Details

Time bar (total: 7.5s)

sample125.0ms

Algorithm
intervals
Results
54.0ms113×body2560valid
28.0ms82×body1280valid
16.0ms278×body80nan
8.0ms30×body640valid
3.0ms18×body320valid
1.0ms7×body160valid
0.0ms6×body80valid

simplify99.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0207
1437
2847
31557
42627
54547
628787
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×expm1-log1p-u log1p-expm1-u add-log-exp
1×acos-asin associate-*r* *-commutative unswap-sqr
Counts
2 → 31
Calls
2 calls:
7.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series31.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify109.0ms

Algorithm
egg-herbie
Counts
37 → 37
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0124206
1355176
2960176
33275176
45001176

prune70.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

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)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
47×*-un-lft-identity
45×add-cube-cbrt
39×prod-diff
37×times-frac
13×fma-neg
8×pow1 add-exp-log add-cbrt-cube
5×add-log-exp
4×div-inv
3×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×asin-acos difference-of-squares
1×sub-neg flip3-- diff-log associate-*r* *-commutative flip-- distribute-lft-out-- associate--r- unswap-sqr
Counts
3 → 101
Calls
3 calls:
14.0ms
(- (/ 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:
35.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
24.0ms
(* 5.0 (* v v))
3.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify195.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 3 (176.0ms)

IterNodesCost
03572531
110021460
248351437
350011428

prune188.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
1.0b
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
50×cbrt-prod
35×*-un-lft-identity
18×cbrt-div
15×add-cube-cbrt
14×difference-of-squares
11×pow1 swap-sqr
9×flip3-- pow1/3 associate-*r* associate-*l* flip-- distribute-lft-out--
7×times-frac
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 115
Calls
4 calls:
61.0ms
(* (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
7.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
7.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
7.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series890.0ms

Counts
4 → 12
Calls
4 calls:
259.0ms
(* (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
208.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
213.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
210.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify103.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
02242796
16842647
229682458
350022437

prune328.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (sqrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) (pow (sqrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) 3))
1.0b
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
55×sqrt-prod
50×cbrt-prod
30×associate-*r*
29×*-un-lft-identity
24×unswap-sqr
21×unpow-prod-down cube-prod
18×cbrt-div
17×add-cube-cbrt
12×sqrt-div associate-*l* difference-of-squares
9×add-exp-log flip3-- flip--
6×cube-div times-frac add-cbrt-cube distribute-lft-out--
5×pow1
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp sqr-pow
3×pow1/3 prod-exp
2×associate-*r/ associate-*l/
1×cube-mult pow-to-exp unpow3 pow-exp *-commutative pow-prod-up cbrt-unprod
Counts
4 → 143
Calls
4 calls:
107.0ms
(* (sqrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) (pow (sqrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) 3))
7.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
7.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
7.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series899.0ms

Counts
4 → 12
Calls
4 calls:
262.0ms
(* (sqrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) (pow (sqrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) 3))
218.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
209.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
209.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify71.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03874179
112533430
250013304

prune464.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

regimes92.0ms

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
0149
1149

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2948×body2560valid
873.0ms2548×body1280valid
452.0ms7928×body80nan
324.0ms1261×body640valid
120.0ms628×body320valid
56.0ms413×body160valid
16.0ms202×body80valid