Details

sample43.0ms

Algorithm

intervals

Results

22.0ms

277×

body

valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

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: 29.4b

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)
1.2b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
29.0b	(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 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)

series902.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
29.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
110.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
723.0ms	(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)

simplify118.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (109.0ms)

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

prune403.0ms

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: 1.0b

Counts

73 → 7

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (/ t (pow z 2)))
3.1b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
6.3b	(/ t (pow z 2))

rewrite18.0ms

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))

series105.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ 3.13060547623 (/ t (pow z 2)))
50.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
27.0ms	(/ t (pow z 2))

simplify153.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (141.0ms)

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

prune240.0ms

Filtered

87 candidates to 59 candidates (67.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	86	8	94

Merged error: 1.0b

Counts

94 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
8.7b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
8.7b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
29.0b	(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)))
2.0ms	(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))
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)

series784.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
101.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
100.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
404.0ms	(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)

simplify150.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (131.0ms)

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

prune507.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	93	8	101

Merged error: 1.0b

Counts

101 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

15.9b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
15.9b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
15.9b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
29.0b	(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)

series875.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
154.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
158.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
414.0ms	(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)

simplify75.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (64.0ms)

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

prune419.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	61	8	69

Merged error: 1.0b

Counts

69 → 8

regimes730.0ms

Accuracy

97.1% (0.8b remaining)

Error of 1.2b against oracle of 0.4b and baseline of 28.1b

bsearch196.0ms

Steps

Iters	Range		Point
7	1.1923609921951673e+42	2.5163598985651363e+43	2.0732080743412183e+42
6	-2.7167357396098293e+32	-2.672507666642824e+31	-9.995160699101284e+31

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	14
1	38	14

end0.0ms

sample1.1s

Algorithm

intervals

Results

594.0ms

8850×

body

valid