Details

Time bar (total: 7.5s)

sample123.0ms

Algorithm
intervals
Results
38.0ms78×body1280valid
29.0ms278×body80valid
26.0ms81×body640valid
10.0ms40×body320valid
2.0ms14×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 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite10.0ms

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))
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series368.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(fma a1 a1 (* a2 a2))
109.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
219.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0205467
11002399
25001393

prune207.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
0.1b
(* (cos th) (pow a2 2))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.3b
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
49×add-sqr-sqrt
43×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×unpow-prod-down
24×add-exp-log
13×add-cbrt-cube
12×associate-/r*
9×associate-/l* unpow2 sqr-pow
8×associate-*r*
7×div-exp
6×prod-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×cbrt-undiv pow-to-exp associate-*l* pow-exp
2×frac-2neg clear-num cbrt-unprod div-inv
1×*-commutative fma-udef
Counts
4 → 148
Calls
4 calls:
0.0ms
(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
6.0ms
(* (cos th) (pow a2 2))
6.0ms
(/ (pow a1 2) (sqrt 2.0))
5.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

series472.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
50.0ms
(* (cos th) (pow a2 2))
59.0ms
(/ (pow a1 2) (sqrt 2.0))
119.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04141106
11719958
25001948

prune453.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* a2 (cos th)) (pow a2 (/ 2 2)))
0.1b
(* a2 (cos th))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.3b
(/ (* (* a2 (cos th)) (pow a2 (/ 2 2))) (sqrt 2.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
46×add-sqr-sqrt
45×add-exp-log
44×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
24×unpow-prod-down
22×add-cbrt-cube
19×prod-exp
12×associate-/r*
10×div-exp associate-*r*
9×associate-/l*
8×sqr-pow
7×cbrt-unprod unpow2
6×pow1
5×pow-to-exp pow-exp
4×cbrt-undiv expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×frac-2neg clear-num *-commutative div-inv
1×pow-prod-down unswap-sqr
Counts
4 → 159
Calls
4 calls:
10.0ms
(* (* a2 (cos th)) (pow a2 (/ 2 2)))
3.0ms
(* a2 (cos th))
5.0ms
(/ (pow a1 2) (sqrt 2.0))
10.0ms
(/ (* (* a2 (cos th)) (pow a2 (/ 2 2))) (sqrt 2.0))

series250.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* a2 (cos th)) (pow a2 (/ 2 2)))
42.0ms
(* a2 (cos th))
59.0ms
(/ (pow a1 2) (sqrt 2.0))
102.0ms
(/ (* (* a2 (cos th)) (pow a2 (/ 2 2))) (sqrt 2.0))

simplify76.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
04941077
12399922
25002921

prune479.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* a2 (cos th))
0.2b
(* (* a2 (cos th)) (/ (pow a2 1) (sqrt 2.0)))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.4b
(/ (pow a2 1) (sqrt 2.0))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
97×add-sqr-sqrt
95×add-cube-cbrt *-un-lft-identity
72×sqrt-prod
60×unpow-prod-down
49×associate-*r*
40×add-exp-log
22×add-cbrt-cube
20×sqr-pow
15×associate-/l*
13×prod-exp
12×div-exp associate-/r*
11×pow1
7×cbrt-unprod unpow2
4×cbrt-undiv expm1-log1p-u pow-to-exp associate-*l* pow-prod-down pow-exp log1p-expm1-u add-log-exp
3×div-inv
2×frac-2neg clear-num *-commutative
1×associate-*r/ unswap-sqr
Counts
4 → 241
Calls
4 calls:
3.0ms
(* a2 (cos th))
24.0ms
(* (* a2 (cos th)) (/ (pow a2 1) (sqrt 2.0)))
6.0ms
(/ (pow a1 2) (sqrt 2.0))
5.0ms
(/ (pow a2 1) (sqrt 2.0))

series444.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* a2 (cos th))
286.0ms
(* (* a2 (cos th)) (/ (pow a2 1) (sqrt 2.0)))
59.0ms
(/ (pow a1 2) (sqrt 2.0))
60.0ms
(/ (pow a2 1) (sqrt 2.0))

simplify86.0ms

Algorithm
egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06921661
131051442
250011430

prune616.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes196.0ms

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
02218
12418
22418

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s2538×body1280valid
829.0ms8149×body80valid
704.0ms2133×body640valid
265.0ms1070×body320valid
94.0ms515×body160valid