Details

Time bar (total: 5.5s)

sample80.0ms

Algorithm
intervals
Results
32.0ms93×body2560valid
18.0ms77×body1280valid
8.0ms46×body640valid
7.0ms247×body80nan
2.0ms16×body320valid
1.0ms14×body160valid
0.0ms10×body80valid

simplify99.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1427
2777
31467
42427
54177
627897
750017

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

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))
0.7b
(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×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)))

series117.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(/ (- 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

prune157.0ms

Filtered
72 candidates to 55 candidates (76.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0)))
0.0b
(/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0)))
0.2b
(* 5.0 (* v v))
1.2b
(acos (/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
177×*-un-lft-identity
166×add-sqr-sqrt
89×add-cube-cbrt
38×difference-of-squares
25×distribute-lft-out
21×associate-/l*
19×sqrt-prod distribute-lft-out--
18×associate-/r/
16×add-exp-log add-cbrt-cube
10×associate-/r*
9×pow1 div-inv
8×flip3-+ flip-+
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×acos-asin associate-*r* *-commutative unswap-sqr
Counts
4 → 213
Calls
4 calls:
27.0ms
(/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0)))
11.0ms
(/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0)))
7.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0)))
83.0ms
(/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0)))
25.0ms
(* 5.0 (* v v))
12.0ms
(acos (/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0))))

simplify120.0ms

Algorithm
egg-herbie
Counts
225 → 225
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
08883496
143063286
250013278

prune489.0ms

Filtered
225 candidates to 139 candidates (61.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 acos-asin pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 83
Calls
4 calls:
0.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
7.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series46.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
17.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
17.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify111.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
01251002
1427888
22342844
35002813

prune148.0ms

Filtered
95 candidates to 49 candidates (51.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
9.0ms
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series767.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
129.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
347.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
134.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify86.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
01171278
14171112
226981044
350011031

prune173.0ms

Filtered
85 candidates to 56 candidates (65.9%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

regimes139.0ms

Accuracy

0% (0.4b remaining)

Error of 0.9b against oracle of 0.6b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01410
11410

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s2963×body2560valid
613.0ms2577×body1280valid
226.0ms7925×body80nan
202.0ms1178×body640valid
77.0ms614×body320valid
38.0ms442×body160valid
11.0ms226×body80valid