Details

sample53.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify238.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (180.0ms)

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 (100.0%)

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

localize18.0ms

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))

rewrite28.0ms

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:

8.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
3.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* (* 2.0 PI) u2)
9.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series214.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
34.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
103.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify55.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	514	738
1	2154	656
2	5001	648

prune191.0ms

Filtered

99 candidates to 66 candidates (33.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	9	100

Merged error: 0.0b

Counts

100 → 9

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

rewrite22.0ms

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:

8.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
3.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* (* 2.0 PI) u2)
4.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series199.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
32.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
92.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	445	720
1	1835	655
2	5001	647

prune176.0ms

Filtered

96 candidates to 67 candidates (30.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	97	8	105

Merged error: 0b

Counts

105 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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

series236.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (* -2.0 (log u1)) 0.5)
107.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
3.0ms	(* (* 2.0 PI) u2)
92.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

simplify65.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	660	1618
1	2852	1464
2	5001	1363

prune274.0ms

Filtered

194 candidates to 106 candidates (45.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Merged error: 0b

Counts

202 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

4.0ms	(* (* 2.0 PI) u2)
7.0ms	(log (+ (* (* 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) 6.0)
10.0ms	(exp (log (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) u2)
91.0ms	(log (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
91.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
73.0ms	(exp (log (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)))

simplify47.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	442	1073
1	1652	974
2	5002	955

prune191.0ms

Filtered

99 candidates to 71 candidates (28.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	99	8	107

Merged error: 0b

Counts

107 → 8

regimes503.0ms

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

sample1.2s

Algorithm

intervals

Results

753.0ms	8000×	body	80	valid
187.0ms	8000×	pre	80	true

Details

sample53.0ms

simplify238.0ms

prune5.0ms

localize18.0ms

rewrite28.0ms

series214.0ms

simplify55.0ms

prune191.0ms

localize18.0ms

rewrite22.0ms

series199.0ms

simplify48.0ms

prune176.0ms

localize17.0ms

rewrite26.0ms

series236.0ms

simplify65.0ms

prune274.0ms

localize20.0ms

rewrite29.0ms

series258.0ms

simplify47.0ms

prune191.0ms

regimes503.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling