Details

sample41.0ms

Algorithm

intervals

Results

20.0ms

297×

body

valid

simplify59.0ms

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

prune14.0ms

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: 28.4b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma z 3.13060547623 11.1667541262) z t)
0.0b	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
1.9b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
27.5b	(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 (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
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)

series898.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
50.0ms	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
116.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
703.0ms	(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)

simplify111.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	265	578
1	824	514
2	3565	508
3	5001	506

prune396.0ms

Filtered

71 candidates to 60 candidates (84.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	7	73

Merged error: 0.3b

Counts

73 → 7

localize8.0ms

Local error

Found 2 expressions with local error:

2.6b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
8.1b	(/ t (pow z 2))

rewrite7.0ms

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))

series77.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
22.0ms	(/ t (pow z 2))

simplify113.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (20.0ms)

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

prune180.0ms

Filtered

67 candidates to 44 candidates (65.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	67	7	74

Merged error: 0.3b

Counts

74 → 7

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (/ t z) z)
2.6b	(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

rewrite10.0ms

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)

simplify38.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (31.0ms)

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

prune236.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	88	7	95

Merged error: 0.3b

Counts

95 → 7

localize21.0ms

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)
0.1b	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
2.0b	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
27.5b	(fma (* y (/ 1 (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)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 91

Calls

4 calls:

1.0ms	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
3.0ms	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
7.0ms	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
1.0ms	(fma (* y (/ 1 (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)

series965.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
76.0ms	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
112.0ms	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
725.0ms	(fma (* y (/ 1 (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)

simplify51.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	374	891
1	1492	776
2	5002	744

prune424.0ms

Filtered

103 candidates to 67 candidates (65.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	104	6	110

Merged error: 0.3b

Counts

110 → 6

regimes604.0ms

Accuracy

96.5% (0.9b remaining)

Error of 1.4b against oracle of 0.4b and baseline of 27.2b

bsearch281.0ms

Steps

Iters	Range		Point
9	6264205.521814494	521787013716.8479	517383397943.66113
11	-4.513793186893353e+38	-1.2908930576288794e+18	-1.459516936470268e+28

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	14
1	37	14

end0.0ms

sample943.0ms

Algorithm

intervals

Results

625.0ms

8893×

body

valid