Details

Time bar (total: 6.1s)

sample46.0ms

Algorithm
intervals
Results
30.0ms433×body80valid

simplify110.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
107×add-exp-log add-cbrt-cube
70×prod-exp cbrt-unprod
51×pow1
48×associate-*l*
42×add-sqr-sqrt
38×times-frac
35×pow-prod-down
33×add-cube-cbrt *-un-lft-identity
15×associate-*l/
13×sqrt-prod
12×frac-add
11×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 173
Calls
4 calls:
19.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
58.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series468.0ms

Counts
4 → 10
Calls
4 calls:
339.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
50.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
79.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify68.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013665031
150013866

prune745.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (fma (* (* (* (pow (fabs x) 3) (fabs x)) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (fabs x) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))))
0.1b
(* (pow (fabs x) 3) (* (fabs x) (fabs x)))
0.2b
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0b
(sqrt PI)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
46×associate-*l*
35×add-exp-log
33×times-frac
32×add-cube-cbrt *-un-lft-identity
19×add-cbrt-cube
17×associate-*r* prod-exp
15×unswap-sqr
13×sqrt-prod
12×pow1
9×unpow-prod-down cube-prod
7×cbrt-unprod
5×pow-prod-up sqr-pow
4×expm1-log1p-u pow-to-exp div-exp pow-exp log1p-expm1-u add-log-exp
3×*-commutative
2×cbrt-undiv cube-mult unpow3 fma-udef div-inv
1×pow2 distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-prod-down associate-*l/ pow-sqr
Counts
4 → 152
Calls
4 calls:
8.0ms
(* (/ 1.0 (sqrt PI)) (fma (* (* (* (pow (fabs x) 3) (fabs x)) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (fabs x) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))))
7.0ms
(* (pow (fabs x) 3) (* (fabs x) (fabs x)))
13.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
2.0ms
(sqrt PI)

series428.0ms

Counts
4 → 10
Calls
4 calls:
335.0ms
(* (/ 1.0 (sqrt PI)) (fma (* (* (* (pow (fabs x) 3) (fabs x)) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (fabs x) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))))
47.0ms
(* (pow (fabs x) 3) (* (fabs x) (fabs x)))
46.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms
(sqrt PI)

simplify102.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
06062325
128541916
250021872

prune730.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 21.0) (fabs x))
1.0b
(sqrt PI)
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
13×associate-*l*
10×times-frac
9×pow1 add-exp-log sqrt-prod add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 79
Calls
4 calls:
6.0ms
(* (/ 1.0 21.0) (fabs x))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series23.0ms

Counts
4 → 6
Calls
4 calls:
23.0ms
(* (/ 1.0 21.0) (fabs x))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify90.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0233347
1796332
23557328
35002328

prune470.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt PI))) (/ (* (fma (pow (fabs x) 6) (* (/ 1.0 21.0) (fabs x)) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))) (cbrt 1.0)) (sqrt (sqrt PI))))
0.3b
(* (/ 1.0 21.0) (fabs x))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
37×add-sqr-sqrt
36×add-cbrt-cube
31×times-frac
27×sqrt-prod
26×associate-*l*
22×add-cube-cbrt *-un-lft-identity
17×prod-exp cbrt-unprod
16×associate-*r*
13×cbrt-undiv div-exp
10×pow1
6×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative
1×frac-times associate-*r/
Counts
4 → 126
Calls
4 calls:
17.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt PI))) (/ (* (fma (pow (fabs x) 6) (* (/ 1.0 21.0) (fabs x)) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))) (cbrt 1.0)) (sqrt (sqrt PI))))
6.0ms
(* (/ 1.0 21.0) (fabs x))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series582.0ms

Counts
4 → 8
Calls
4 calls:
559.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt PI))) (/ (* (fma (pow (fabs x) 6) (* (/ 1.0 21.0) (fabs x)) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))) (cbrt 1.0)) (sqrt (sqrt PI))))
23.0ms
(* (/ 1.0 21.0) (fabs x))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify83.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06193013
129242424
250012222

prune643.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes66.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04128
14128

end0.0ms

sample1.1s

Algorithm
intervals
Results
971.0ms13823×body80valid