Details

sample52.0ms

Algorithm

intervals

Results

23.0ms

282×

body

valid

simplify60.0ms

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: 28.7b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
0.1b	(fma (fma z 3.13060547623 11.1667541262) z t)
1.5b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
28.2b	(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 (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
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)

series937.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
28.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
108.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
710.0ms	(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)

simplify128.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (115.0ms)

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

prune385.0ms

Filtered

71 candidates to 60 candidates (84.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	67	6	73

Merged error: 0.0b

Counts

73 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (/ t (pow z 2)))
3.0b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
6.5b	(/ 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:

9.0ms	(+ 3.13060547623 (/ t (pow z 2)))
1.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
5.0ms	(/ t (pow z 2))

series102.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ 3.13060547623 (/ t (pow z 2)))
53.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
22.0ms	(/ t (pow z 2))

simplify134.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (127.0ms)

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

prune204.0ms

Filtered

87 candidates to 59 candidates (67.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	86	7	93

Merged error: 0.0b

Counts

93 → 7

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (* (/ 1 z) (/ t z)))
0.2b	(* (/ 1 z) (/ t z))
3.0b	(fma y (+ 3.13060547623 (* (/ 1 z) (/ t z))) x)

rewrite17.0ms

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)

series82.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 3.13060547623 (* (/ 1 z) (/ t z)))
22.0ms	(* (/ 1 z) (/ t z))
45.0ms	(fma y (+ 3.13060547623 (* (/ 1 z) (/ t z))) x)

simplify54.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (47.0ms)

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

prune200.0ms

Filtered

93 candidates to 64 candidates (68.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	93	7	100

Merged error: 0.0b

Counts

100 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
16.3b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
16.3b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
28.2b	(fma (* (/ 1 (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (/ y (cbrt (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)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series847.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
148.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
147.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
403.0ms	(fma (* (/ 1 (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (/ y (cbrt (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)

simplify65.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	186	768
1	514	682
2	2091	652
3	5003	625

prune370.0ms

Filtered

61 candidates to 56 candidates (91.8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	61	7	68

Merged error: 0.0b

Counts

68 → 7

regimes543.0ms

Accuracy

97.1% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 26.7b

bsearch155.0ms

Steps

Iters	Range		Point
6	2.3207200166070574e+43	1.0035707230662013e+44	3.6643853739374403e+43
5	-5.405497302646586e+52	-1.6395025180632993e+52	-1.7382398347914852e+52

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	14
1	38	14

end0.0ms

sample930.0ms

Algorithm

intervals

Results

617.0ms

8849×

body

valid