Details

Time bar (total: 5.2s)

sample85.0ms

Algorithm
intervals
Results
36.0ms102×body2560valid
17.0ms73×body1280valid
9.0ms288×body80nan
7.0ms41×body640valid
3.0ms22×body320valid
1.0ms12×body160valid
0.0ms6×body80valid

simplify98.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1427
2777
31467
42427
54177
627897
750017

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.5b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b
(* 5.0 (* v v))
0.5b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×times-frac
10×add-exp-log add-cbrt-cube
8×pow1
4×associate-/r* difference-of-squares
3×associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l* add-log-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv acos-asin frac-2neg div-sub div-exp associate-*r* clear-num *-commutative div-inv unswap-sqr
Counts
3 → 63
Calls
3 calls:
11.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series106.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify40.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0336587
11261535
25002531

prune131.0ms

Filtered
72 candidates to 55 candidates (76.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New69372
Fresh000
Picked101
Done000
Total70373

Merged error: 0.5b

Counts
73 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b
(* 5.0 (* v v))
0.5b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp difference-of-squares
4×associate-/r*
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod associate-/l*
2×asin-acos associate-/r/ associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num *-commutative div-inv distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 79
Calls
4 calls:
7.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
8.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms
(* 5.0 (* v v))
1.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series139.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
78.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
27.0ms
(* 5.0 (* v v))
3.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify45.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0409840
11459784
25001780

prune179.0ms

Filtered
91 candidates to 69 candidates (75.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New90191
Fresh022
Picked011
Done000
Total90494

Merged error: 0.5b

Counts
94 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (- (pow (/ PI 2) 3) (pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)) (+ (* (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))) (* (/ PI 2) (/ PI 2))))
1.0b
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
1.0b
(pow (/ PI 2) 3)
1.2b
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
244×add-sqr-sqrt
149×times-frac
102×*-un-lft-identity
96×difference-of-squares
88×unpow-prod-down cube-prod
60×add-cube-cbrt
42×sqr-pow
33×associate-/l*
20×distribute-lft-out--
10×add-exp-log add-cbrt-cube
8×associate-*r/ associate-/r/
6×pow1 pow-unpow frac-add add-log-exp
5×flip3-+ flip-+
4×difference-cubes
3×pow-exp associate-/r* div-inv rem-cube-cbrt
2×cbrt-undiv cube-mult frac-times pow-to-exp pow-pow unpow3 div-exp associate-*l/ associate-/l/
1×+-commutative cube-div associate-+l- asin-acos flip3-- frac-2neg div-sub clear-num sum-log flip-- distribute-lft-out
Counts
4 → 240
Calls
4 calls:
39.0ms
(/ (- (pow (/ PI 2) 3) (pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)) (+ (* (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))) (* (/ PI 2) (/ PI 2))))
2.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
5.0ms
(pow (/ PI 2) 3)
6.0ms
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

series488.0ms

Counts
4 → 10
Calls
4 calls:
414.0ms
(/ (- (pow (/ PI 2) 3) (pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)) (+ (* (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))) (* (/ PI 2) (/ PI 2))))
48.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
0.0ms
(pow (/ PI 2) 3)
26.0ms
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

simplify223.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
094410140
145809889
250019889

prune573.0ms

Filtered
250 candidates to 135 candidates (54.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2473250
Fresh202
Picked101
Done011
Total2504254

Merged error: 0.5b

Counts
254 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
1.0b
(pow (/ PI 2) 3)
1.2b
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
22×add-sqr-sqrt add-cube-cbrt
18×times-frac
16×unpow-prod-down cube-prod
8×add-exp-log add-cbrt-cube
6×pow1 pow-unpow add-log-exp
3×pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp asin-acos pow-pow unpow3 div-inv sqr-pow
1×cbrt-undiv +-commutative cube-div associate-+l- flip3-+ div-exp sum-log flip-+ distribute-lft-out
Counts
4 → 90
Calls
4 calls:
1.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
3.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
5.0ms
(pow (/ PI 2) 3)
6.0ms
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

series77.0ms

Counts
4 → 10
Calls
4 calls:
3.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
48.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
0.0ms
(pow (/ PI 2) 3)
26.0ms
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

simplify66.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0410835
11950703
25001692

prune227.0ms

Filtered
100 candidates to 57 candidates (57.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New991100
Fresh022
Picked011
Done011
Total995104

Merged error: 0.5b

Counts
104 → 5

regimes80.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03034
13034

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s2922×body2560valid
608.0ms2479×body1280valid
236.0ms7924×body80nan
226.0ms1288×body640valid
82.0ms642×body320valid
42.0ms455×body160valid
11.0ms214×body80valid