Details

Time bar (total: 5.7s)

sample82.0ms

Algorithm
intervals
Results
33.0ms95×body2560valid
16.0ms73×body1280valid
10.0ms46×body640valid
7.0ms254×body80nan
2.0ms19×body320valid
1.0ms12×body160valid
1.0ms11×body80valid

simplify97.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1427
2777
31467
42427
54177
627897
750017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b
(* 5.0 (* v v))
0.9b
(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:
10.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series114.0ms

Counts
3 → 9
Calls
3 calls:
81.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0336587
11261535
25002531

prune165.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.1b
(* 5.0 (* v v))
0.9b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite29.0ms

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:
10.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
10.0ms
(- (/ PI 2) (asin (/ (- 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)))

series144.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
26.0ms
(* 5.0 (* v v))
7.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0409840
11459784
25001780

prune235.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (- (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)
1.8b
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

rewrite151.0ms

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:
124.0ms
(/ (- (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))))
1.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
4.0ms
(pow (/ PI 2) 3)
6.0ms
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

series497.0ms

Counts
4 → 10
Calls
4 calls:
427.0ms
(/ (- (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))))
43.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
0.0ms
(pow (/ PI 2) 3)
27.0ms
(+ (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
094410059
146339809
250019809

prune663.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
0.0b
(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.1b
(* 5.0 (* v v))
0.9b
(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
9×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
8×add-log-exp
5×add-cube-cbrt
4×difference-of-squares
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×sub-neg asin-acos flip3-- times-frac diff-log flip-- distribute-lft-out--
1×associate-*r* *-commutative frac-sub associate--r- unswap-sqr
Counts
4 → 59
Calls
4 calls:
17.0ms
(- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
79.0ms
(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
6.0ms
(* 5.0 (* v v))
23.0ms
(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series184.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
121.0ms
(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
26.0ms
(* 5.0 (* v v))
5.0ms
(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify145.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0325837
11068770
24840764
35001764

prune173.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

regimes144.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01712
11712

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s2980×body2560valid
554.0ms2437×body1280valid
219.0ms8120×body80nan
214.0ms1284×body640valid
79.0ms634×body320valid
35.0ms426×body160valid
12.0ms239×body80valid