Details

analyze312.0ms

Algorithm

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
0%	6.2%	93.8%	3
3.1%	3.1%	93.8%	4
3.1%	3.1%	93.8%	5
4.7%	1.6%	93.8%	6
4.7%	1.6%	93.8%	7
5.5%	0.8%	93.8%	8
5.5%	0.8%	93.8%	9
5.8%	0.4%	93.8%	10
5.8%	0.4%	93.8%	11
6%	0.2%	93.8%	12
6%	0.2%	93.8%	13
6.1%	0.1%	93.8%	14

sample81.0ms

Algorithm

intervals

Results

29.0ms

256×

body

valid

simplify499.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4872	19
1	4872	19

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.3b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (* 1.0 (* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))))
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* PI u2)
0.4b	(* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
25×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`prod-exp`
11×	`times-frac` `add-cbrt-cube`
9×	`pow1`
8×	`associate-l`
6×	`pow-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`div-exp` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `cbrt-unprod`
2×	`unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-*r/` `sum-log` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

4.0ms	(+ 0.5 (* 1.0 (* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))))
4.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* PI u2)
11.0ms	(* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))

series207.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ 0.5 (* 1.0 (* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))))
35.0ms	(pow (* -2.0 (log u1)) 0.5)
2.0ms	(* PI u2)
90.0ms	(* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4957	1396
1	4957	1396

prune213.0ms

Filtered

67 candidates to 99 candidates (-47.8%)

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

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

4.0ms	(+ 0.5 (* 1.0 (/ (* (cos (* 2.0 (* PI u2))) (pow (* -2.0 (log u1)) 0.5)) 6.0)))
4.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* PI u2)
7.0ms	(/ (* (cos (* 2.0 (* PI u2))) (pow (* -2.0 (log u1)) 0.5)) 6.0)

series179.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ 0.5 (* 1.0 (/ (* (cos (* 2.0 (* PI u2))) (pow (* -2.0 (log u1)) 0.5)) 6.0)))
36.0ms	(pow (* -2.0 (log u1)) 0.5)
2.0ms	(* PI u2)
69.0ms	(/ (* (cos (* 2.0 (* PI u2))) (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4968	1043
1	4968	1043

prune155.0ms

Filtered

54 candidates to 82 candidates (-51.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Merged error: 0b

Counts

90 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* PI u2)
1.2b	(pow (exp (pow (* -2.0 (log u1)) 0.5)) (/ (cos (* 2.0 (* PI u2))) 6.0))
2.5b	(exp (pow (* -2.0 (log u1)) 0.5))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
16×	`pow-unpow`
10×	`pow1` `exp-prod`
9×	`add-exp-log` `times-frac`
8×	`pow-pow`
6×	`unpow-prod-down` `add-cbrt-cube`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`associate-r` `associate-l` `pow-exp`
2×	`pow-to-exp` `pow-prod-down` `prod-exp`
1×	`*-commutative` `cbrt-unprod` `div-inv` `rem-exp-log` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

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

series153.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow (* -2.0 (log u1)) 0.5)
2.0ms	(* PI u2)
67.0ms	(pow (exp (pow (* -2.0 (log u1)) 0.5)) (/ (cos (* 2.0 (* PI u2))) 6.0))
46.0ms	(exp (pow (* -2.0 (log u1)) 0.5))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4949	1054
1	4949	1054

prune222.0ms

Filtered

63 candidates to 92 candidates (-46.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	92	7	99

Merged error: 0b

Counts

99 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI u2)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.5b	(cbrt (pow (* (/ (pow (* -2.0 (log u1)) 0.5) 6.0) (cos (* 2.0 (* PI u2)))) 3))
0.8b	(pow (* (/ (pow (* -2.0 (log u1)) 0.5) 6.0) (cos (* 2.0 (* PI u2)))) 3)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
14×	`add-cbrt-cube`
10×	`pow-exp`
9×	`pow1`
8×	`cbrt-prod` `div-exp` `prod-exp`
6×	`unpow-prod-down` `sqr-pow`
5×	`associate-/l*`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `associate-l` `associate-/r*` `cbrt-unprod` `rem-cube-cbrt`
2×	`cbrt-undiv` `cube-div` `cube-mult` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `associate-*l/`
1×	`cbrt-div` `frac-2neg` `pow1/3` `clear-num` `*-commutative` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

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

series271.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* PI u2)
99.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
76.0ms	(cbrt (pow (* (/ (pow (* -2.0 (log u1)) 0.5) 6.0) (cos (* 2.0 (* PI u2)))) 3))
93.0ms	(pow (* (/ (pow (* -2.0 (log u1)) 0.5) 6.0) (cos (* 2.0 (* PI u2)))) 3)

simplify42.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4938	1532
1	4938	1532

prune222.0ms

Filtered

79 candidates to 114 candidates (-44.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	114	7	121

Merged error: 0b

Counts

121 → 7

regimes328.0ms

Accuracy

0% (0.2b 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	19
1	24	19

end0.0ms

sample2.2s

Algorithm

intervals

Results

747.0ms

8000×

body

valid

Details

analyze312.0ms

sample81.0ms

simplify499.0ms

prune12.0ms

localize31.0ms

rewrite26.0ms

series207.0ms

simplify76.0ms

prune213.0ms

localize19.0ms

rewrite21.0ms

series179.0ms

simplify50.0ms

prune155.0ms

localize28.0ms

rewrite20.0ms

series153.0ms

simplify47.0ms

prune222.0ms

localize23.0ms

rewrite23.0ms

series271.0ms

simplify42.0ms

prune222.0ms

regimes328.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling