Details

Time bar (total: 3.6s)

sample41.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 46.482521%

Space saved by search: 25.073242%

Guaranteed chance to sample good point: 0%

Results
23.0ms256×body80valid
3.0ms256×pre80true

simplify108.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06942
123142
290042
3375342
4500142

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize25.0ms

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)

rewrite99.0ms

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:
57.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
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 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)))
1.0ms
(sqrt PI)

series78.0ms

Counts
4 → 10
Calls
4 calls:
12.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
57.0ms
(* (/ 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)))))
8.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify60.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
013384946
150014033

prune377.0ms

Filtered
109 candidates to 175 candidates (-60.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1714175
Fresh000
Picked101
Done000
Total1724176

Merged error: 0b

Counts
176 → 4

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

rewrite59.0ms

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
35×*-un-lft-identity
33×add-cube-cbrt
22×pow-prod-down
13×sqrt-prod
12×frac-add
9×cbrt-undiv div-exp
7×associate-*l/
6×frac-times flip3-+ associate-*r/ associate-*r* flip-+
4×add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 distribute-lft-out
Counts
4 → 156
Calls
4 calls:
23.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
17.0ms
(* (/ 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 (pow (fabs x) 6)) (fabs x)) 21.0)))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series76.0ms

Counts
4 → 10
Calls
4 calls:
10.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
59.0ms
(* (/ 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 (pow (fabs x) 6)) (fabs x)) 21.0)))
7.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify56.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011923891
150023235

prune387.0ms

Filtered
108 candidates to 166 candidates (-53.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1651166
Fresh213
Picked011
Done000
Total1673170

Merged error: 0b

Counts
170 → 3

localize27.0ms

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)))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(/ (* 1.0 (+ (+ (+ (* 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 PI))
1.0b
(sqrt PI)

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
107×add-exp-log add-cbrt-cube
69×prod-exp cbrt-unprod
49×pow1
34×pow-prod-down
26×associate-*l*
24×add-sqr-sqrt times-frac
23×add-cube-cbrt *-un-lft-identity
12×cbrt-undiv div-exp
9×sqrt-prod
8×associate-*l/
6×associate-*r/ frac-add associate-/r* associate-/l/
4×add-log-exp
3×flip3-+ flip-+ div-inv
2×associate-*r* *-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l*
Counts
4 → 142
Calls
4 calls:
57.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
15.0ms
(/ (* 1.0 (+ (+ (+ (* 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 PI))
1.0ms
(sqrt PI)

series79.0ms

Counts
4 → 10
Calls
4 calls:
12.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
7.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
60.0ms
(/ (* 1.0 (+ (+ (+ (* 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 PI))
0.0ms
(sqrt PI)

simplify121.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
09923136
146252222
250012063

prune230.0ms

Filtered
86 candidates to 152 candidates (-76.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1520152
Fresh011
Picked011
Done011
Total1523155

Merged error: 0b

Counts
155 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 5.0) (pow (fabs x) 3))
0.2b
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
0.3b
(/ (* (+ (+ (/ (* (* 1.0 (pow (fabs x) 6)) (fabs x)) 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)

rewrite42.0ms

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:
9.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
7.0ms
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
19.0ms
(/ (* (+ (+ (/ (* (* 1.0 (pow (fabs x) 6)) (fabs x)) 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)

series70.0ms

Counts
4 → 10
Calls
4 calls:
7.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
5.0ms
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
58.0ms
(/ (* (+ (+ (/ (* (* 1.0 (pow (fabs x) 6)) (fabs x)) 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)

simplify102.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07921875
139551620
250021593

prune365.0ms

Filtered
100 candidates to 143 candidates (-43.0%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1430143
Fresh000
Picked011
Done022
Total1433146

Merged error: 0b

Counts
146 → 3

regimes111.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04133
14133

end0.0ms

sample933.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 46.482521%

Space saved by search: 25.073242%

Guaranteed chance to sample good point: 0%

Results
739.0ms8000×body80valid
84.0ms8000×pre80true

Profiling

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