Details

Time bar (total: 4.8s)

sample85.0ms

Algorithm
intervals
Results
39.0ms117×body2560valid
17.0ms75×body1280valid
8.0ms259×body80nan
4.0ms27×body640valid
2.0ms20×body320valid
1.0ms13×body160valid
0.0ms4×body80valid

simplify95.0ms

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: 0.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1.0 (* 5.0 (* v v)))
0.2b
(* 5.0 (* v v))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-exp-log add-cbrt-cube
5×add-sqr-sqrt add-log-exp
4×add-cube-cbrt *-un-lft-identity
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
1×acos-asin sub-neg flip3-- diff-log associate-*r* *-commutative flip-- unswap-sqr
Counts
3 → 39
Calls
3 calls:
6.0ms
(- 1.0 (* 5.0 (* v v)))
16.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series92.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(- 1.0 (* 5.0 (* v v)))
29.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify54.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0167261
1516228
21812228
35002228

prune101.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

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))
0.4b
(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))

rewrite57.0ms

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×add-log-exp
3×associate-*r* *-commutative unswap-sqr
1×acos-asin
Counts
4 → 65
Calls
4 calls:
16.0ms
(* 5.0 (* v v))
16.0ms
(* 5.0 (* v v))
20.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))

series86.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 5.0 (* v v))
24.0ms
(* 5.0 (* v v))
29.0ms
(* 5.0 (* v v))
9.0ms
(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))

simplify72.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0174461
1607394
22607394
35001394

prune199.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))
1.0b
(sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0))))
1.0b
(sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0))))
1.0b
(* (sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))) (sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))))

rewrite20.0ms

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:
3.0ms
(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))
1.0ms
(sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0))))
1.0ms
(sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0))))
13.0ms
(* (sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))) (sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))))

series84.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))
29.0ms
(sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0))))
29.0ms
(sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0))))
17.0ms
(* (sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))) (sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))))

simplify165.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 3 (140.0ms)

IterNodesCost
01832274
17352006
239691896
350021821

prune253.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))
1.0b
(sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0))))
1.0b
(sqrt (acos (/ (- 1.0 (* 125.0 (pow v 6))) (* (+ (* 5.0 (pow v 2)) (+ (* 25.0 (pow v 4)) 1.0)) (- (pow v 2) 1.0)))))
1.0b
(* (sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 125.0 (pow v 6))) (* (+ (* 5.0 (pow v 2)) (+ (* 25.0 (pow v 4)) 1.0)) (- (pow v 2) 1.0))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×sqrt-prod
10×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
4×sqrt-pow1 pow1/2 add-log-exp unswap-sqr
3×pow-prod-down
2×rem-sqrt-square
1×acos-asin sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 64
Calls
4 calls:
3.0ms
(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))
1.0ms
(sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0))))
1.0ms
(sqrt (acos (/ (- 1.0 (* 125.0 (pow v 6))) (* (+ (* 5.0 (pow v 2)) (+ (* 25.0 (pow v 4)) 1.0)) (- (pow v 2) 1.0)))))
13.0ms
(* (sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 125.0 (pow v 6))) (* (+ (* 5.0 (pow v 2)) (+ (* 25.0 (pow v 4)) 1.0)) (- (pow v 2) 1.0))))))

series82.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))
28.0ms
(sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0))))
34.0ms
(sqrt (acos (/ (- 1.0 (* 125.0 (pow v 6))) (* (+ (* 5.0 (pow v 2)) (+ (* 25.0 (pow v 4)) 1.0)) (- (pow v 2) 1.0)))))
11.0ms
(* (sqrt (acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 125.0 (pow v 6))) (* (+ (* 5.0 (pow v 2)) (+ (* 25.0 (pow v 4)) 1.0)) (- (pow v 2) 1.0))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
01832157
16662022
227762018
350022018

prune595.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

regimes97.0ms

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
02714
12714

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s2980×body2560valid
591.0ms2581×body1280valid
228.0ms7853×body80nan
193.0ms1176×body640valid
80.0ms643×body320valid
33.0ms397×body160valid
11.0ms223×body80valid