Details

Time bar (total: 4.6s)

sample83.0ms

Algorithm
intervals
Results
31.0ms88×body2560valid
21.0ms90×body1280valid
8.0ms277×body80nan
5.0ms32×body640valid
3.0ms22×body320valid
2.0ms18×body160valid
0.0ms6×body80valid

simplify102.0ms

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: 0.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b
(* 5.0 (* v v))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite22.0ms

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)))

series112.0ms

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

simplify40.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0336587
11261535
25002531

prune162.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* v v) 3)
0.1b
(* (* v v) (* v v))
0.1b
(* 5.0 (* v v))
0.4b
(acos (* (/ (- 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)))))

rewrite30.0ms

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×acos-asin cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod swap-sqr sqr-pow
Counts
4 → 116
Calls
4 calls:
3.0ms
(pow (* v v) 3)
12.0ms
(* (* v v) (* v v))
10.0ms
(* 5.0 (* v v))
1.0ms
(acos (* (/ (- 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)))))

series111.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(pow (* v v) 3)
36.0ms
(* (* v v) (* v v))
25.0ms
(* 5.0 (* v v))
9.0ms
(acos (* (/ (- 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)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0313432
11243366
25001366

prune237.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (* (/ (- 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)))))
0.9b
(sqrt (acos (* (/ (- 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))))))
0.9b
(sqrt (acos (* (/ (- 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))))))
1.0b
(* (sqrt (acos (* (/ (- 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)))))) (sqrt (acos (* (/ (- 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)))))))

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:
1.0ms
(acos (* (/ (- 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)))))
1.0ms
(sqrt (acos (* (/ (- 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))))))
1.0ms
(sqrt (acos (* (/ (- 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))))))
7.0ms
(* (sqrt (acos (* (/ (- 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)))))) (sqrt (acos (* (/ (- 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)))))))

series81.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(acos (* (/ (- 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)))))
28.0ms
(sqrt (acos (* (/ (- 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))))))
31.0ms
(sqrt (acos (* (/ (- 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))))))
13.0ms
(* (sqrt (acos (* (/ (- 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)))))) (sqrt (acos (* (/ (- 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)))))))

simplify157.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 3 (136.0ms)

IterNodesCost
01942262
17421994
236901884
350011809

prune246.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.9b
(sqrt (acos (* (/ (- 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))))))
1.0b
(* (sqrt (acos (* (/ (- 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)))))) (cbrt (pow (sqrt (acos (* (/ (- 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)))))) 3)))
1.0b
(cbrt (pow (sqrt (acos (* (/ (- 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)))))) 3))
1.0b
(pow (sqrt (acos (* (/ (- 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)))))) 3)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
48×cbrt-prod
35×sqrt-prod
23×add-cube-cbrt *-un-lft-identity
22×unpow-prod-down cube-prod
21×associate-*r*
14×unswap-sqr
9×pow1
7×add-exp-log
6×associate-*l* add-cbrt-cube
5×sqr-pow
4×add-log-exp
3×cube-mult pow-unpow pow-pow unpow3
2×sqrt-pow1 pow1/2
1×pow-to-exp rem-sqrt-square pow1/3 pow-prod-down pow-exp prod-exp *-commutative sqrt-pow2 rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 124
Calls
4 calls:
1.0ms
(sqrt (acos (* (/ (- 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))))))
15.0ms
(* (sqrt (acos (* (/ (- 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)))))) (cbrt (pow (sqrt (acos (* (/ (- 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)))))) 3)))
2.0ms
(cbrt (pow (sqrt (acos (* (/ (- 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)))))) 3))
2.0ms
(pow (sqrt (acos (* (/ (- 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)))))) 3)

series164.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(sqrt (acos (* (/ (- 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))))))
12.0ms
(* (sqrt (acos (* (/ (- 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)))))) (cbrt (pow (sqrt (acos (* (/ (- 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)))))) 3)))
28.0ms
(cbrt (pow (sqrt (acos (* (/ (- 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)))))) 3))
92.0ms
(pow (sqrt (acos (* (/ (- 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)))))) 3)

simplify76.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03014414
112923538
250013318

prune305.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes105.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02318
12318

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s2933×body2560valid
612.0ms2603×body1280valid
228.0ms8062×body80nan
207.0ms1219×body640valid
76.0ms623×body320valid
38.0ms421×body160valid
10.0ms201×body80valid