Details

sample285.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
5.0ms	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

prune12.0ms

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:

0.0b	(+ (* (* (/ 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)
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (/ 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:

10.0ms	(+ (* (* (/ 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)
19.0ms	(* (* 2.0 PI) u2)
10.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

446.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
259.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
676.0ms	(* (/ 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

prune326.0ms

Filtered

108 candidates to 80 candidates (74.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 0b

Counts

109 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.3b	(* (* 2.0 PI) u2)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

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

series1.4s

Counts

4 → 12

Calls

4 calls:

452.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
255.0ms	(pow (* -2.0 (log u1)) 0.5)
674.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
35.0ms	(* (* 2.0 PI) u2)

simplify57.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	456	752
1	1915	695
2	5001	695

prune306.0ms

Filtered

105 candidates to 81 candidates (77.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Merged error: 0b

Counts

113 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b	(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

1.0ms	(log1p (* (/ 1.0 6.0) (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))
1.0ms	(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

series2.4s

Counts

4 → 12

Calls

4 calls:

811.0ms	(log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
31.0ms	(* (* 2.0 PI) u2)
683.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
863.0ms	(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

simplify45.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	394	641
1	1461	570
2	5001	570

prune310.0ms

Filtered

97 candidates to 70 candidates (72.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	97	8	105

Merged error: 0b

Counts

105 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) u2)
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.6b	(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))
7.0ms	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

series2.3s

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) u2)
720.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
711.0ms	(cbrt (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3))
805.0ms	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

simplify64.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	491	825
1	2035	784
2	5002	782

prune374.0ms

Filtered

127 candidates to 88 candidates (69.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	129	6	135

Merged error: 0b

Counts

135 → 6

regimes317.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample973.0ms

Algorithm

intervals

Results

692.0ms	8000×	body	80	valid
129.0ms	8000×	pre	80	true