Details

Time bar (total: 5.1s)

sample46.0ms

Algorithm
intervals
Results
29.0ms412×body80valid

simplify111.0ms

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

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
147×add-exp-log add-cbrt-cube
98×prod-exp cbrt-unprod
69×pow1
49×pow-prod-down
39×associate-*l*
27×add-sqr-sqrt times-frac
26×add-cube-cbrt *-un-lft-identity
15×cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l/ sqrt-prod *-commutative div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 165
Calls
4 calls:
63.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
24.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
17.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series190.0ms

Counts
4 → 10
Calls
4 calls:
77.0ms
(* (/ 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)))
47.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify101.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
09572149
140491345
250011165

prune530.0ms

Filtered
175 candidates to 94 candidates (53.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1723175
Fresh000
Picked011
Done000
Total1724176

Merged error: 0.1b

Counts
176 → 4

localize25.0ms

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) (pow (fabs x) 6)) (fabs x))))
0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite68.0ms

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
23×associate-*l/
22×pow-prod-down
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:
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) (pow (fabs x) 6)) (fabs x))))
24.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
16.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series459.0ms

Counts
4 → 10
Calls
4 calls:
346.0ms
(* (/ 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) (pow (fabs x) 6)) (fabs x))))
60.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
52.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify64.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012253945
150023174

prune737.0ms

Filtered
173 candidates to 118 candidates (68.2%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1685173
Fresh202
Picked011
Done101
Total1716177

Merged error: 0b

Counts
177 → 6

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
0.1b
(* 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
13×add-exp-log
12×add-sqr-sqrt
10×associate-*r* add-cbrt-cube
8×pow1
7×add-cube-cbrt *-un-lft-identity
6×prod-exp
4×unpow-prod-down associate-*l* cbrt-unprod
3×expm1-log1p-u pow-prod-down fma-udef log1p-expm1-u add-log-exp 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
3 → 60
Calls
3 calls:
1.0ms
(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))
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))))))

series581.0ms

Counts
3 → 9
Calls
3 calls:
168.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
71.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
341.0ms
(* (* 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
69 → 69
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0280772
11309662
25001661

prune273.0ms

Filtered
69 candidates to 45 candidates (65.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New68169
Fresh134
Picked011
Done011
Total69675

Merged error: 0b

Counts
75 → 6

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)

rewrite6.0ms

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)
2.0ms
(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)

simplify47.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
087284
1261272
21174264
35002264

prune345.0ms

Filtered
56 candidates to 48 candidates (85.7%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New56056
Fresh033
Picked011
Done022
Total56662

Merged error: 0b

Counts
62 → 6

regimes99.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04133
14133

end0.0ms

sample1.2s

Algorithm
intervals
Results
988.0ms14056×body80valid

Profiling

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