Details

Time bar (total: 7.4s)

sample74.0ms

Algorithm
intervals
Results
20.0ms66×body1280valid
14.0ms282×body80valid
13.0ms64×body640valid
6.0ms38×body320valid
2.0ms23×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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite31.0ms

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:
8.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
21.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series331.0ms

Counts
2 → 6
Calls
2 calls:
113.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
218.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0202424
1995365
25001359

prune156.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite57.0ms

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:
9.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
24.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
13.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

series659.0ms

Counts
3 → 9
Calls
3 calls:
120.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
228.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
311.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

simplify82.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06233219
129922787
250012785

prune412.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
72×sqrt-prod
44×add-sqr-sqrt
42×add-cube-cbrt *-un-lft-identity
36×cbrt-prod
35×add-exp-log add-cbrt-cube
15×div-inv
13×cbrt-undiv div-exp associate-/r*
9×prod-exp cbrt-unprod
6×associate-/l*
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* 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 → 145
Calls
3 calls:
9.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
16.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
29.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0))))

series1.6s

Counts
3 → 9
Calls
3 calls:
114.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
577.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
919.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0))))

simplify97.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
06153107
133532825
250012807

prune510.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 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))

rewrite29.0ms

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:
19.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
6.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series329.0ms

Counts
2 → 6
Calls
2 calls:
227.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
102.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0253776
11117684
25001659

prune200.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes148.0ms

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
01815
11815

end0.0ms

sample2.4s

Algorithm
intervals
Results
755.0ms2422×body1280valid
585.0ms7959×body80valid
439.0ms2129×body640valid
158.0ms1061×body320valid
54.0ms549×body160valid