Details

sample281.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify66.0ms

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

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (* (/ 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))

rewrite53.0ms

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×	`expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 96

Calls

4 calls:

27.0ms	(+ (* (* (/ 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:

445.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
259.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
677.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify62.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	523	772
1	2229	700
2	5001	697

prune345.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (/ (* 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)

rewrite26.0ms

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`
6×	`add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`pow-unpow` `times-frac` `associate-r` `associate-/r*`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow`
1×	`+-commutative` `unpow-prod-down` `fma-def` `frac-2neg` `flip3-+` `associate-l` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `associate-/l` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

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

series1.4s

Counts

4 → 12

Calls

4 calls:

453.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
253.0ms	(pow (* -2.0 (log u1)) 0.5)
30.0ms	(* (* 2.0 PI) u2)
678.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	472	641
1	2101	569
2	5002	564

prune285.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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)
0.9b	(exp (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

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

series1.7s

Counts

4 → 12

Calls

4 calls:

255.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
682.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
723.0ms	(exp (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	373	525
1	1494	464
2	5001	464

prune316.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-exp-log`
54×	`prod-exp`
35×	`add-sqr-sqrt`
34×	`add-cbrt-cube`
23×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
21×	`div-exp`
19×	`associate-l`
14×	`pow-exp` `cbrt-unprod`
13×	`associate-r`
9×	`pow1`
8×	`unswap-sqr`
7×	`pow-to-exp`
6×	`cbrt-undiv` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative` `div-inv` `associate-/l*`
2×	`unpow-prod-down` `associate-*l/` `associate-/r/`
1×	`flip3--` `frac-2neg` `clear-num` `flip--`

Counts

4 → 144

Calls

4 calls:

6.0ms	(* (* 2.0 PI) u2)
18.0ms	(* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
10.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
36.0ms	(/ (fma (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (- (* 0.5 0.5))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) u2)
698.0ms	(* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
687.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
853.0ms	(/ (fma (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (- (* 0.5 0.5))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

simplify115.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	944	2481
1	4110	2193
2	5002	2164

prune664.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes417.0ms

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	26	12
1	26	12

end0.0ms

sample936.0ms

Algorithm

intervals

Results

651.0ms	8000×	body	80	valid
131.0ms	8000×	pre	80	true