Details

Time bar (total: 6.3s)

sample84.0ms

Algorithm
intervals
Results
27.0ms73×body1280valid
16.0ms76×body640valid
13.0ms251×body80valid
4.0ms28×body320valid
3.0ms28×body160valid

simplify21.0ms

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: 0.3b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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))
9.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
13.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series591.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(fma a1 a1 (* a2 a2))
319.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
236.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0205467
11002399
25001393

prune177.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))))
0.3b
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
4.4b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite68.0ms

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))))
26.0ms
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
4.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (cos th) (hypot a1 a2))
196.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
303.0ms
(/ (* (* (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

prune283.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

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))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
25×associate-*r*
21×sqrt-prod
19×add-exp-log add-cbrt-cube
10×pow1
7×prod-exp cbrt-unprod
6×associate-/r*
4×associate-*l* pow-prod-down
3×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u associate-/l* add-log-exp
2×*-commutative div-inv
1×sqrt-undiv hypot-udef frac-2neg associate-*r/ clear-num unswap-sqr
Counts
3 → 106
Calls
3 calls:
9.0ms
(* (cos th) (hypot a1 a2))
34.0ms
(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
7.0ms
(/ (hypot a1 a2) (sqrt 2.0))

series477.0ms

Counts
3 → 9
Calls
3 calls:
111.0ms
(* (cos th) (hypot a1 a2))
257.0ms
(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
109.0ms
(/ (hypot a1 a2) (sqrt 2.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0358850
12005753
25001735

prune264.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.1b
(* (cos th) (hypot a1 a2))
0.3b
(* (* (cos th) (hypot a1 a2)) (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)))
4.6b
(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt sqrt-prod
21×add-cube-cbrt *-un-lft-identity
19×times-frac associate-*r*
12×pow1
11×add-exp-log add-cbrt-cube
6×add-log-exp
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×rem-sqrt-square sqrt-div *-commutative div-inv
1×+-commutative fma-def sqrt-pow1 flip3-+ pow1/2 associate-*r/ sum-log flip-+ unswap-sqr
Counts
4 → 95
Calls
4 calls:
9.0ms
(+ (* a1 a1) (* a2 a2))
12.0ms
(* (cos th) (hypot a1 a2))
39.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)))
10.0ms
(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))

series481.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* a1 a1) (* a2 a2))
112.0ms
(* (cos th) (hypot a1 a2))
268.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)))
73.0ms
(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0381803
11791697
25001688

prune293.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes151.0ms

Accuracy

0% (0.3b 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
0169
1169

end0.0ms

sample2.4s

Algorithm
intervals
Results
822.0ms2511×body1280valid
486.0ms2182×body640valid
398.0ms7971×body80valid
165.0ms1046×body320valid
62.0ms589×body160valid