Details

Time bar (total: 6.8s)

sample44.0ms

Algorithm
intervals
Results
28.0ms437×body80valid

simplify110.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
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)))
1.0b
(sqrt PI)

rewrite63.0ms

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:
23.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
20.0ms
(* (/ 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)))))
12.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series438.0ms

Counts
4 → 10
Calls
4 calls:
57.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
331.0ms
(* (/ 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)))))
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 (29.0ms)

IterNodesCost
012244595
150013688

prune689.0ms

Filtered
173 candidates to 117 candidates (67.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1685173
Fresh000
Picked101
Done000
Total1695174

Merged error: 0b

Counts
174 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
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)))))
0.1b
(* 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))))))

rewrite16.0ms

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:
1.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
1.0ms
(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)))))
5.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
8.0ms
(* (* 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))))))

series772.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
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)))))
68.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
331.0ms
(* (* 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))))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0283952
11318819
25001818

prune306.0ms

Filtered
82 candidates to 55 candidates (67.1%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New81182
Fresh224
Picked011
Done000
Total83487

Merged error: 0b

Counts
87 → 4

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

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:
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(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)

simplify51.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
099312
1323300
21495292
35001292

prune331.0ms

Filtered
56 candidates to 48 candidates (85.7%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New56056
Fresh022
Picked011
Done011
Total56460

Merged error: 0b

Counts
60 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.5b
(* (sqrt (* (/ 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)))))) (sqrt (* (/ 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)))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
378×associate-*l/
364×sqrt-div
337×frac-times
336×frac-add
181×associate-*r/
168×flip3-+ flip-+
64×pow1
30×sqrt-pow1
27×add-exp-log add-cbrt-cube
26×pow-prod-down
21×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity associate-*l*
13×prod-exp cbrt-unprod
12×pow1/2
10×sqrt-prod pow-prod-up
9×times-frac
6×pow-sqr
5×associate-*r*
4×expm1-log1p-u swap-sqr log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×rem-sqrt-square *-commutative
1×pow2 pow-plus sqrt-unprod rem-square-sqrt div-inv unswap-sqr
Counts
4 → 316
Calls
4 calls:
12.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
48.0ms
(* (sqrt (* (/ 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)))))) (sqrt (* (/ 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)))))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series418.0ms

Counts
4 → 8
Calls
4 calls:
44.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
375.0ms
(* (sqrt (* (/ 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)))))) (sqrt (* (/ 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)))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify454.0ms

Algorithm
egg-herbie
Counts
324 → 324
Iterations

Useful iterations: 2 (122.0ms)

IterNodesCost
0117748269
1465647246
2500147191

prune1.6s

Filtered
324 candidates to 180 candidates (55.6%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New3240324
Fresh011
Picked011
Done022
Total3244328

Merged error: 0b

Counts
328 → 4

regimes140.0ms

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
910.0ms13908×body80valid