Details

sample282.0ms

Algorithm

intervals

Results

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

simplify67.0ms

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

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:

35.0ms	(+ (* (* (/ 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)
8.0ms	(* (* 2.0 PI) u2)
12.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts

4 → 12

Calls

4 calls:

461.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
262.0ms	(pow (* -2.0 (log u1)) 0.5)
39.0ms	(* (* 2.0 PI) u2)
692.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify63.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (54.0ms)

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

prune366.0ms

Filtered

108 candidates to 80 candidates (74.1%)

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

rewrite37.0ms

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

Counts

4 → 93

Calls

4 calls:

22.0ms	(+ (* (* 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	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series1.5s

Counts

4 → 12

Calls

4 calls:

460.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
270.0ms	(pow (* -2.0 (log u1)) 0.5)
32.0ms	(* (* 2.0 PI) u2)
697.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	456	752
1	1915	695
2	5001	695

prune352.0ms

Filtered

105 candidates to 81 candidates (77.1%)

Pruning

7 alts after pruning (6 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	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.3b	(exp (log (/ (pow (* -2.0 (log u1)) 0.5) 6.0)))
0.3b	(log (/ (pow (* -2.0 (log u1)) 0.5) 6.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
38×	`log-prod`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
26×	`add-exp-log`
19×	`exp-sum`
11×	`pow1` `add-cbrt-cube`
10×	`unpow-prod-down` `sqr-pow`
8×	`div-exp`
5×	`rem-log-exp` `prod-exp` `associate-/l*`
4×	`expm1-log1p-u` `exp-prod` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `pow-prod-down` `associate-/r*` `cbrt-unprod` `div-inv`
2×	`pow-to-exp` `log-div` `log-pow`
1×	`cbrt-undiv` `frac-2neg` `exp-diff` `associate-l` `clear-num` `*-commutative` `rem-exp-log`

Counts

4 → 129

Calls

4 calls:

10.0ms	(* (* 2.0 PI) u2)
3.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
4.0ms	(exp (log (/ (pow (* -2.0 (log u1)) 0.5) 6.0)))
3.0ms	(log (/ (pow (* -2.0 (log u1)) 0.5) 6.0))

series2.3s

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 PI) u2)
697.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
699.0ms	(exp (log (/ (pow (* -2.0 (log u1)) 0.5) 6.0)))
816.0ms	(log (/ (pow (* -2.0 (log u1)) 0.5) 6.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	434	1041
1	1471	984
2	5002	955

prune525.0ms

Filtered

141 candidates to 107 candidates (75.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
0.4b	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
0.7b	(pow (pow (* -2.0 (log u1)) 0.5) 3)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
44×	`cbrt-prod`
25×	`unpow-prod-down`
22×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
19×	`cube-prod`
18×	`add-exp-log`
16×	`times-frac`
15×	`sqr-pow`
14×	`associate-l` `unswap-sqr`
13×	`add-cbrt-cube`
11×	`pow1`
6×	`pow-exp` `prod-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`pow-to-exp` `*-commutative`
1×	`cbrt-undiv` `pow-pow` `pow1/3` `div-exp` `associate-*l/` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 141

Calls

4 calls:

6.0ms	(* (* 2.0 PI) u2)
19.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
2.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
3.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

series1.8s

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* 2.0 PI) u2)
724.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
678.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
327.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

simplify72.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	622	1074
1	2551	1028
2	5002	1003

prune438.0ms

Filtered

153 candidates to 95 candidates (62.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes385.0ms

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

sample1.0s

Algorithm

intervals

Results

711.0ms	8000×	body	80	valid
130.0ms	8000×	pre	80	true