Details

Time bar (total: 11.2s)

sample91.0ms

Algorithm
intervals
Results
30.0ms71×body1280valid
20.0ms251×body80valid
16.0ms56×body640valid
6.0ms27×body320valid
4.0ms24×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.8b
(/ (cos th) (sqrt 2.0))
0.8b
(/ (cos th) (sqrt 2.0))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
32×add-exp-log add-cbrt-cube
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 168
Calls
4 calls:
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms
(/ (cos th) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series341.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
110.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
60.0ms
(/ (cos th) (sqrt 2.0))
63.0ms
(/ (cos th) (sqrt 2.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05041284
120091156
250011136

prune444.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))
0.8b
(/ (cos th) (sqrt 2.0))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
1149×sqrt-prod
1137×times-frac
626×add-sqr-sqrt
592×add-cube-cbrt *-un-lft-identity
283×associate-*l*
37×associate-/l*
34×add-exp-log add-cbrt-cube
24×associate-/r*
23×div-inv
13×unswap-sqr
11×cbrt-undiv div-exp
9×pow1 prod-exp cbrt-unprod
4×add-log-exp
3×frac-2neg pow-prod-down clear-num
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 744
Calls
4 calls:
96.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
4.0ms
(/ (cos th) (sqrt 2.0))

series340.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
61.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
101.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
58.0ms
(/ (cos th) (sqrt 2.0))

simplify106.0ms

Algorithm
egg-herbie
Counts
756 → 756
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015449868
150018666

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))) (* a2 a2))
0.8b
(/ (cos th) (sqrt 2.0))
1.0b
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
783×sqrt-prod
768×times-frac
416×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
192×cbrt-prod
124×add-exp-log
78×add-cbrt-cube
53×prod-exp
43×div-exp
37×associate-/l*
33×cbrt-unprod
27×associate-/r*
23×cbrt-undiv
20×pow1
16×div-inv
8×pow-prod-down
7×pow-flip sqrt-pow1
6×rec-exp 1-exp
4×associate-*l/ add-log-exp
3×frac-2neg pow1/2 clear-num
2×pow1/3 pow-div
1×frac-times associate-*r/ associate-*r* associate-*l* *-commutative associate-/l/ inv-pow
Counts
4 → 585
Calls
4 calls:
133.0ms
(* (* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))) (* a2 a2))
4.0ms
(/ (cos th) (sqrt 2.0))
20.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
5.0ms
(/ 1 (sqrt (sqrt 2.0)))

series622.0ms

Counts
4 → 8
Calls
4 calls:
556.0ms
(* (* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))) (* a2 a2))
65.0ms
(/ (cos th) (sqrt 2.0))
0.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify104.0ms

Algorithm
egg-herbie
Counts
593 → 593
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015999407
150018383

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))
1.0b
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
1365×sqrt-prod
1326×times-frac
709×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
192×cbrt-prod
68×associate-/l*
39×associate-/r*
27×div-inv
24×add-exp-log
18×add-cbrt-cube
12×div-exp
8×pow1 cbrt-undiv
7×pow-flip sqrt-pow1
4×frac-2neg clear-num add-log-exp
3×pow1/2
2×rec-exp pow1/3 1-exp associate-/l/ pow-div
1×inv-pow
Counts
4 → 878
Calls
4 calls:
20.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
20.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
5.0ms
(/ 1 (sqrt (sqrt 2.0)))

series389.0ms

Counts
4 → 8
Calls
4 calls:
280.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
108.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
0.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify137.0ms

Algorithm
egg-herbie
Counts
886 → 886
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0182413869
1500212577

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes289.0ms

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
03633
13633

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s2545×body1280valid
640.0ms8084×body80valid
625.0ms2132×body640valid
219.0ms993×body320valid
90.0ms541×body160valid