Details

sample41.0ms

Algorithm

intervals

Results

20.0ms

284×

body

valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	62	11
1	132	11
2	377	10
3	1105	10
4	3599	10
5	5001	10

prune19.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 30.2b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma z 3.13060547623 11.1667541262) z t)
0.0b	(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
2.1b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
29.4b	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

1.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
1.0ms	(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
3.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

series922.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
89.0ms	(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
105.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
700.0ms	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

simplify107.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	269	578
1	828	514
2	3590	508
3	5001	504

prune381.0ms

Filtered

71 candidates to 60 candidates (84.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	66	7	73

Merged error: 0.2b

Counts

73 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
0.0b	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
2.1b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
11.4b	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma a z b) x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

1.0ms	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
1.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
3.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma a z b) x)

series565.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
40.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
113.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
360.0ms	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma a z b) x)

simplify123.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	265	555
1	845	501
2	3585	491
3	5002	488

prune296.0ms

Filtered

71 candidates to 62 candidates (87.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	71	7	78

Merged error: 0.0b

Counts

78 → 7

localize9.0ms

Local error

Found 2 expressions with local error:

3.3b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
9.7b	(/ t (pow z 2))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
8×	`associate-/r*`
7×	`add-exp-log`
4×	`add-cbrt-cube` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 61

Calls

2 calls:

1.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
5.0ms	(/ t (pow z 2))

series76.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
27.0ms	(/ t (pow z 2))

simplify118.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	191	332
1	664	290
2	3660	281
3	5001	281

prune179.0ms

Filtered

67 candidates to 44 candidates (65.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	66	8	74

Merged error: 0.0b

Counts

74 → 8

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (/ t z) z)
3.3b	(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-/l*`
7×	`add-exp-log` `add-cbrt-cube`
5×	`div-inv`
3×	`cbrt-undiv` `div-exp` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`frac-2neg` `clear-num` `fma-udef` `associate-/l/`

Counts

2 → 82

Calls

2 calls:

6.0ms	(/ (/ t z) z)
1.0ms	(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

series78.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(/ (/ t z) z)
56.0ms	(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	349	537
1	1283	488
2	5001	480

prune188.0ms

Filtered

88 candidates to 61 candidates (69.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	88	8	96

Merged error: 0.0b

Counts

96 → 8

regimes628.0ms

Accuracy

95.4% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 22.6b

bsearch247.0ms

Steps

Iters	Range		Point
9	3.9382216925127664e+36	2.498391355682403e+42	1.5541736008584482e+37
8	-5.055849782424677e+30	-2.2430599195790272e+27	-3.236446819036177e+28

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	19
1	44	19

end0.0ms

sample939.0ms

Algorithm

intervals

Results

633.0ms

8903×

body

valid