Details

sample314.0ms

Algorithm

intervals

Results

38.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify65.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

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

rewrite36.0ms

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)
3.0ms	(pow (* -2.0 (log u1)) 0.5)
6.0ms	(* (* 2.0 PI) u2)
13.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

460.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
264.0ms	(pow (* -2.0 (log u1)) 0.5)
30.0ms	(* (* 2.0 PI) u2)
691.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify51.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (11.0ms)

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

prune338.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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

rewrite16.0ms

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

series1.4s

Counts

4 → 12

Calls

4 calls:

451.0ms	(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
257.0ms	(pow (* -2.0 (log u1)) 0.5)
37.0ms	(* (* 2.0 PI) u2)
688.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 1 (10.0ms)

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

prune278.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ 1 u1))
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)
0.2b	(* u2 PI)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-exp-log`
59×	`pow-exp`
58×	`prod-exp`
29×	`pow-to-exp`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`log-prod`
9×	`pow1` `times-frac`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `rem-log-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `pow-prod-down` `log-pow`
2×	`pow-pow` `div-exp`
1×	`unpow-prod-down` `log-div` `rec-exp` `pow-flip` `1-exp` `log-rec` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `inv-pow` `unswap-sqr` `sqr-pow`

Counts

4 → 109

Calls

4 calls:

2.0ms	(log (/ 1 u1))
14.0ms	(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)
6.0ms	(* u2 PI)

series1.9s

Counts

4 → 12

Calls

4 calls:

114.0ms	(log (/ 1 u1))
1.1s	(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)
578.0ms	(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)
20.0ms	(* u2 PI)

simplify51.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	501	915
1	1420	861
2	5001	850

prune367.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
20×	`cbrt-prod` `add-cbrt-cube`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
14×	`unpow-prod-down` `cube-prod`
13×	`prod-exp`
10×	`pow1` `div-exp` `pow-exp`
5×	`cbrt-unprod` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `pow-prod-down` `associate-/r*` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `unpow3` `sqr-pow`
1×	`cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `associate-l` `clear-num` `-commutative` `rem-cbrt-cube` `associate-/l`

Counts

4 → 119

Calls

4 calls:

7.0ms	(* (* 2.0 PI) u2)
4.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
3.0ms	(cbrt (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3))
5.0ms	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

series2.2s

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 PI) u2)
693.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
682.0ms	(cbrt (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3))
788.0ms	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

simplify65.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	503	909
1	2311	848
2	5001	840

prune362.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes313.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
135.0ms	8000×	pre	80	true