Details

Time bar (total: 6.8s)

sample45.0ms

Algorithm
intervals
Results
29.0ms433×body80valid

simplify109.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06942
123142
290042
3375342
4500142

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

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

rewrite104.0ms

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×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 → 165
Calls
4 calls:
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)))
62.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series459.0ms

Counts
4 → 10
Calls
4 calls:
335.0ms
(* (/ 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)))
79.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify70.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013384946
150014032

prune694.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sqrt 1.0) 21.0) (pow (fabs x) 6))
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)))) (* (/ (sqrt 1.0) 1) (* (* (/ (sqrt 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)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
57×associate-*l*
55×associate-*l/
53×times-frac
43×add-exp-log
41×add-cube-cbrt *-un-lft-identity
36×frac-add
35×add-cbrt-cube
25×sqrt-prod
22×frac-times associate-*r/
20×prod-exp
16×pow1 cbrt-unprod
14×flip3-+ flip-+
12×unswap-sqr
11×associate-*r*
7×div-exp pow-prod-down
6×unpow-prod-down
5×cbrt-undiv
4×add-log-exp sqr-pow
3×*-commutative div-inv
2×pow-to-exp pow-exp
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 178
Calls
4 calls:
10.0ms
(* (/ (sqrt 1.0) 21.0) (pow (fabs x) 6))
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)))) (* (/ (sqrt 1.0) 1) (* (* (/ (sqrt 1.0) 21.0) (pow (fabs x) 6)) (fabs x)))))
15.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series597.0ms

Counts
4 → 10
Calls
4 calls:
103.0ms
(* (/ (sqrt 1.0) 21.0) (pow (fabs x) 6))
443.0ms
(* (/ 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)))) (* (/ (sqrt 1.0) 1) (* (* (/ (sqrt 1.0) 21.0) (pow (fabs x) 6)) (fabs x)))))
51.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify73.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
014265622
150014916

prune991.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.2 (pow (fabs x) 5))
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.1b
(* (sqrt (/ 1 PI)) (+ (+ (+ (* (* 0.047619047619047616 (pow (fabs x) 7)) 1.0) (* 2.0 (fabs x))) (* 0.2 (pow (fabs x) 5))) (* 0.6666666666666666 (pow (fabs x) 3))))
0.3b
(* 0.047619047619047616 (pow (fabs x) 7))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
29×associate-*r*
25×associate-*l*
24×*-un-lft-identity
23×add-cube-cbrt
21×add-exp-log
16×sqrt-prod
14×unswap-sqr
12×unpow-prod-down add-cbrt-cube
11×times-frac
10×prod-exp
6×pow1 sqr-pow
4×cube-prod *-commutative cbrt-unprod add-log-exp
3×pow-to-exp sqrt-div pow-exp
2×frac-times flip3-+ associate-*r/ flip-+
1×distribute-rgt-in cube-mult distribute-lft-in unpow3 pow-prod-down associate-*l/ div-inv
Counts
4 → 122
Calls
4 calls:
5.0ms
(* 0.2 (pow (fabs x) 5))
6.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
16.0ms
(* (sqrt (/ 1 PI)) (+ (+ (+ (* (* 0.047619047619047616 (pow (fabs x) 7)) 1.0) (* 2.0 (fabs x))) (* 0.2 (pow (fabs x) 5))) (* 0.6666666666666666 (pow (fabs x) 3))))
6.0ms
(* 0.047619047619047616 (pow (fabs x) 7))

series466.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* 0.2 (pow (fabs x) 5))
48.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
286.0ms
(* (sqrt (/ 1 PI)) (+ (+ (+ (* (* 0.047619047619047616 (pow (fabs x) 7)) 1.0) (* 2.0 (fabs x))) (* 0.2 (pow (fabs x) 5))) (* 0.6666666666666666 (pow (fabs x) 3))))
75.0ms
(* 0.047619047619047616 (pow (fabs x) 7))

simplify84.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06081492
128591382
250021378

prune545.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (/ 1 PI)) (+ (+ (* (* 0.047619047619047616 (pow (fabs x) 7)) 1.0) (* 2.0 (fabs x))) (* 0.2 (pow (fabs x) 5))))
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.1b
(* (sqrt (/ 1 PI)) (* 0.6666666666666666 (pow (fabs x) 3)))
0.3b
(* 0.047619047619047616 (pow (fabs x) 7))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
38×associate-*l*
29×*-un-lft-identity sqrt-prod
28×add-cube-cbrt
26×add-exp-log
23×associate-*r*
20×times-frac
15×add-cbrt-cube
14×prod-exp
11×unswap-sqr
8×pow1 unpow-prod-down
6×cbrt-unprod
4×sqrt-div cube-prod *-commutative add-log-exp sqr-pow
3×pow-to-exp pow-exp
2×frac-times flip3-+ associate-*r/ pow-prod-down associate-*l/ flip-+ div-inv
1×distribute-rgt-in cube-mult distribute-lft-in unpow3
Counts
4 → 130
Calls
4 calls:
14.0ms
(* (sqrt (/ 1 PI)) (+ (+ (* (* 0.047619047619047616 (pow (fabs x) 7)) 1.0) (* 2.0 (fabs x))) (* 0.2 (pow (fabs x) 5))))
6.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
9.0ms
(* (sqrt (/ 1 PI)) (* 0.6666666666666666 (pow (fabs x) 3)))
6.0ms
(* 0.047619047619047616 (pow (fabs x) 7))

series495.0ms

Counts
4 → 12
Calls
4 calls:
245.0ms
(* (sqrt (/ 1 PI)) (+ (+ (* (* 0.047619047619047616 (pow (fabs x) 7)) 1.0) (* 2.0 (fabs x))) (* 0.2 (pow (fabs x) 5))))
50.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
121.0ms
(* (sqrt (/ 1 PI)) (* 0.6666666666666666 (pow (fabs x) 3)))
79.0ms
(* 0.047619047619047616 (pow (fabs x) 7))

simplify82.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06221400
129521278
250011274

prune575.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes69.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04837
14837

end0.0ms

sample1.1s

Algorithm
intervals
Results
950.0ms13823×body80valid