1500226339

prune3.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes167.0ms

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
01722
11722

end0.0ms

sample2.2s

Algorithm
intervals
Results
806.0ms2518×body1280valid
445.0ms2077×body640valid
390.0ms8125×body80valid
171.0ms1074×body320valid
53.0ms516×body160valid