Details

analyze315.0ms

Algorithm: search

sample42.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify426.0ms

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

localize20.0ms

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)
0.2b	(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))

rewrite41.0ms

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)
21.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series233.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
35.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
112.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify59.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (50.0ms)

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

prune198.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

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: 0.0b

Counts

100 → 8

localize16.0ms

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

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

series221.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
37.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
101.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (45.0ms)

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

prune189.0ms

Filtered

67 candidates to 96 candidates (-43.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	96	8	104

Merged error: 0b

Counts

104 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) (/ 0.5 2))
0.2b	(* (* 2.0 PI) u2)
0.3b	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-exp-log`
99×	`prod-exp`
40×	`pow-exp`
29×	`add-sqr-sqrt`
23×	`add-cbrt-cube`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`pow-to-exp` `times-frac` `div-exp`
15×	`associate-l`
13×	`pow-unpow` `associate-r`
12×	`pow1`
10×	`cbrt-unprod`
5×	`sqr-pow`
4×	`pow-prod-down` `add-log-exp` `unswap-sqr`
3×	`unpow-prod-down` `associate-l/` `-commutative`
2×	`cbrt-undiv` `pow-pow` `div-inv`

Counts

4 → 140

Calls

4 calls:

5.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
5.0ms	(* (* 2.0 PI) u2)
10.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
10.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
3.0ms	(* (* 2.0 PI) u2)
102.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
104.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify65.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	617	1345
1	2368	1017
2	5002	1007

prune248.0ms

Filtered

79 candidates to 152 candidates (-92.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	152	8	160

Merged error: 0b

Counts

160 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.5b	(cbrt (pow (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5) 3))
0.7b	(pow (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5) 3)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log`
15×	`times-frac`
12×	`cbrt-prod` `add-cbrt-cube`
10×	`pow1` `unpow-prod-down`
6×	`cube-prod` `sqr-pow`
5×	`associate-/l*`
4×	`cube-div` `div-exp` `prod-exp` `add-log-exp`
3×	`pow-unpow` `associate-r` `pow-prod-down` `pow-exp` `associate-/r*` `cbrt-unprod`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `flip3-+` `unpow3` `flip-+`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `pow1/3` `associate-l` `clear-num` `*-commutative` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 104

Calls

4 calls:

5.0ms	(* (* 2.0 PI) u2)
5.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
9.0ms	(cbrt (pow (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5) 3))
10.0ms	(pow (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5) 3)

series304.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) u2)
101.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
78.0ms	(cbrt (pow (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5) 3))
122.0ms	(pow (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5) 3)

simplify80.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	622	1453
1	2739	1334
2	5001	1327

prune217.0ms

Filtered

74 candidates to 116 candidates (-56.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	116	8	124

Merged error: 0b

Counts

124 → 8

regimes838.0ms

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

analyze114.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

771.0ms	8000×	body	80	valid
184.0ms	8000×	pre	80	true

Details

analyze315.0ms

sample42.0ms

simplify426.0ms

prune5.0ms

localize20.0ms

rewrite41.0ms

series233.0ms

simplify59.0ms

prune198.0ms

localize16.0ms

rewrite23.0ms

series221.0ms

simplify54.0ms

prune189.0ms

localize19.0ms

rewrite35.0ms

series244.0ms

simplify65.0ms

prune248.0ms

localize21.0ms

rewrite30.0ms

series304.0ms

simplify80.0ms

prune217.0ms

regimes838.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze114.0ms

sample1.1s

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