Details

Time bar (total: 6.4s)

sample81.0ms

Algorithm
intervals
Results
35.0ms93×body2560valid
17.0ms77×body1280valid
7.0ms46×body640valid
7.0ms247×body80nan
2.0ms16×body320valid
1.0ms14×body160valid
0.0ms10×body80valid

simplify101.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0207
1437
2847
31557
42627
54547
628787
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)))

rewrite20.0ms

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:
11.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series111.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
28.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0349623
11288567
25001565

prune175.0ms

Filtered
78 candidates to 61 candidates (78.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.0b
(/ (* 5.0 (* v v)) (- (* v v) 1.0))
0.2b
(* 5.0 (* v v))
0.7b
(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
435×add-sqr-sqrt
389×times-frac
300×prod-diff
267×*-un-lft-identity
199×add-cube-cbrt
166×difference-of-squares
84×associate-/r/
43×flip3-- flip--
42×div-inv
34×distribute-lft-out--
33×unpow-prod-down unpow2 sqr-pow
30×fma-neg
18×add-exp-log add-cbrt-cube
9×pow1
6×prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×cbrt-undiv div-exp associate-*l* pow-prod-down
1×acos-asin sub-neg frac-2neg diff-log associate-*r* clear-num *-commutative frac-sub associate-/l* unswap-sqr
Counts
4 → 408
Calls
4 calls:
106.0ms
(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
12.0ms
(/ (* 5.0 (* v v)) (- (* v v) 1.0))
6.0ms
(* 5.0 (* v v))
39.0ms
(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series221.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
71.0ms
(/ (* 5.0 (* v v)) (- (* v v) 1.0))
31.0ms
(* 5.0 (* v v))
5.0ms
(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify189.0ms

Algorithm
egg-herbie
Counts
420 → 420
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
0124813858
139859584
250019584

prune871.0ms

Filtered
420 candidates to 201 candidates (47.9%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (- (* v v) 1.0))
0.1b
(pow (pow v 2) 3)
0.2b
(* (/ (* v v) (cbrt (- (* v v) 1.0))) (/ 5.0 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))))
0.7b
(acos (+ (- (/ (* 1.0 (fma 1.0 (fma v v 1.0) (pow v 4))) (- (pow (pow v 2) 3) (pow 1.0 3))) (* (/ (* v v) (cbrt (- (* v v) 1.0))) (/ 5.0 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))))) (* (/ 5.0 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (+ (- (/ (* v v) (cbrt (- (* v v) 1.0)))) (/ (* v v) (cbrt (- (* v v) 1.0)))))))

rewrite366.0ms

Algorithm
rewrite-expression-head
Rules
42×add-exp-log
29×add-sqr-sqrt add-cbrt-cube
17×times-frac
16×cbrt-div
15×add-cube-cbrt *-un-lft-identity associate-*r* prod-exp cbrt-unprod
14×unpow-prod-down
13×associate-*l*
12×cbrt-undiv div-exp
10×cbrt-prod associate-/r/
8×flip3-- cube-prod flip--
6×pow1 unswap-sqr
5×frac-times
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×pow-unpow associate-*r/ associate-*l/ sqr-pow
2×pow-to-exp div-inv unpow2 difference-of-squares
1×acos-asin cube-mult pow-pow pow1/3 unpow3 pow-prod-down *-commutative rem-cube-cbrt
Counts
4 → 129
Calls
4 calls:
3.0ms
(cbrt (- (* v v) 1.0))
3.0ms
(pow (pow v 2) 3)
63.0ms
(* (/ (* v v) (cbrt (- (* v v) 1.0))) (/ 5.0 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))))
293.0ms
(acos (+ (- (/ (* 1.0 (fma 1.0 (fma v v 1.0) (pow v 4))) (- (pow (pow v 2) 3) (pow 1.0 3))) (* (/ (* v v) (cbrt (- (* v v) 1.0))) (/ 5.0 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))))) (* (/ 5.0 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (+ (- (/ (* v v) (cbrt (- (* v v) 1.0)))) (/ (* v v) (cbrt (- (* v v) 1.0)))))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(cbrt (- (* v v) 1.0))
41.0ms
(pow (pow v 2) 3)
73.0ms
(* (/ (* v v) (cbrt (- (* v v) 1.0))) (/ 5.0 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))))
14.0ms
(acos (+ (- (/ (* 1.0 (fma 1.0 (fma v v 1.0) (pow v 4))) (- (pow (pow v 2) 3) (pow 1.0 3))) (* (/ (* v v) (cbrt (- (* v v) 1.0))) (/ 5.0 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))))) (* (/ 5.0 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (+ (- (/ (* v v) (cbrt (- (* v v) 1.0)))) (/ (* v v) (cbrt (- (* v v) 1.0)))))))

simplify123.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
08212109
140741774
250021714

prune662.0ms

Filtered
141 candidates to 95 candidates (67.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))
1.0b
(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
1.0b
(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
1.0b
(* (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))) (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))

rewrite50.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 91
Calls
4 calls:
39.0ms
(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))
1.0ms
(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
1.0ms
(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
7.0ms
(* (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))) (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))

series58.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))
26.0ms
(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
21.0ms
(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
6.0ms
(* (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))) (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))

simplify124.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
01371466
14841298
227111236
350011193

prune198.0ms

Filtered
103 candidates to 57 candidates (55.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

regimes29.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03547
13847
23847

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s2963×body2560valid
596.0ms2577×body1280valid
222.0ms7925×body80nan
193.0ms1178×body640valid
75.0ms614×body320valid
39.0ms442×body160valid
11.0ms226×body80valid