Details

sample326.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
7.0ms	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

localize41.0ms

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))

rewrite32.0ms

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:

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)
11.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

455.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
262.0ms	(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))

simplify60.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

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

prune311.0ms

Filtered

99 candidates to 71 candidates (71.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 0b

Counts

100 → 8

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)

series1.5s

Counts

4 → 12

Calls

4 calls:

456.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
268.0ms	(pow (* -2.0 (log u1)) 0.5)
32.0ms	(* (* 2.0 PI) u2)
696.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (11.0ms)

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

prune288.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Merged error: 0b

Counts

104 → 7

localize19.0ms

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)
0.2b	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

rewrite33.0ms

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

series1.7s

Counts

4 → 12

Calls

4 calls:

261.0ms	(pow (* -2.0 (log u1)) 0.5)
764.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
32.0ms	(* (* 2.0 PI) u2)
688.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

simplify73.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (56.0ms)

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

prune419.0ms

Filtered

194 candidates to 108 candidates (55.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	194	7	201

Merged error: 0b

Counts

201 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.2b	(/ 1 (* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5)))
0.3b	(* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5))
0.3b	(/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

431×	`add-exp-log`
270×	`prod-exp`
214×	`pow-exp`
168×	`div-exp`
94×	`pow-to-exp`
84×	`rec-exp` `1-exp`
21×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
14×	`associate-r`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`unpow-prod-down`
6×	`cbrt-unprod` `associate-/l*`
4×	`cbrt-undiv` `associate-l` `pow-prod-down` `add-log-exp`
3×	`pow-flip` `div-inv` `unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `inv-pow` `sqr-pow`

Counts

4 → 252

Calls

4 calls:

5.0ms	(* (* 2.0 PI) u2)
12.0ms	(/ 1 (* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5)))
11.0ms	(* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5))
8.0ms	(/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0)))

series2.2s

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) u2)
717.0ms	(/ 1 (* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5)))
766.0ms	(* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5))
732.0ms	(/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	772	2128
1	2703	2013
2	5001	1998

prune338.0ms

Filtered

264 candidates to 69 candidates (26.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	264	0	264
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	264	7	271

Merged error: 0b

Counts

271 → 7

regimes331.0ms

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

sample1.2s

Algorithm

intervals

Results

810.0ms	8000×	body	80	valid
192.0ms	8000×	pre	80	true

Details

sample326.0ms

simplify68.0ms

prune5.0ms

localize41.0ms

rewrite32.0ms

series1.4s

simplify60.0ms

prune311.0ms

localize17.0ms

rewrite25.0ms

series1.5s

simplify54.0ms

prune288.0ms

localize19.0ms

rewrite33.0ms

series1.7s

simplify73.0ms

prune419.0ms

localize27.0ms

rewrite52.0ms

series2.2s

simplify75.0ms

prune338.0ms

regimes331.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling