Details

Time bar (total: 6.7s)

sample48.0ms

Algorithm
intervals
Results
32.0ms433×body80valid

simplify107.0ms

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: 0.4b

localize32.0ms

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)

rewrite116.0ms

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:
21.0ms
(* (/ 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)))))
13.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
70.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series467.0ms

Counts
4 → 10
Calls
4 calls:
341.0ms
(* (/ 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)))
81.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify69.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013384946
150014032

prune706.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 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)))) (* 1.0 (* (* (/ 1 21.0) (pow (fabs x) 6)) (fabs x)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
53×add-exp-log
48×associate-*l*
44×times-frac
38×*-un-lft-identity
35×add-cube-cbrt add-cbrt-cube
26×prod-exp
23×associate-*l/
16×pow1 cbrt-unprod
14×associate-*r/
13×sqrt-prod
12×frac-add unswap-sqr
11×associate-*r*
10×div-exp
7×pow-prod-down
6×frac-times unpow-prod-down flip3-+ flip-+
5×cbrt-undiv
4×pow-to-exp pow-exp add-log-exp sqr-pow
3×rec-exp 1-exp *-commutative div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 159
Calls
4 calls:
9.0ms
(* (/ 1 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)))) (* 1.0 (* (* (/ 1 21.0) (pow (fabs x) 6)) (fabs x)))))
13.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series622.0ms

Counts
4 → 10
Calls
4 calls:
61.0ms
(* (/ 1 21.0) (pow (fabs x) 6))
510.0ms
(* (/ 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 (* (* (/ 1 21.0) (pow (fabs x) 6)) (fabs x)))))
51.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify59.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011453665
150023261

prune744.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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:
6.0ms
(* 0.2 (pow (fabs x) 5))
17.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))
7.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
6.0ms
(* 0.047619047619047616 (pow (fabs x) 7))

series471.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* 0.2 (pow (fabs x) 5))
288.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))
48.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
71.0ms
(* 0.047619047619047616 (pow (fabs x) 7))

simplify82.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
05931430
127951324
250021320

prune530.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))
7.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
10.0ms
(* (sqrt (/ 1 PI)) (* 0.6666666666666666 (pow (fabs x) 3)))
6.0ms
(* 0.047619047619047616 (pow (fabs x) 7))

series478.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))
44.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
125.0ms
(* (sqrt (/ 1 PI)) (* 0.6666666666666666 (pow (fabs x) 3)))
75.0ms
(* 0.047619047619047616 (pow (fabs x) 7))

simplify79.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06111342
128981225
250011220

prune571.0ms

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
04634
14634

end0.0ms

sample1.2s

Algorithm
intervals
Results
1.1s13823×body80valid