Details

Time bar (total: 9.1s)

sample79.0ms

Algorithm
intervals
Results
23.0ms71×body1280valid
16.0ms272×body80valid
16.0ms77×body640valid
6.0ms38×body320valid
2.0ms21×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

Filtered
1 candidates to 1 candidates (100.0%)
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))
0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite12.0ms

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:
1.0ms
(fma a1 a1 (* a2 a2))
4.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
6.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series558.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(fma a1 a1 (* a2 a2))
306.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
219.0ms
(/ (* (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

Filtered
70 candidates to 49 candidates (70.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (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)))

rewrite32.0ms

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:
1.0ms
(fma a1 a1 (* a2 a2))
4.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
9.0ms
(/ (* (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 (sqrt 2.0)))

series995.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma a1 a1 (* a2 a2))
110.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
636.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
213.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify73.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04912250
125351935
250011905

prune420.0ms

Filtered
149 candidates to 102 candidates (68.5%)
Pruning

8 alts after pruning (7 fresh and 1 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)))) (cbrt (cbrt (sqrt 2.0))))
0.3b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b
(* (/ 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)))))

rewrite92.0ms

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:
4.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
13.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
9.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
41.0ms
(* (/ 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)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
840.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
652.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
222.0ms
(* (/ 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)))))

simplify83.0ms

Algorithm
egg-herbie
Counts
317 → 317
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013317346
150016415

prune984.0ms

Filtered
317 candidates to 200 candidates (63.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.3b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
0.3b
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
234×sqrt-prod
216×times-frac
96×add-sqr-sqrt
94×add-cube-cbrt *-un-lft-identity
20×add-exp-log add-cbrt-cube
18×associate-/r*
14×associate-/l*
12×div-inv
7×cbrt-undiv div-exp
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* prod-exp cbrt-unprod fma-udef
2×frac-2neg clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
4 → 225
Calls
4 calls:
1.0ms
(fma a1 a1 (* a2 a2))
4.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
10.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
12.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series664.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(fma a1 a1 (* a2 a2))
107.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
310.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
214.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify85.0ms

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06263262
129992821
250012813

prune434.0ms

Filtered
237 candidates to 111 candidates (46.8%)
Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes182.0ms

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
01413
11413

end0.0ms

sample2.2s

Algorithm
intervals
Results
806.0ms2495×body1280valid
456.0ms2147×body640valid
397.0ms8009×body80valid
174.0ms1109×body320valid
56.0ms534×body160valid