Details

Time bar (total: 6.5s)

sample52.0ms

Algorithm
intervals
Results
35.0ms470×body80valid

simplify115.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

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
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite671.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1
33×add-cube-cbrt *-un-lft-identity
22×pow-prod-down
15×associate-*l/
13×sqrt-prod
12×frac-add
9×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 → 163
Calls
4 calls:
321.0ms
(* (/ 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)))))
312.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
29.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series456.0ms

Counts
4 → 10
Calls
4 calls:
340.0ms
(* (/ 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)))))
67.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
49.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify67.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012244595
150013688

prune757.0ms

Filtered
173 candidates to 117 candidates (67.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))
0.0b
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
0.1b
(* 0.047619047619047616 (pow (fabs x) 7))
0.1b
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log
13×add-sqr-sqrt
11×add-cbrt-cube
10×associate-*r*
9×pow1
8×add-cube-cbrt *-un-lft-identity
6×prod-exp
4×expm1-log1p-u unpow-prod-down associate-*l* cbrt-unprod fma-udef log1p-expm1-u add-log-exp
3×pow-prod-down unswap-sqr
2×*-commutative sqr-pow
1×distribute-rgt-in pow-to-exp distribute-lft-in sqrt-div associate-*r/ associate-*l/ pow-exp
Counts
4 → 70
Calls
4 calls:
0.0ms
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))
0.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
5.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
18.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

series793.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))
169.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
75.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
334.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0283952
11318819
25001818

prune343.0ms

Filtered
82 candidates to 55 candidates (67.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))))))
0.1b
(* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))
7.6b
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))
7.6b
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
26×pow1
11×add-exp-log add-sqr-sqrt add-cbrt-cube
10×sqrt-pow1 pow1/2
9×add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×pow-prod-down sqrt-prod
5×associate-*l* pow-prod-up
4×expm1-log1p-u swap-sqr prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-sqr
2×*-commutative fma-udef
1×pow2 distribute-rgt-in distribute-lft-in pow-plus sqrt-unprod sqrt-div associate-*r/ associate-*l/ rem-square-sqrt unswap-sqr
Counts
4 → 87
Calls
4 calls:
22.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))))))
15.0ms
(* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))
2.0ms
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))
2.0ms
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))

series727.0ms

Counts
4 → 12
Calls
4 calls:
410.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))))))
112.0ms
(* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))
102.0ms
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))
103.0ms
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))

simplify58.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
02871079
11444830
25002810

prune579.0ms

Filtered
99 candidates to 60 candidates (60.6%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
1.0ms
(cbrt PI)

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)

simplify53.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0103332
1341320
21598312
35002312

prune370.0ms

Filtered
56 candidates to 48 candidates (85.7%)
Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes120.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02916
12916

end0.0ms

sample1.1s

Algorithm
intervals
Results
938.0ms13889×body80valid