Details

sample40.0ms

Algorithm

intervals

Results

19.0ms

282×

body

valid

simplify62.0ms

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

prune20.0ms

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: 27.2b

Counts

2 → 2

localize20.0ms

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)
2.7b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.5b	(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 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)

series941.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
30.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
119.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
748.0ms	(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)

simplify115.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	269	563
1	827	501
2	3522	493
3	5002	491

prune344.0ms

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

localize25.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
9.8b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
9.8b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.5b	(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)

series840.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
108.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
116.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
431.0ms	(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)

simplify144.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	313	1000
1	985	909
2	4342	879
3	5001	877

prune461.0ms

Filtered

93 candidates to 69 candidates (74.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Merged error: 0.2b

Counts

100 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

18.7b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
18.7b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
18.7b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.5b	(fma (/ (/ y (* (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)))) (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 (/ (/ y (* (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)))) (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)

series1.5s

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
166.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
159.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
954.0ms	(fma (/ (/ y (* (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)))) (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 (54.0ms)

Iter	Nodes	Cost
0	181	755
1	472	661
2	1648	642
3	5002	619

prune385.0ms

Filtered

61 candidates to 56 candidates (91.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	61	7	68

Merged error: 0.2b

Counts

68 → 7

localize25.0ms

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)
2.6b	(/ (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771) y)
27.7b	(/ (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) (/ (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771) y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

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	(/ (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771) y)
7.0ms	(/ (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) (/ (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771) y))

series483.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
31.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
97.0ms	(/ (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771) y)
311.0ms	(/ (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) (/ (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771) y))

simplify76.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	531	1885
1	1964	1771
2	5001	1769

prune604.0ms

Filtered

141 candidates to 116 candidates (82.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	140	8	148

Merged error: 0.2b

Counts

148 → 8

regimes623.0ms

Accuracy

97.5% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 28.0b

bsearch280.0ms

Steps

Iters	Range		Point
10	1.0775587966213066e+52	1.6132141776490707e+64	8.338434349578698e+52
8	-2.368357192809402e+37	-6.033090478811128e+32	-8.792536100027591e+36

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	17
1	49	17
2	52	17
3	52	17

end0.0ms

sample908.0ms

Algorithm

intervals

Results

605.0ms

8833×

body

valid