Details

sample334.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	9
1	74	9
2	160	9
3	483	9
4	1845	9
5	5001	9

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* (/ 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)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite58.0ms

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`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `associate-*l/` `fma-udef` `div-inv`

Counts

4 → 92

Calls

4 calls:

0.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
13.0ms	(pow (* -2.0 (log u1)) 0.5)
16.0ms	(* (* 2.0 PI) u2)
24.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

451.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
253.0ms	(pow (* -2.0 (log u1)) 0.5)
32.0ms	(* (* 2.0 PI) u2)
663.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify53.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	456	686
1	1839	619
2	5001	619

prune355.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`pow1`
9×	`prod-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`div-exp`
4×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `associate-r` `associate-/r*`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow`
1×	`unpow-prod-down` `frac-2neg` `associate-l` `clear-num` `-commutative` `fma-udef` `div-inv` `associate-/l` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

0.0ms	(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
8.0ms	(pow (* -2.0 (log u1)) 0.5)
14.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
17.0ms	(* (* 2.0 PI) u2)

series1.4s

Counts

4 → 12

Calls

4 calls:

458.0ms	(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
259.0ms	(pow (* -2.0 (log u1)) 0.5)
674.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
33.0ms	(* (* 2.0 PI) u2)

simplify48.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	405	555
1	1722	486
2	5001	486

prune299.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-sqr-sqrt`
33×	`associate-l`
30×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
7×	`cbrt-unprod`
6×	`pow-exp` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down` `sqr-pow`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 120

Calls

4 calls:

6.0ms	(pow (* -2.0 (log u1)) 0.5)
58.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
27.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
17.0ms	(* (* 2.0 PI) u2)

series1.7s

Counts

4 → 12

Calls

4 calls:

262.0ms	(pow (* -2.0 (log u1)) 0.5)
739.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
693.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
32.0ms	(* (* 2.0 PI) u2)

simplify52.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	455	972
1	1801	875
2	5001	871

prune493.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b

(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)

0.2b

(fma 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI)))) 0.5)

0.3b

(* u2 PI)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-exp-log`
59×	`pow-exp`
58×	`prod-exp`
29×	`pow-to-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
3×	`expm1-log1p-u` `pow-unpow` `associate-r` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow`
1×	`unpow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr` `sqr-pow`

Counts

3 → 78

Calls

3 calls:

31.0ms

(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)

0.0ms

(fma 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI)))) 0.5)

7.0ms

(* u2 PI)

series1.8s

Counts

3 → 9

Calls

3 calls:

1.1s

(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)

580.0ms

(fma 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI)))) 0.5)

21.0ms

(* u2 PI)

simplify123.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	413	776
1	1187	733
2	4816	728
3	5001	728

prune254.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes386.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	13
1	30	13

end0.0ms

sample970.0ms

Algorithm

intervals

Results

653.0ms	8000×	body	80	valid
114.0ms	8000×	pre	80	true