Details

sample299.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	9
1	74	9
2	160	9
3	483	9
4	1845	9
5	5001	9

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.4b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp` `add-cbrt-cube`
12×	`pow1`
11×	`times-frac`
8×	`associate-r`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 96

Calls

4 calls:

9.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(* (* 2.0 PI) u2)
25.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

452.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
257.0ms	(pow (* -2.0 (log u1)) 0.5)
37.0ms	(* (* 2.0 PI) u2)
689.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify63.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	523	772
1	2229	700
2	5001	697

prune333.0ms

Filtered

108 candidates to 80 candidates (74.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	99	9	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	9	109

Merged error: 0b

Counts

109 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
0.2b	(* (* 2.0 PI) u2)
0.3b	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-sqr-sqrt`
33×	`associate-l`
30×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
7×	`cbrt-unprod`
6×	`pow-exp` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down` `sqr-pow`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 120

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
16.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
5.0ms	(* (* 2.0 PI) u2)
9.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series1.7s

Counts

4 → 12

Calls

4 calls:

255.0ms	(pow (* -2.0 (log u1)) 0.5)
723.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
37.0ms	(* (* 2.0 PI) u2)
696.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify55.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	455	972
1	1801	875
2	5001	871

prune411.0ms

Filtered

132 candidates to 97 candidates (73.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Merged error: 0b

Counts

141 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.9b	(exp (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp` `add-cbrt-cube`
12×	`pow1`
11×	`times-frac`
8×	`associate-r`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `exp-prod` `exp-to-pow` `associate-*l/` `div-inv` `rem-exp-log`

Counts

4 → 94

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(* (* 2.0 PI) u2)
8.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
7.0ms	(exp (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

series1.7s

Counts

4 → 12

Calls

4 calls:

260.0ms	(pow (* -2.0 (log u1)) 0.5)
36.0ms	(* (* 2.0 PI) u2)
681.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
728.0ms	(exp (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

simplify46.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	412	623
1	1591	564
2	5001	564

prune315.0ms

Filtered

106 candidates to 73 candidates (68.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	106	7	113

Merged error: 0b

Counts

113 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.5b	(cbrt (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3))
0.7b	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
23×	`add-sqr-sqrt` `prod-exp`
20×	`add-cbrt-cube`
17×	`pow-exp`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-l`
11×	`times-frac`
10×	`pow1`
8×	`cbrt-prod` `div-exp` `associate-r`
7×	`cbrt-unprod`
5×	`pow-to-exp` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`unpow-prod-down` `pow-unpow` `pow-prod-down` `associate-*l/` `rem-cube-cbrt`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `cube-prod` `*-commutative`
1×	`cbrt-div` `pow-pow` `pow1/3` `rem-cbrt-cube` `div-inv`

Counts

4 → 115

Calls

4 calls:

5.0ms	(* (* 2.0 PI) u2)
8.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
3.0ms	(cbrt (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3))
8.0ms	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

series2.2s

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 PI) u2)
697.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
705.0ms	(cbrt (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3))
774.0ms	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

simplify62.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	491	821
1	2035	782
2	5001	780

prune362.0ms

Filtered

127 candidates to 87 candidates (68.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	127	7	134

Merged error: 0b

Counts

134 → 7

regimes343.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	27	14

end0.0ms

sample1.3s

Algorithm

intervals

Results

932.0ms	8000×	body	80	valid
205.0ms	8000×	pre	80	true

Details

sample299.0ms

simplify67.0ms

prune11.0ms

localize20.0ms

rewrite47.0ms

series1.4s

simplify63.0ms

prune333.0ms

localize19.0ms

rewrite38.0ms

series1.7s

simplify55.0ms

prune411.0ms

localize20.0ms

rewrite27.0ms

series1.7s

simplify46.0ms

prune315.0ms

localize20.0ms

rewrite27.0ms

series2.2s

simplify62.0ms

prune362.0ms

regimes343.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling