Details

Time bar (total: 4.5s)

sample81.0ms

Algorithm
intervals
Results
33.0ms95×body2560valid
20.0ms87×body1280valid
7.0ms45×body640valid
7.0ms242×body80nan
2.0ms14×body320valid
1.0ms7×body160valid
0.0ms8×body80valid

simplify101.0ms

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)))

rewrite16.0ms

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:
8.0ms
(/ (- 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)))

series116.0ms

Counts
3 → 9
Calls
3 calls:
83.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify41.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0349623
11288567
25001565

prune183.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

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)))

rewrite29.0ms

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:
8.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
9.0ms
(- (/ 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)))

series147.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
35.0ms
(- (/ 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)))

simplify68.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05762948
119411851
250031839

prune322.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (/ PI 2) (asin (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
0.7b
(asin (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
45×*-un-lft-identity
43×add-cube-cbrt
39×prod-diff
37×times-frac
13×fma-neg
4×div-inv add-log-exp
2×pow1 add-exp-log expm1-log1p-u asin-acos add-cbrt-cube log1p-expm1-u difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- associate--r-
Counts
2 → 80
Calls
2 calls:
9.0ms
(- (/ PI 2) (asin (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
1.0ms
(asin (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series44.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(- (/ PI 2) (asin (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
7.0ms
(asin (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify160.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (144.0ms)

IterNodesCost
02621948
17051130
237131107
350011078

prune185.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

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 (sqrt 1.0))) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0)))))

rewrite23.0ms

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))
9.0ms
(* 5.0 (* v v))
5.0ms
(* 5.0 (* v v))
1.0ms
(asin (* (/ (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (+ v (sqrt 1.0))) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0)))))

series88.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* 5.0 (* v v))
23.0ms
(* 5.0 (* v v))
24.0ms
(* 5.0 (* v v))
12.0ms
(asin (* (/ (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (+ v (sqrt 1.0))) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0153560
1505472
21506472
35001472

prune244.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

regimes104.0ms

Accuracy

0% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02525
12525

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s2999×body2560valid
575.0ms2518×body1280valid
226.0ms7917×body80nan
201.0ms1219×body640valid
75.0ms632×body320valid
37.0ms415×body160valid
11.0ms217×body80valid