Details

Time bar (total: 6.9s)

sample27.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
7.0ms234×body80nan

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03210
19110
227510
367210
4130310
5173710
6180210
7180210

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.0b
(* (* 3.0 PI) (- 1.0 (* v v)))
0.1b
(* 6.0 (* v v))
1.0b
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log add-cbrt-cube
23×pow1
18×associate-*r/ prod-exp cbrt-unprod
14×add-sqr-sqrt
13×flip3-- flip--
12×add-cube-cbrt *-un-lft-identity sqrt-div pow-prod-down
11×associate-*r*
8×frac-times associate-/r/
6×prod-diff
5×distribute-rgt-in distribute-lft-in associate-*l*
4×cbrt-undiv expm1-log1p-u div-exp associate-*l/ log1p-expm1-u add-log-exp
3×times-frac sqrt-prod *-commutative associate-/l*
2×sub-neg
1×frac-2neg clear-num associate-/r* div-inv difference-of-squares unswap-sqr
Counts
4 → 123
Calls
4 calls:
32.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
10.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
6.0ms
(* 6.0 (* v v))
29.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series872.0ms

Counts
4 → 12
Calls
4 calls:
285.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
117.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
28.0ms
(* 6.0 (* v v))
443.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify110.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
09551468
146961282
250011281

prune316.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4.0 (fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI))))))))
1.0b
(* 3.0 (sqrt 2.0))
1.0b
(fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI)))))))
1.0b
(pow (sqrt 2.0) 3)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
10×sqrt-prod
9×add-exp-log times-frac add-cbrt-cube
8×pow1
6×unpow-prod-down cube-prod associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow pow-pow associate-*l* associate-/r* associate-/l*
2×unswap-sqr
1×cbrt-undiv cube-mult pow-to-exp frac-2neg sqrt-pow1 pow1/2 unpow3 div-exp pow-prod-down pow-exp prod-exp clear-num *-commutative sqrt-pow2 cbrt-unprod fma-udef div-inv rem-cube-cbrt sqr-pow
Counts
4 → 97
Calls
4 calls:
2.0ms
(/ 4.0 (fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI))))))))
4.0ms
(* 3.0 (sqrt 2.0))
0.0ms
(fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI)))))))
2.0ms
(pow (sqrt 2.0) 3)

series1.4s

Counts
4 → 8
Calls
4 calls:
974.0ms
(/ 4.0 (fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI))))))))
0.0ms
(* 3.0 (sqrt 2.0))
415.0ms
(fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI)))))))
0.0ms
(pow (sqrt 2.0) 3)

simplify89.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05482041
130531856
250011845

prune420.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 4.0 (* 3.0 PI)) (* (fma v v 1.0) (* (- 1.0 (* v v)) (sqrt (- 2.0 (* 6.0 (* v v)))))))
0.0b
(* (- 1.0 (* v v)) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.0b
(* (/ (/ 4.0 (* 3.0 PI)) (* (fma v v 1.0) (* (- 1.0 (* v v)) (sqrt (- 2.0 (* 6.0 (* v v))))))) (+ 1.0 (* v v)))
0.1b
(* 6.0 (* v v))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
94×add-exp-log add-cbrt-cube
38×prod-exp cbrt-unprod
30×cbrt-undiv div-exp
26×associate-*l*
24×add-sqr-sqrt associate-*r/
23×times-frac
18×flip3-- sqrt-div flip--
16×add-cube-cbrt *-un-lft-identity associate-/r/
14×frac-times
13×pow1
10×associate-*r*
7×associate-*l/ associate-/l*
5×pow-prod-down div-inv
4×expm1-log1p-u sqrt-prod log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×flip3-+ flip-+
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* associate-/l/ difference-of-squares
Counts
4 → 169
Calls
4 calls:
20.0ms
(/ (/ 4.0 (* 3.0 PI)) (* (fma v v 1.0) (* (- 1.0 (* v v)) (sqrt (- 2.0 (* 6.0 (* v v)))))))
14.0ms
(* (- 1.0 (* v v)) (sqrt (- 2.0 (* 6.0 (* v v)))))
85.0ms
(* (/ (/ 4.0 (* 3.0 PI)) (* (fma v v 1.0) (* (- 1.0 (* v v)) (sqrt (- 2.0 (* 6.0 (* v v))))))) (+ 1.0 (* v v)))
6.0ms
(* 6.0 (* v v))

series1.3s

Counts
4 → 12
Calls
4 calls:
415.0ms
(/ (/ 4.0 (* 3.0 PI)) (* (fma v v 1.0) (* (- 1.0 (* v v)) (sqrt (- 2.0 (* 6.0 (* v v)))))))
374.0ms
(* (- 1.0 (* v v)) (sqrt (- 2.0 (* 6.0 (* v v)))))
506.0ms
(* (/ (/ 4.0 (* 3.0 PI)) (* (fma v v 1.0) (* (- 1.0 (* v v)) (sqrt (- 2.0 (* 6.0 (* v v))))))) (+ 1.0 (* v v)))
25.0ms
(* 6.0 (* v v))

simplify56.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014142862
150012474

prune588.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 6.0 (* v v))
0.1b
(* 6.0 (* v v))
0.1b
(* 6.0 (* v v))
0.1b
(* 6.0 (* v v))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt associate-*l* pow-prod-down prod-exp cbrt-unprod
8×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u associate-*r* *-commutative log1p-expm1-u add-log-exp unswap-sqr
Counts
4 → 84
Calls
4 calls:
6.0ms
(* 6.0 (* v v))
6.0ms
(* 6.0 (* v v))
6.0ms
(* 6.0 (* v v))
6.0ms
(* 6.0 (* v v))

series107.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* 6.0 (* v v))
24.0ms
(* 6.0 (* v v))
24.0ms
(* 6.0 (* v v))
28.0ms
(* 6.0 (* v v))

simplify100.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
088324
1292264
2832264
32900264
45002264

prune337.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03426
13426

end0.0ms

sample723.0ms

Algorithm
intervals
Results
283.0ms8000×body80valid
264.0ms8044×body80nan