Details

sample50.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify604.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

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

localize32.0ms

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))

rewrite31.0ms

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)
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))

series224.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (* (* (/ 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)
108.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify60.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (51.0ms)

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

prune198.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

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: 0b

Counts

100 → 9

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

rewrite23.0ms

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

series208.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
34.0ms	(pow (* -2.0 (log u1)) 0.5)
96.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
3.0ms	(* (* 2.0 PI) u2)

simplify53.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (44.0ms)

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

prune183.0ms

Filtered

67 candidates to 96 candidates (-43.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	96	9	105

Merged error: 0b

Counts

105 → 9

localize21.0ms

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

rewrite28.0ms

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)
7.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
7.0ms	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
5.0ms	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) u2)
96.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
118.0ms	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
96.0ms	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

simplify45.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	394	637
1	1569	568
2	5001	564

prune193.0ms

Filtered

65 candidates to 104 candidates (-60.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	104	9	113

Merged error: 0b

Counts

113 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) u2)
0.3b	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
0.5b	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
0.7b	(pow (pow (* -2.0 (log u1)) 0.5) 3)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
44×	`cbrt-prod`
25×	`unpow-prod-down`
22×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
19×	`cube-prod`
18×	`add-exp-log`
16×	`times-frac`
15×	`sqr-pow`
14×	`associate-l` `unswap-sqr`
13×	`add-cbrt-cube`
11×	`pow1`
6×	`pow-exp` `prod-exp`
5×	`cbrt-unprod`
4×	`pow-prod-down` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`pow-to-exp` `*-commutative`
1×	`cbrt-undiv` `pow-pow` `pow1/3` `div-exp` `associate-*l/` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 133

Calls

4 calls:

4.0ms	(* (* 2.0 PI) u2)
12.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
3.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
4.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

series234.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) u2)
95.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
90.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
46.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

simplify75.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	609	1038
1	2514	992
2	5001	964

prune207.0ms

Filtered

80 candidates to 145 candidates (-81.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	145	9	154

Merged error: 0b

Counts

154 → 9

regimes749.0ms

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

780.0ms	8000×	body	80	valid
175.0ms	8000×	pre	80	true

Details

sample50.0ms

simplify604.0ms

prune5.0ms

localize32.0ms

rewrite31.0ms

series224.0ms

simplify60.0ms

prune198.0ms

localize17.0ms

rewrite23.0ms

series208.0ms

simplify53.0ms

prune183.0ms

localize21.0ms

rewrite28.0ms

series312.0ms

simplify45.0ms

prune193.0ms

localize21.0ms

rewrite28.0ms

series234.0ms

simplify75.0ms

prune207.0ms

regimes749.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

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