Details

Time bar (total: 5.9s)

sample121.0ms

Algorithm
intervals
Results
53.0ms113×body2560valid
29.0ms82×body1280valid
15.0ms278×body80nan
7.0ms30×body640valid
3.0ms18×body320valid
1.0ms7×body160valid
0.0ms6×body80valid

simplify93.0ms

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: 0.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 5.0 (* v v))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-sqr-sqrt
3×add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
2×add-log-exp
1×acos-asin associate-*r* *-commutative unswap-sqr
Counts
2 → 27
Calls
2 calls:
6.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series28.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify107.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0119184
1350154
2945154
33243154
45001154

prune62.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 5.0 (* v v))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-sqr-sqrt
3×add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
2×add-log-exp
1×acos-asin associate-*r* *-commutative unswap-sqr
Counts
2 → 27
Calls
2 calls:
6.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series28.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify108.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0119184
1350154
2945154
33243154
45001154

prune61.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.1b
(* 5.0 (* v v))
0.4b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×pow1 add-exp-log add-cbrt-cube
6×*-un-lft-identity
5×add-log-exp
4×add-cube-cbrt
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×asin-acos difference-of-squares
1×sub-neg flip3-- times-frac diff-log associate-*r* *-commutative flip-- distribute-lft-out-- associate--r- unswap-sqr
Counts
3 → 43
Calls
3 calls:
10.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
7.0ms
(* 5.0 (* v v))
1.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series62.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
24.0ms
(* 5.0 (* v v))
4.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0195437
1533403
21403403
35002403

prune113.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

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 (/ PI 2) 3)
1.0b
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
1.4b
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

rewrite153.0ms

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:
126.0ms
(/ (- (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))))
4.0ms
(pow (/ PI 2) 3)
1.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
6.0ms
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

series493.0ms

Counts
4 → 10
Calls
4 calls:
418.0ms
(/ (- (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))))
0.0ms
(pow (/ PI 2) 3)
49.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
26.0ms
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

simplify218.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
094810059
146989809
250019809

prune632.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

regimes97.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
032100
134100
234100

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s2948×body2560valid
839.0ms2548×body1280valid
426.0ms7928×body80nan
312.0ms1261×body640valid
116.0ms628×body320valid
53.0ms413×body160valid
15.0ms202×body80valid