Details

Time bar (total: 4.7s)

sample80.0ms

Algorithm
intervals
Results
33.0ms96×body2560valid
19.0ms82×body1280valid
7.0ms265×body80nan
6.0ms35×body640valid
3.0ms24×body320valid
1.0ms12×body160valid
0.0ms7×body80valid

simplify100.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 0.5b

localize11.0ms

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))
0.5b
(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)))

series109.0ms

Counts
3 → 9
Calls
3 calls:
81.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify41.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0336587
11261535
25002531

prune158.0ms

Filtered
72 candidates to 55 candidates (76.4%)
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)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp difference-of-squares
4×associate-/r*
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 div-inv distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 79
Calls
4 calls:
9.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
10.0ms
(- (/ 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)))

series148.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
36.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
27.0ms
(* 5.0 (* v v))
3.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify47.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0409840
11459784
25001780

prune229.0ms

Filtered
91 candidates to 69 candidates (75.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* v v) 3)
0.1b
(* (* v v) (* v v))
0.2b
(* 5.0 (* v v))
0.6b
(asin (* (/ (- 1.0 (* 5.0 (* v v))) (- (pow (* v v) 3) (pow 1.0 3))) (+ (* (* v v) (* v v)) (+ (* 1.0 1.0) (* (* v v) 1.0)))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
128×pow1
37×pow-prod-up
27×pow-prod-down
24×add-exp-log add-cbrt-cube
23×pow-sqr
19×pow-plus
14×pow2
12×prod-exp cbrt-unprod
7×add-sqr-sqrt
6×add-cube-cbrt pow-pow *-un-lft-identity
4×associate-*l* add-log-exp
3×pow-unpow
2×associate-*r* pow-exp *-commutative rem-cube-cbrt unswap-sqr
1×cube-mult pow-to-exp unpow-prod-down asin-acos unpow3 cube-prod swap-sqr sqr-pow
Counts
4 → 116
Calls
4 calls:
2.0ms
(pow (* v v) 3)
12.0ms
(* (* v v) (* v v))
6.0ms
(* 5.0 (* v v))
1.0ms
(asin (* (/ (- 1.0 (* 5.0 (* v v))) (- (pow (* v v) 3) (pow 1.0 3))) (+ (* (* v v) (* v v)) (+ (* 1.0 1.0) (* (* v v) 1.0)))))

series108.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(pow (* v v) 3)
33.0ms
(* (* v v) (* v v))
24.0ms
(* 5.0 (* v v))
9.0ms
(asin (* (/ (- 1.0 (* 5.0 (* v v))) (- (pow (* v v) 3) (pow 1.0 3))) (+ (* (* v v) (* v v)) (+ (* 1.0 1.0) (* (* v v) 1.0)))))

simplify46.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0313444
11243366
25001366

prune241.0ms

Filtered
128 candidates to 54 candidates (42.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

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:
0.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms
(* (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
128.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
133.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
159.0ms
(* (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify85.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
01171278
14251112
227051044
350011031

prune194.0ms

Filtered
85 candidates to 56 candidates (65.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes79.0ms

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
02720
12720

end0.0ms

sample2.3s

Algorithm
intervals
Results
973.0ms2937×body2560valid
567.0ms2559×body1280valid
206.0ms7763×body80nan
198.0ms1239×body640valid
72.0ms629×body320valid
33.0ms419×body160valid
10.0ms217×body80valid