Details

Time bar (total: 15.2s)

sample51.0ms

Algorithm
intervals
Results
33.0ms452×body80valid

simplify106.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06942
123142
290042
3375342
4500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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)

rewrite1.3s

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 div-exp 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 → 135
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)))))
60.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series367.0ms

Counts
4 → 10
Calls
4 calls:
24.0ms
(* (* (fabs x) (fabs x)) (fabs x))
298.0ms
(* (/ 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)))))
44.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify57.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09774021
150013349

prune557.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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)))))
0.3b
(* (sqrt (/ 1.0 (sqrt PI))) (* (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)

rewrite4.2s

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×associate-*l*
47×add-sqr-sqrt
40×associate-*l/
38×times-frac
36×frac-add
35×add-cube-cbrt *-un-lft-identity sqrt-div
31×frac-times associate-*r/
18×flip3-+ flip-+
13×pow1
11×add-exp-log add-cbrt-cube
5×distribute-rgt-in distribute-lft-in
4×associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp unswap-sqr
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
Counts
4 → 155
Calls
4 calls:
1.2s
(* (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)))))
3.0s
(* (sqrt (/ 1.0 (sqrt PI))) (* (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))))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series812.0ms

Counts
4 → 8
Calls
4 calls:
478.0ms
(* (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)))))
333.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (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)

simplify84.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09348633
150017497

prune973.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (sqrt (/ 1.0 (sqrt PI))) (sqrt (/ 1.0 (sqrt PI)))) (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))))
0.1b
(/ (* 2.0 (pow (fabs x) 3)) 3.0)
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite3.9s

Algorithm
rewrite-expression-head
Rules
37×associate-*r/
28×sqrt-div
25×frac-times
24×frac-add
19×add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt flip3-+ flip-+
11×pow1
10×associate-*l/
9×add-cube-cbrt *-un-lft-identity
6×prod-exp sqrt-prod
4×div-exp cbrt-unprod add-log-exp
3×times-frac associate-*r* pow-prod-down associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2
1×distribute-rgt-in pow-to-exp frac-2neg distribute-lft-in associate-*l* pow-exp clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 97
Calls
4 calls:
3.9s
(* (* (sqrt (/ 1.0 (sqrt PI))) (sqrt (/ 1.0 (sqrt PI)))) (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))))
15.0ms
(/ (* 2.0 (pow (fabs x) 3)) 3.0)
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series385.0ms

Counts
4 → 8
Calls
4 calls:
344.0ms
(* (* (sqrt (/ 1.0 (sqrt PI))) (sqrt (/ 1.0 (sqrt PI)))) (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))))
40.0ms
(/ (* 2.0 (pow (fabs x) 3)) 3.0)
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify150.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09003755
148953456
250013456

prune493.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log rem-sqrt-square sqrt-pow1 pow1/2 add-cbrt-cube add-log-exp
Counts
4 → 52
Calls
4 calls:
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series0.0ms

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

simplify70.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0100304
1370304
22074304
35001304

prune322.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes104.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04439
14639
24639

end0.0ms

sample1.2s

Algorithm
intervals
Results
956.0ms13988×body80valid