Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 59.527588%

Guaranteed chance to sample good point: 68.194842%

Results

19.0ms	256×	body	80	valid
2.0ms	24×	body	80	nan
1.0ms	16×	body	80	invalid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	12
1	84	12
2	245	12
3	581	12
4	1280	12
5	2462	12
6	5001	12

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 6.3b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `associate-+l+` `add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*l/` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

10.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
9.0ms	(* (- x 0.5) (log x))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series120.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
38.0ms	(- (* (- x 0.5) (log x)) x)
22.0ms	(* (- x 0.5) (log x))
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	543	875
1	1816	820
2	5001	763

prune230.0ms

Filtered

83 candidates to 110 candidates (-32.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	97	13	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 5.0b

Counts

111 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(* (- x 0.5) (log x))
0.3b	(+ (* (- x 0.5) (log x)) (- 0.91893853320467 x))
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac` `add-log-exp`
8×	`associate-l` `associate-*l/`
7×	`associate-r`
6×	`distribute-rgt-in` `associate-+l+` `flip3--` `distribute-lft-in` `flip--`
4×	`frac-add`
3×	`associate-/r` `associate-/l`
2×	`associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `log-pow` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 103

Calls

4 calls:

8.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
7.0ms	(* (- x 0.5) (log x))
10.0ms	(+ (* (- x 0.5) (log x)) (- 0.91893853320467 x))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series93.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
22.0ms	(* (- x 0.5) (log x))
37.0ms	(+ (* (- x 0.5) (log x)) (- 0.91893853320467 x))
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	698	970
1	2640	893
2	5001	867

prune216.0ms

Filtered

86 candidates to 115 candidates (-33.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	114	14	128

Merged error: 5.0b

Counts

128 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series91.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
22.0ms	(cbrt x)
22.0ms	(cbrt x)
25.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify95.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	231	498
1	697	460
2	3102	429
3	5001	426

prune170.0ms

Filtered

59 candidates to 74 candidates (-25.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	75	13	88

Merged error: 5.0b

Counts

88 → 13

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
5.0b	(pow x 1/3)
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log`
6×	`cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-/r` `associate-/l`
2×	`pow1/3` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow1/3` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(pow x 1/3)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series90.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
22.0ms	(cbrt x)
21.0ms	(pow x 1/3)
25.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify38.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	283	499
1	1126	444
2	5001	409

prune149.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	81	13	94

Merged error: 5.0b

Counts

94 → 13

regimes552.0ms

Accuracy

79.3% (0.3b remaining)

Error of 5.2b against oracle of 4.9b and baseline of 6.2b

bsearch48.0ms

Steps

Iters	Range		Point
8	1.5645001152328957e+149	1.0266221152892574e+153	3.061596538394931e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	35
1	65	35

end0.0ms

sample2.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 59.527588%

Guaranteed chance to sample good point: 68.194842%

Results

594.0ms	8000×	body	80	valid
53.0ms	772×	body	80	nan
52.0ms	694×	body	80	invalid

Details

sample1.1s

simplify52.0ms

prune4.0ms

localize17.0ms

rewrite39.0ms

series120.0ms

simplify51.0ms

prune230.0ms

localize17.0ms

rewrite41.0ms

series93.0ms

simplify70.0ms

prune216.0ms

localize26.0ms

rewrite16.0ms

series91.0ms

simplify95.0ms

prune170.0ms

localize32.0ms

rewrite17.0ms

series90.0ms

simplify38.0ms

prune149.0ms

regimes552.0ms

bsearch48.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling