Details

Time bar (total: 6.8s)

sample51.0ms

Algorithm
intervals
Results
31.0ms452×body80valid

simplify117.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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) (* (* (* (* (* (* (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)

rewrite1.2s

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
17×prod-exp cbrt-unprod
14×associate-*l/
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:
18.0ms
(* (* (fabs x) (fabs x)) (fabs x))
1.2s
(* (/ 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)))))
61.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series366.0ms

Counts
4 → 10
Calls
4 calls:
24.0ms
(* (* (fabs x) (fabs x)) (fabs x))
299.0ms
(* (/ 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)))))
43.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify61.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010064086
150013203

prune624.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

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)

simplify50.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
092312
1290300
21422292
35002292

prune360.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
1.0ms
(sqrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)

series0.0ms

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

simplify131.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 8 (128.0ms)

IterNodesCost
033155
137146
244140
365140
4111140
5223140
6872140
72973139
85001136

prune386.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

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
8×sqrt-div
6×add-exp-log add-cbrt-cube
5×associate-*l/
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp unswap-sqr
3×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/
2×flip3-+ frac-add flip-+
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod div-inv distribute-lft-out
Counts
4 → 100
Calls
4 calls:
76.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (+ (* (sqrt (/ 1.0 (sqrt PI))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* (sqrt (/ 1.0 (sqrt PI))) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series1.2s

Counts
4 → 6
Calls
4 calls:
1.2s
(* (sqrt (/ 1.0 (sqrt PI))) (+ (* (sqrt (/ 1.0 (sqrt PI))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* (sqrt (/ 1.0 (sqrt PI))) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify83.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05062845
121582619
250022548

prune556.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes199.0ms

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
04142
14142

end0.0ms

sample1.2s

Algorithm
intervals
Results
943.0ms13988×body80valid