Details

Time bar (total: 6.0s)

sample76.0ms

Algorithm
intervals
Results
28.0ms88×body1280valid
14.0ms67×body640valid
12.0ms246×body80valid
5.0ms35×body320valid
2.0ms15×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: 0.6b

localize10.0ms

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))

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))

series327.0ms

Counts
2 → 6
Calls
2 calls:
107.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
220.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify33.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0202424
1995365
25001359

prune345.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (hypot a1 a2))
0.1b
(* (* (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))
6.8b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite25.0ms

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:
4.0ms
(* (cos th) (hypot a1 a2))
8.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
9.0ms
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series615.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (cos th) (hypot a1 a2))
178.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
287.0ms
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
46.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify47.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0305785
11700625
25001573

prune284.0ms

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
(hypot a1 a2)
0.1b
(* (cos th) (hypot a1 a2))
0.3b
(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
0.4b
(/ (hypot a1 a2) (sqrt 2.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
25×associate-*r*
21×sqrt-prod
20×add-exp-log add-cbrt-cube
11×pow1
7×prod-exp cbrt-unprod
6×associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-/l*
2×hypot-udef *-commutative div-inv
1×sqrt-undiv frac-2neg associate-*r/ clear-num unswap-sqr
Counts
4 → 116
Calls
4 calls:
0.0ms
(hypot a1 a2)
3.0ms
(* (cos th) (hypot a1 a2))
13.0ms
(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
3.0ms
(/ (hypot a1 a2) (sqrt 2.0))

series489.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(hypot a1 a2)
102.0ms
(* (cos th) (hypot a1 a2))
239.0ms
(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
103.0ms
(/ (hypot a1 a2) (sqrt 2.0))

simplify59.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0363877
12010777
25002759

prune311.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot a1 a2)
0.1b
(* (hypot a1 a2) (cos th))
0.3b
(* (* (hypot a1 a2) (cos th)) (/ (hypot a1 a2) (sqrt 2.0)))
0.4b
(/ (hypot a1 a2) (sqrt 2.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
25×associate-*r*
21×sqrt-prod
20×add-exp-log add-cbrt-cube
11×pow1
7×prod-exp cbrt-unprod
6×associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-/l*
2×hypot-udef *-commutative div-inv
1×sqrt-undiv frac-2neg associate-*r/ clear-num unswap-sqr
Counts
4 → 116
Calls
4 calls:
0.0ms
(hypot a1 a2)
3.0ms
(* (hypot a1 a2) (cos th))
15.0ms
(* (* (hypot a1 a2) (cos th)) (/ (hypot a1 a2) (sqrt 2.0)))
3.0ms
(/ (hypot a1 a2) (sqrt 2.0))

series451.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(hypot a1 a2)
98.0ms
(* (hypot a1 a2) (cos th))
199.0ms
(* (* (hypot a1 a2) (cos th)) (/ (hypot a1 a2) (sqrt 2.0)))
104.0ms
(/ (hypot a1 a2) (sqrt 2.0))

simplify58.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0365877
11966777
25001759

prune295.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes154.0ms

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
0127
1127

end0.0ms

sample2.3s

Algorithm
intervals
Results
808.0ms2539×body1280valid
495.0ms2251×body640valid
407.0ms8054×body80valid
162.0ms1053×body320valid
55.0ms473×body160valid