Details

Time bar (total: 9.6s)

sample48.0ms

Algorithm
intervals
Results
32.0ms470×body80valid

simplify110.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

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)

rewrite657.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 163
Calls
4 calls:
308.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
315.0ms
(* (/ 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)))))
26.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series422.0ms

Counts
4 → 10
Calls
4 calls:
61.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
314.0ms
(* (/ 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)))))
47.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify62.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012244595
150013688

prune693.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt
47×associate-*l*
46×times-frac
39×add-cube-cbrt *-un-lft-identity
35×add-exp-log
28×associate-*r*
19×add-cbrt-cube unswap-sqr
14×prod-exp
13×sqrt-prod
10×unpow-prod-down cube-prod
7×pow1 div-exp
6×cbrt-unprod sqr-pow
4×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u add-log-exp
3×cbrt-undiv *-commutative div-inv
2×cube-mult unpow3 associate-*l/ fma-udef
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*r/ pow-prod-down
Counts
4 → 165
Calls
4 calls:
11.0ms
(* (/ 1.0 (sqrt PI)) (fma (/ 1.0 21.0) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x)) (fabs x) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))))
12.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
12.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0ms
(sqrt PI)

series408.0ms

Counts
4 → 10
Calls
4 calls:
317.0ms
(* (/ 1.0 (sqrt PI)) (fma (/ 1.0 21.0) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x)) (fabs x) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))))
43.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
48.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms
(sqrt PI)

simplify124.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
07032447
136342201
250012160

prune813.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
30×add-exp-log
26×add-cube-cbrt *-un-lft-identity times-frac
25×associate-*r* associate-*l*
16×unswap-sqr
14×add-cbrt-cube
12×prod-exp
10×unpow-prod-down cube-prod
6×pow1 div-exp sqrt-prod sqr-pow
4×expm1-log1p-u pow-to-exp pow-exp cbrt-unprod log1p-expm1-u add-log-exp
2×cbrt-undiv cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 *-commutative div-inv
1×associate-*r/ associate-*l/
Counts
4 → 134
Calls
4 calls:
12.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
11.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series94.0ms

Counts
4 → 8
Calls
4 calls:
44.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
50.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify96.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0506813
12663763
25001763

prune729.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.4b
(* (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)))))) (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)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
378×associate-*l/
364×sqrt-div
337×frac-times
336×frac-add
181×associate-*r/
168×flip3-+ flip-+
64×pow1
30×sqrt-pow1
27×add-exp-log add-cbrt-cube
26×pow-prod-down
21×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity associate-*l*
13×prod-exp cbrt-unprod
12×pow1/2
10×sqrt-prod pow-prod-up
9×times-frac
6×pow-sqr
5×associate-*r*
4×expm1-log1p-u swap-sqr log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×rem-sqrt-square *-commutative
1×pow2 pow-plus sqrt-unprod rem-square-sqrt div-inv unswap-sqr
Counts
4 → 316
Calls
4 calls:
27.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
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)))))) (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)

series419.0ms

Counts
4 → 8
Calls
4 calls:
43.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
376.0ms
(* (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)))))) (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)

simplify447.0ms

Algorithm
egg-herbie
Counts
324 → 324
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
0117748279
1470847246
2500147191

prune1.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes192.0ms

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
04436
14436

end0.0ms

sample1.2s

Algorithm
intervals
Results
987.0ms14154×body80valid