Details

Time bar (total: 7.5s)

sample55.0ms

Algorithm
intervals
Results
38.0ms466×body80valid

simplify112.0ms

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

localize25.0ms

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 (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)

rewrite103.0ms

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:
54.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
24.0ms
(* (/ 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)))
2.0ms
(sqrt PI)

series451.0ms

Counts
4 → 10
Calls
4 calls:
75.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (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)))))
45.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify64.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013665031
150013864

prune688.0ms

Filtered
183 candidates to 117 candidates (63.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1794183
Fresh000
Picked101
Done000
Total1804184

Merged error: 0b

Counts
184 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (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 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
54×associate-*l/
37×add-sqr-sqrt
36×associate-*l* frac-add
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
22×frac-times associate-*r/
17×prod-exp cbrt-unprod
14×flip3-+ flip-+
13×sqrt-prod
10×pow-prod-down
7×associate-*r*
6×pow-plus pow-prod-up
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow3
Counts
4 → 159
Calls
4 calls:
6.0ms
(* (* (fabs x) (fabs x)) (fabs x))
18.0ms
(* (/ 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 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series553.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(* (* (fabs x) (fabs x)) (fabs x))
471.0ms
(* (/ 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 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
50.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify69.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012725377
150014609

prune819.0ms

Filtered
169 candidates to 120 candidates (71.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1690169
Fresh033
Picked011
Done000
Total1694173

Merged error: 0b

Counts
173 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (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) (pow (fabs x) 6)) (fabs x))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×associate-*l*
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
22×associate-*l/
17×prod-exp cbrt-unprod
13×sqrt-prod
12×frac-add
10×pow-prod-down
7×associate-*r*
6×frac-times flip3-+ pow-plus associate-*r/ pow-prod-up flip-+
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow3
Counts
4 → 143
Calls
4 calls:
6.0ms
(* (* (fabs x) (fabs x)) (fabs x))
17.0ms
(* (/ 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))))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series409.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(* (* (fabs x) (fabs x)) (fabs x))
327.0ms
(* (/ 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))))
50.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify52.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010063435
150012727

prune615.0ms

Filtered
153 candidates to 103 candidates (67.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1521153
Fresh112
Picked101
Done011
Total1543157

Merged error: 0b

Counts
157 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1.0 (sqrt PI))) (fma (sqrt (/ 1.0 (sqrt PI))) (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)))) (* (sqrt (/ 1.0 (sqrt PI))) (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x)))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
44×sqrt-prod
35×add-sqr-sqrt
25×associate-*l*
22×add-cube-cbrt *-un-lft-identity
20×times-frac
9×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r*
2×fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 93
Calls
4 calls:
9.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (fma (sqrt (/ 1.0 (sqrt PI))) (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)))) (* (sqrt (/ 1.0 (sqrt PI))) (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x)))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series1.5s

Counts
4 → 6
Calls
4 calls:
1.5s
(* (sqrt (/ 1.0 (sqrt PI))) (fma (sqrt (/ 1.0 (sqrt PI))) (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)))) (* (sqrt (/ 1.0 (sqrt PI))) (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x)))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify53.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02752134
19831984
250011771

prune482.0ms

Filtered
99 candidates to 75 candidates (75.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New99099
Fresh011
Picked011
Done011
Total993102

Merged error: 0b

Counts
102 → 3

regimes53.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04837
14837

end0.0ms

sample1.2s

Algorithm
intervals
Results
1.0s13842×body80valid