Details

Time bar (total: 6.9s)

sample116.0ms

Algorithm
intervals
Results
40.0ms85×body2560valid
28.0ms84×body1280valid
18.0ms243×body80nan
11.0ms45×body640valid
5.0ms25×body320valid
1.0ms10×body160valid
1.0ms7×body80valid

simplify97.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0207
1437
2847
31557
42627
54547
628787
750017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

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))
0.6b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite18.0ms

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×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u 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 → 69
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)))

series116.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
26.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify46.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0349623
11288567
25001565

prune180.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

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))))
0.2b
(* 5.0 (* v v))
0.6b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
57×*-un-lft-identity
55×add-cube-cbrt
49×times-frac
39×prod-diff
13×fma-neg
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp difference-of-squares
5×div-inv
4×expm1-log1p-u associate-/r* log1p-expm1-u
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 distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 139
Calls
4 calls:
10.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
17.0ms
(- (/ 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)))

series154.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
37.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
26.0ms
(* 5.0 (* v v))
3.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify67.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05762948
119411851
250031839

prune321.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.2b
(* 5.0 (* v v))
0.2b
(* 5.0 (* v v))
0.6b
(asin (/ (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (/ (- (* v v) 1.0) (cbrt (- 1.0 (* 5.0 (* v v)))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×associate-*l* pow-prod-down prod-exp cbrt-unprod
7×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* *-commutative unswap-sqr
1×asin-acos
Counts
4 → 73
Calls
4 calls:
6.0ms
(* 5.0 (* v v))
6.0ms
(* 5.0 (* v v))
6.0ms
(* 5.0 (* v v))
0.0ms
(asin (/ (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (/ (- (* v v) 1.0) (cbrt (- 1.0 (* 5.0 (* v v)))))))

series85.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 5.0 (* v v))
25.0ms
(* 5.0 (* v v))
31.0ms
(* 5.0 (* v v))
4.0ms
(asin (/ (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (/ (- (* v v) 1.0) (cbrt (- 1.0 (* 5.0 (* v v)))))))

simplify115.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0131511
1376429
21002429
33365429
45001429

prune240.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize14.0ms

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)))))

rewrite79.0ms

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:
56.0ms
(* (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))))))
6.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
6.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
6.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
266.0ms
(* (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))))))
216.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
216.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
410.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify109.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 3 (81.0ms)

IterNodesCost
02242796
16842647
229682458
350022437

prune321.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

regimes133.0ms

Accuracy

0% (0.1b 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
01720
11720

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s3022×body2560valid
855.0ms2511×body1280valid
453.0ms8041×body80nan
321.0ms1234×body640valid
123.0ms642×body320valid
53.0ms399×body160valid
15.0ms192×body80valid