Details

Time bar (total: 11.1s)

sample112.0ms

Algorithm
intervals
Results
44.0ms78×body1280valid
21.0ms65×body640valid
17.0ms234×body80valid
10.0ms40×body320valid
2.0ms12×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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.6b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite28.0ms

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:
13.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
14.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series294.0ms

Counts
2 → 6
Calls
2 calls:
98.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
196.0ms
(/ (* (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

prune209.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (hypot a1 a2))
0.2b
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
0.6b
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
4.8b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×pow1 sqrt-prod
9×associate-*r*
7×prod-exp cbrt-unprod
6×times-frac associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×*-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num fma-udef hypot-def div-inv associate-/l* unswap-sqr
Counts
4 → 90
Calls
4 calls:
9.0ms
(* (cos th) (hypot a1 a2))
24.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
29.0ms
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
2.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series583.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (cos th) (hypot a1 a2))
171.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
271.0ms
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
42.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0305785
11700625
25001573

prune427.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (hypot a1 a2))
0.2b
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.2b
(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
0.3b
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-sqr-sqrt
59×times-frac
48×add-cube-cbrt *-un-lft-identity
44×cbrt-prod
43×add-cbrt-cube
34×associate-*r*
23×prod-exp cbrt-unprod
22×sqrt-prod
18×cbrt-undiv div-exp
10×associate-/r*
8×pow1 associate-*l*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative
1×frac-times associate-*r/ associate-*l/
Counts
4 → 170
Calls
4 calls:
11.0ms
(* (cos th) (hypot a1 a2))
18.0ms
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
7.0ms
(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
68.0ms
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (cos th) (hypot a1 a2))
551.0ms
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
272.0ms
(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
233.0ms
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

simplify117.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06362325
137671967
250011857

prune780.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b
(/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
0.3b
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
0.4b
(/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
235×cbrt-prod
144×add-sqr-sqrt
132×add-exp-log
118×add-cube-cbrt *-un-lft-identity
88×associate-*r*
80×add-cbrt-cube
52×cbrt-undiv div-exp
47×prod-exp sqrt-prod cbrt-unprod
30×div-inv
14×associate-/r*
11×associate-/l*
9×unswap-sqr
6×pow1
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 324
Calls
4 calls:
19.0ms
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
29.0ms
(/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
119.0ms
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
17.0ms
(/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
550.0ms
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
286.0ms
(/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
237.0ms
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
365.0ms
(/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify78.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013217574
150016396

prune1.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes188.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01514
11514

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s2501×body1280valid
712.0ms2123×body640valid
608.0ms8060×body80valid
240.0ms1008×body320valid
80.0ms507×body160valid