Details

sample351.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify64.0ms

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

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

rewrite106.0ms

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:

56.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms	(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:

420.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
247.0ms	(pow (* -2.0 (log u1)) 0.5)
35.0ms	(* (* 2.0 PI) u2)
656.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify66.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	507	728
1	2155	656
2	5001	656

prune324.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize18.0ms

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

rewrite82.0ms

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:

46.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms	(pow (* -2.0 (log u1)) 0.5)
19.0ms	(* (* 2.0 PI) u2)
8.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

425.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
251.0ms	(pow (* -2.0 (log u1)) 0.5)
30.0ms	(* (* 2.0 PI) u2)
651.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	438	710
1	1838	655
2	5001	655

prune311.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

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:

18.0ms	(* (* 2.0 PI) u2)
16.0ms	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
28.0ms	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
25.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.1s

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* 2.0 PI) u2)
774.0ms	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
656.0ms	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
661.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify43.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	396	631
1	1598	565
2	5001	564

prune346.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
24×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-l` `add-cbrt-cube`
13×	`prod-exp`
11×	`pow1` `times-frac`
8×	`associate-r`
6×	`log-prod`
5×	`cbrt-unprod`
4×	`log-div` `exp-prod` `div-exp` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`exp-sum` `pow-prod-down` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `exp-diff` `log-pow` `*-commutative` `flip-+`
1×	`cbrt-undiv` `unpow-prod-down` `rem-log-exp` `associate-*l/` `div-inv` `rem-exp-log`

Counts

4 → 90

Calls

4 calls:

80.0ms	(log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
16.0ms	(* (* 2.0 PI) u2)
81.0ms	(exp (log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
25.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.6s

Counts

4 → 12

Calls

4 calls:

504.0ms	(log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
37.0ms	(* (* 2.0 PI) u2)
433.0ms	(exp (log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
666.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify57.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	511	1079
1	1983	972
2	5001	954

prune359.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes431.0ms

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	24	10
1	24	10

end0.0ms

sample964.0ms

Algorithm

intervals

Results

653.0ms	8000×	body	80	valid
110.0ms	8000×	pre	80	true