Details

Time bar (total: 7.4s)

sample99.0ms

Algorithm
intervals
Results
36.0ms91×body1280valid
20.0ms255×body80valid
17.0ms58×body640valid
7.0ms32×body320valid
3.0ms16×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: 0.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite9.0ms

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))

series319.0ms

Counts
2 → 6
Calls
2 calls:
107.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
212.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0202424
1995365
25001359

prune161.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
9×add-exp-log add-cbrt-cube
6×associate-/r*
4×pow1
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
2 → 85
Calls
2 calls:
11.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
3.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series319.0ms

Counts
2 → 6
Calls
2 calls:
213.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
106.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0253776
11117684
25001659

prune230.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2.0) (hypot a1 a2))))
0.2b
(/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2.0) (hypot a1 a2)))
0.4b
(/ (sqrt 2.0) (hypot a1 a2))
6.4b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
526×times-frac
306×add-sqr-sqrt
281×add-cube-cbrt *-un-lft-identity
272×sqrt-prod
137×associate-*r*
25×associate-/r*
20×add-exp-log add-cbrt-cube
16×div-inv
12×associate-/l*
7×pow1 cbrt-undiv div-exp unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-undiv associate-*l* prod-exp cbrt-unprod
2×hypot-udef frac-2neg clear-num associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down *-commutative fma-udef hypot-def
Counts
4 → 401
Calls
4 calls:
52.0ms
(* (cos th) (/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2.0) (hypot a1 a2))))
9.0ms
(/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2.0) (hypot a1 a2)))
3.0ms
(/ (sqrt 2.0) (hypot a1 a2))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series589.0ms

Counts
4 → 12
Calls
4 calls:
287.0ms
(* (cos th) (/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2.0) (hypot a1 a2))))
178.0ms
(/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2.0) (hypot a1 a2)))
82.0ms
(/ (sqrt 2.0) (hypot a1 a2))
42.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify75.0ms

Algorithm
egg-herbie
Counts
413 → 413
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09845123
150014454

prune928.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b
(/ (* (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)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
234×sqrt-prod
216×times-frac
95×add-sqr-sqrt
93×add-cube-cbrt *-un-lft-identity
19×add-exp-log add-cbrt-cube
18×associate-/r*
14×associate-/l*
12×div-inv
7×cbrt-undiv div-exp
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 215
Calls
3 calls:
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
6.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
13.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series813.0ms

Counts
3 → 9
Calls
3 calls:
110.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
293.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
410.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify80.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06233219
129922787
250022779

prune404.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes154.0ms

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
01515
11515

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.0s2496×body1280valid
640.0ms8079×body80valid
630.0ms2118×body640valid
233.0ms1068×body320valid
77.0ms492×body160valid