Details

sample297.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	10
1	71	10
2	154	10
3	469	10
4	1812	10
5	5001	10

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.4b

Counts

2 → 1

localize19.0ms

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

rewrite48.0ms

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×	`div-exp` `pow-prod-down` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

24.0ms	(+ (* (* (/ 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)
10.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

454.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
267.0ms	(pow (* -2.0 (log u1)) 0.5)
32.0ms	(* (* 2.0 PI) u2)
691.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify64.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	507	728
1	2155	656
2	5001	656

prune301.0ms

Filtered

99 candidates to 71 candidates (71.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	90	9	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	10	100

Merged error: 0.0b

Counts

100 → 10

localize17.0ms

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	(* (* 2.0 PI) u2)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

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×	`div-exp` `pow-prod-down` `pow-exp`
3×	`pow-unpow` `associate-r` `associate-/r*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `associate-l` `clear-num` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 84

Calls

4 calls:

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

series1.4s

Counts

4 → 12

Calls

4 calls:

454.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
260.0ms	(pow (* -2.0 (log u1)) 0.5)
37.0ms	(* (* 2.0 PI) u2)
677.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	438	710
1	1838	655
2	5001	655

prune287.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	96	10	106

Merged error: 0b

Counts

106 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
0.2b	(* (* 2.0 PI) u2)
0.3b	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`add-exp-log`
26×	`div-exp`
24×	`associate-/r*`
17×	`unpow-prod-down` `sqr-pow`
16×	`add-cbrt-cube`
13×	`pow1`
10×	`pow-exp`
8×	`prod-exp`
6×	`div-inv` `associate-/l*`
5×	`pow-to-exp` `rec-exp` `1-exp`
4×	`cbrt-undiv` `pow-prod-down` `add-log-exp`
3×	`pow-unpow` `associate-r` `cbrt-unprod`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`pow-flip` `associate-l` `associate-/r/` `*-commutative` `inv-pow`

Counts

4 → 182

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
8.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
5.0ms	(* (* 2.0 PI) u2)
5.0ms	(/ 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)
673.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
36.0ms	(* (* 2.0 PI) u2)
738.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))

simplify73.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	655	1612
1	2878	1461
2	5001	1360

prune414.0ms

Filtered

194 candidates to 109 candidates (56.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	196	8	204

Merged error: 0b

Counts

204 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.3b	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
0.3b	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
23×	`prod-exp`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
11×	`pow1` `times-frac`
9×	`rem-log-exp`
8×	`div-exp` `associate-r` `pow-exp`
5×	`cbrt-unprod`
4×	`pow-to-exp` `exp-prod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-*l/` `sqr-pow`
2×	`log-div` `log-prod` `log-pow` `*-commutative`
1×	`cbrt-undiv` `unpow-prod-down` `exp-diff` `exp-sum` `div-inv` `rem-exp-log`

Counts

4 → 92

Calls

4 calls:

5.0ms	(* (* 2.0 PI) u2)
10.0ms	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
6.0ms	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
8.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 2.0 PI) u2)
830.0ms	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
708.0ms	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
699.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify46.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	396	631
1	1598	565
2	5001	564

prune299.0ms

Filtered

104 candidates to 71 candidates (68.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	104	8	112

Merged error: 0b

Counts

112 → 8

regimes472.0ms

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	24	10
1	24	10

end0.0ms

sample934.0ms

Algorithm

intervals

Results

653.0ms	8000×	body	80	valid
126.0ms	8000×	pre	80	true