Details

Time bar (total: 4.6s)

sample78.0ms

Algorithm
intervals
Results
30.0ms89×body2560valid
18.0ms82×body1280valid
8.0ms273×body80nan
7.0ms45×body640valid
3.0ms22×body320valid
1.0ms11×body160valid
0.0ms7×body80valid

simplify96.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1427
2777
31467
42427
54177
627897
750017

prune2.0ms

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)))

series113.0ms

Counts
3 → 9
Calls
3 calls:
80.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms
(* 5.0 (* v v))
7.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify40.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0336587
11261535
25002531

prune153.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow v 2) (pow v 4))
0.0b
(* 4.0 (+ (pow v 2) (pow v 4)))
0.7b
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-exp-log add-cube-cbrt add-cbrt-cube add-log-exp
4×associate-*r*
3×associate-*l*
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×+-commutative distribute-rgt-in acos-asin distribute-lft-in pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
3 → 43
Calls
3 calls:
8.0ms
(+ (pow v 2) (pow v 4))
32.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
0.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series164.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(+ (pow v 2) (pow v 4))
90.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify157.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0177315
1834276
24136273
35001273

prune112.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
0.0b
(exp (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))
0.0b
(* 4.0 (+ (pow v 2) (pow v 4)))
0.7b
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt
8×pow1
7×add-exp-log
6×log-prod add-cbrt-cube
4×exp-prod associate-*r* add-log-exp
3×associate-*l* exp-sum
2×associate-*r/ log-pow
1×distribute-rgt-in acos-asin distribute-lft-in flip3-+ rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ rem-exp-log distribute-lft-out unswap-sqr
Counts
4 → 58
Calls
4 calls:
1.0ms
(log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
2.0ms
(exp (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))
29.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
0.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series180.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
4.0ms
(exp (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))
89.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify149.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (143.0ms)

IterNodesCost
0193551
1815484
23988468
35002462

prune172.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
1.0b
(pow (cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))) 2)
1.0b
(cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0b
(cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down
5×pow1 add-exp-log
4×add-cbrt-cube add-log-exp
3×pow-unpow pow1/3
2×pow-pow
1×acos-asin pow-to-exp pow-exp unpow2 sqr-pow
Counts
4 → 52
Calls
4 calls:
0.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
2.0ms
(pow (cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))) 2)
0.0ms
(cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0ms
(cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
166.0ms
(pow (cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))) 2)
142.0ms
(cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
136.0ms
(cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))

simplify71.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0139614
1431542
21816529
35001526

prune174.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

regimes29.0ms

Accuracy

0% (0.0b remaining)

Error of 0.7b against oracle of 0.7b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0158
1158

end0.0ms

sample2.4s

Algorithm
intervals
Results
984.0ms2911×body2560valid
582.0ms2578×body1280valid
228.0ms8140×body80nan
205.0ms1259×body640valid
75.0ms624×body320valid
36.0ms422×body160valid
13.0ms206×body80valid