Details

sample47.0ms

Algorithm

intervals

Results

24.0ms

294×

body

valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune15.0ms

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: 28.9b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
0.1b	(fma (fma z 3.13060547623 11.1667541262) z t)
1.9b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
28.3b	(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)

rewrite7.0ms

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 15.234687407) z 31.4690115749) z 11.9400905721)
1.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
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)

series852.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
26.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
104.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
687.0ms	(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)

simplify110.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	270	563
1	830	501
2	3551	493
3	5002	491

prune374.0ms

Filtered

71 candidates to 60 candidates (84.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	65	8	73

Merged error: 0.5b

Counts

73 → 8

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (/ t (pow z 2)))
2.9b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
9.7b	(/ t (pow z 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`unpow-prod-down`
8×	`add-exp-log` `associate-/r*`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow2` `sqr-pow`
3×	`pow1` `expm1-log1p-u` `fma-def` `div-exp` `log1p-expm1-u` `associate-/l*`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `sum-log` `flip-+` `fma-udef` `div-inv` `distribute-lft-out`

Counts

3 → 78

Calls

3 calls:

10.0ms	(+ 3.13060547623 (/ t (pow z 2)))
1.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
5.0ms	(/ t (pow z 2))

series106.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ 3.13060547623 (/ t (pow z 2)))
48.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
26.0ms	(/ t (pow z 2))

simplify145.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	255	414
1	847	369
2	4454	360
3	5001	359

prune211.0ms

Filtered

87 candidates to 59 candidates (67.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	86	9	95

Merged error: 0.5b

Counts

95 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (* (/ 1 z) (/ t z)))
0.2b	(* (/ 1 z) (/ t z))
2.9b	(fma y (+ 3.13060547623 (* (/ 1 z) (/ t z))) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `times-frac`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
8×	`div-exp` `prod-exp`
6×	`unswap-sqr`
5×	`pow1` `add-log-exp`
4×	`cbrt-undiv` `cbrt-unprod`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`rec-exp` `1-exp` `div-inv`
1×	`+-commutative` `frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative` `flip-+` `fma-udef`

Counts

3 → 84

Calls

3 calls:

3.0ms	(+ 3.13060547623 (* (/ 1 z) (/ t z)))
10.0ms	(* (/ 1 z) (/ t z))
1.0ms	(fma y (+ 3.13060547623 (* (/ 1 z) (/ t z))) x)

series75.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 3.13060547623 (* (/ 1 z) (/ t z)))
16.0ms	(* (/ 1 z) (/ t z))
43.0ms	(fma y (+ 3.13060547623 (* (/ 1 z) (/ t z))) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	426	495
1	1969	421
2	5001	381

prune207.0ms

Filtered

93 candidates to 64 candidates (68.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	93	9	102

Merged error: 0.5b

Counts

102 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
9.6b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
9.6b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
28.3b	(fma (* (/ 1 (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ y (sqrt (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)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

4.0ms	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
1.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
2.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(fma (* (/ 1 (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ y (sqrt (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)

series772.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
99.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
99.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
399.0ms	(fma (* (/ 1 (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ y (sqrt (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)

simplify148.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (129.0ms)

Iter	Nodes	Cost
0	316	998
1	1006	909
2	4476	879
3	5001	877

prune432.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	3	5
Picked	0	1	1
Done	1	2	3
Total	94	8	102

Merged error: 0.5b

Counts

102 → 8

regimes523.0ms

Accuracy

96.6% (0.9b remaining)

Error of 1.4b against oracle of 0.5b and baseline of 26.8b

bsearch268.0ms

Steps

Iters	Range		Point
6	5.449069412576061e+25	2.826963092117455e+26	1.2370298024693897e+26
10	-1.2853898846943825e+28	-31770318212.664288	-1.5402377518021936e+26

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	36
1	53	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

763.0ms

8888×

body

valid