Details

Time bar (total: 6.7s)

sample60.0ms

Algorithm
intervals
Results
43.0ms454×body80valid

simplify113.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (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)

rewrite109.0ms

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×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 → 173
Calls
4 calls:
62.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (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)))))
14.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series447.0ms

Counts
4 → 10
Calls
4 calls:
74.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
327.0ms
(* (/ 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)))))
46.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify65.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013665031
150013864

prune659.0ms

Filtered
183 candidates to 117 candidates (63.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1794183
Fresh000
Picked011
Done000
Total1795184

Merged error: 0b

Counts
184 → 5

localize27.0ms

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 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 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
54×associate-*l/
37×add-sqr-sqrt
36×associate-*l* frac-add
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
22×frac-times associate-*r/
17×prod-exp cbrt-unprod
14×flip3-+ flip-+
13×sqrt-prod
10×pow-prod-down
7×associate-*r*
6×pow-plus pow-prod-up
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u 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 → 159
Calls
4 calls:
6.0ms
(* (* (fabs x) (fabs x)) (fabs x))
23.0ms
(* (/ 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 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series539.0ms

Counts
4 → 10
Calls
4 calls:
26.0ms
(* (* (fabs x) (fabs x)) (fabs x))
468.0ms
(* (/ 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 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
44.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify70.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
012725377
150014609

prune813.0ms

Filtered
169 candidates to 120 candidates (71.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1690169
Fresh033
Picked011
Done011
Total1695174

Merged error: 0b

Counts
174 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
162×add-exp-log
114×prod-exp
74×add-cbrt-cube
46×cbrt-unprod
43×add-sqr-sqrt
26×associate-*r*
23×add-cube-cbrt *-un-lft-identity
22×times-frac
18×div-exp
15×pow1
13×associate-*l*
10×pow-to-exp pow-exp
8×cbrt-undiv unswap-sqr
6×pow-prod-down sqrt-prod
5×unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqr-pow
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ *-commutative div-inv
1×cube-mult unpow3
Counts
4 → 154
Calls
4 calls:
20.0ms
(* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))
10.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series124.0ms

Counts
4 → 8
Calls
4 calls:
75.0ms
(* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))
48.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify124.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (110.0ms)

IterNodesCost
07681521
135661038
25002913

prune467.0ms

Filtered
162 candidates to 87 candidates (53.7%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1620162
Fresh022
Picked011
Done022
Total1625167

Merged error: 0b

Counts
167 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
164×add-exp-log
114×prod-exp
76×add-cbrt-cube
58×add-sqr-sqrt
46×times-frac cbrt-unprod
39×add-cube-cbrt *-un-lft-identity
26×associate-*r*
19×div-exp
18×sqrt-prod
14×pow1
13×associate-*l*
10×pow-to-exp pow-exp
9×cbrt-undiv
8×unswap-sqr
7×distribute-lft-out
6×pow-prod-down associate-/r*
5×unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×div-inv sqr-pow
2×associate-*r/ *-commutative associate-/l/
1×cube-mult rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 unpow3 clear-num flip-+
Counts
4 → 189
Calls
4 calls:
24.0ms
(* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))
10.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
7.0ms
(/ (+ (* 1.0 (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* 1.0 (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))) (sqrt PI))
2.0ms
(sqrt PI)

series446.0ms

Counts
4 → 10
Calls
4 calls:
76.0ms
(* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))
49.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
320.0ms
(/ (+ (* 1.0 (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* 1.0 (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify159.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (128.0ms)

IterNodesCost
09453859
143243211
250023167

prune607.0ms

Filtered
199 candidates to 119 candidates (59.8%)
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1990199
Fresh011
Picked011
Done033
Total1995204

Merged error: 0b

Counts
204 → 5

regimes228.0ms

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
04837
14837

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.3s13961×body80valid