Details

Time bar (total: 10.8s)

sample76.0ms

Algorithm
intervals
Results
27.0ms76×body1280valid
14.0ms66×body640valid
13.0ms258×body80valid
4.0ms27×body320valid
2.0ms17×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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

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)))
0.6b
(/ (* (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)))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series357.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(fma a1 a1 (* a2 a2))
112.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
211.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0205467
11002399
25001393

prune189.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

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))))
0.5b
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite31.0ms

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))))
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))
106.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
646.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
217.0ms
(/ (/ (* (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 (57.0ms)

IterNodesCost
04912250
125351935
250011905

prune431.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

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

rewrite89.0ms

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)))
9.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
39.0ms
(* (/ 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)))))
16.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))

series2.0s

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
833.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
231.0ms
(* (/ 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)))))
821.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))

simplify82.0ms

Algorithm
egg-herbie
Counts
317 → 317
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013317346
150016415

prune971.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
0.5b
(* (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (sqrt (cbrt (cbrt (sqrt 2.0))))))
1.0b
(/ (/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (sqrt (cbrt (cbrt (sqrt 2.0)))))
1.0b
(/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
455×times-frac
371×add-exp-log
300×cbrt-prod sqrt-prod
247×add-sqr-sqrt
182×div-exp
173×*-un-lft-identity
163×add-cube-cbrt
149×add-cbrt-cube
128×prod-exp
109×associate-*r*
92×cbrt-undiv
62×cbrt-unprod
39×div-inv
32×unswap-sqr
29×associate-/l*
23×associate-*l*
19×pow1
18×rec-exp 1-exp
17×associate-/r*
13×pow-flip
10×pow1/3
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp pow-div
3×frac-2neg pow-prod-down clear-num pow-sqr pow-prod-up
2×pow2 pow-plus associate-/l/
1×frac-times associate-*r/ associate-*l/ *-commutative inv-pow
Counts
4 → 517
Calls
4 calls:
16.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
79.0ms
(* (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (sqrt (cbrt (cbrt (sqrt 2.0))))))
15.0ms
(/ (/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (sqrt (cbrt (cbrt (sqrt 2.0)))))
7.0ms
(/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series1.0s

Counts
4 → 8
Calls
4 calls:
765.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
237.0ms
(* (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (sqrt (cbrt (cbrt (sqrt 2.0))))))
0.0ms
(/ (/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (sqrt (cbrt (cbrt (sqrt 2.0)))))
0.0ms
(/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify130.0ms

Algorithm
egg-herbie
Counts
525 → 525
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0190014069
1500212043

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

regimes302.0ms

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
02429
12429

end0.0ms

sample2.2s

Algorithm
intervals
Results
780.0ms2456×body1280valid
467.0ms2105×body640valid
405.0ms8133×body80valid
157.0ms1017×body320valid
56.0ms537×body160valid