Details

Time bar (total: 7.5s)

sample47.0ms

Algorithm
intervals
Results
30.0ms459×body80valid

simplify104.0ms

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: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (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)

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1
33×add-cube-cbrt *-un-lft-identity
22×pow-prod-down
15×associate-*l/
13×sqrt-prod
12×frac-add
9×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 → 155
Calls
4 calls:
23.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
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)))))
12.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series436.0ms

Counts
4 → 10
Calls
4 calls:
62.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
329.0ms
(* (/ 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)

simplify58.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011964518
150023785

prune653.0ms

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
(* 0.047619047619047616 (pow (fabs x) 7))
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))

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
(* 0.047619047619047616 (pow (fabs x) 7))
5.0ms
(* 0.2 (pow (fabs x) 5))
16.0ms
(* (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))

series471.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
58.0ms
(* 0.2 (pow (fabs x) 5))
289.0ms
(* (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))))))
49.0ms
(* 0.6666666666666666 (pow (fabs x) 3))

simplify79.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
05931430
127951324
250021320

prune516.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (pow (fabs x) 3))
0.2b
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
0.3b
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) 1.0) (sqrt PI))
1.0b
(sqrt PI)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
34×add-exp-log
29×times-frac
26×add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
16×associate-*l/
13×associate-*r* prod-exp
10×pow1 unswap-sqr
9×sqrt-prod cbrt-unprod
8×frac-add associate-/l/
7×div-exp
6×flip3-+ associate-*r/ associate-/r* flip-+
5×cbrt-undiv unpow-prod-down cube-prod
4×add-log-exp
3×pow-prod-down div-inv sqr-pow
2×pow-to-exp pow-exp *-commutative
1×cube-mult rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 unpow3 clear-num associate-/l*
Counts
4 → 133
Calls
4 calls:
10.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
8.0ms
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
28.0ms
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) 1.0) (sqrt PI))
1.0ms
(sqrt PI)

series423.0ms

Counts
4 → 10
Calls
4 calls:
50.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
33.0ms
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
340.0ms
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) 1.0) (sqrt PI))
0.0ms
(sqrt PI)

simplify110.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
08032156
140531809
250011729

prune701.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.3b
(* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))))
0.3b
(* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))))
0.5b
(* (* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))) (* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
140×sqrt-div
102×sqrt-prod
81×add-sqr-sqrt
67×pow1
53×frac-times
42×associate-*l*
41×pow-prod-down
34×*-un-lft-identity
33×associate-*r/
30×add-cube-cbrt
28×flip3-+ flip-+
26×times-frac
25×add-exp-log associate-*r*
24×unswap-sqr
22×add-cbrt-cube
20×sqrt-pow1 pow1/2
19×associate-*l/
13×prod-exp
11×cbrt-unprod
8×pow-prod-up
7×sqrt-unprod
6×pow-sqr
4×unpow-prod-down cube-prod *-commutative add-log-exp
2×pow-plus div-inv sqr-pow
1×pow2 cube-mult pow-to-exp unpow3 swap-sqr pow-exp rem-square-sqrt
Counts
4 → 218
Calls
4 calls:
7.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
20.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))))
19.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))))
36.0ms
(* (* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))) (* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
50.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
502.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))))
503.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))))
297.0ms
(* (* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))) (* (sqrt (sqrt (/ 1 PI))) (sqrt (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))))

simplify120.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06206767
125975889
250015841

prune923.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes54.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03819
13819

end0.0ms

sample1.1s

Algorithm
intervals
Results
937.0ms13807×body80valid