Details

analyze1.4s (20.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.5s (22.1%)

Results

920.0ms	7050×	body	128	valid
163.0ms	372×	body	1024	valid
126.0ms	425×	body	512	valid
92.0ms	740×	body	128	invalid
72.0ms	343×	body	256	valid
31.0ms	66×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify138.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

10.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.4b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	16.8b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	4.5b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series58.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

38.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
20.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite73.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

541×	`fma-def_binary64`
271×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`

Counts

2 → 78

Calls

2 calls:

71.0ms	(/.f64 (-.f64 t z) (-.f64 a t))
71.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	257	27
2	3781	27
3	5388	27
0	0	0
1	0	0

simplify94.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

901×	`fma-def_binary64`
642×	`times-frac_binary64`
593×	`fma-neg_binary64`
512×	`cancel-sign-sub-inv_binary64`
365×	`sub-neg_binary64`

Counts

174 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	3029
1	521	3008
2	1916	2394
3	4513	2376
4	5051	2376

prune140.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	149	7	156
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	151	7	158

Error

0.0b

Counts

158 → 7

Alt Table

Status	Error	Program
	12.0b	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
▶	11.3b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	33.7b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
	47.5b	(/.f64 (+.f64 (pow.f64 (.f64 y (/.f64 (-.f64 t z) (-.f64 a t))) 3) (pow.f64 (+.f64 y x) 3)) (fma.f64 (.f64 y (/.f64 (-.f64 t z) (-.f64 a t))) (.f64 y (/.f64 (-.f64 t z) (-.f64 a t))) (-.f64 (pow.f64 (+.f64 y x) 2) (.f64 (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))) (+.f64 y x)))))
	45.0b	(fma.f64 y (pow.f64 (sqrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) 2) (+.f64 x y))
	27.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	37.0b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 3998 to 1331 computations (66.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
✓	5.5b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))

series60.0ms (0.9%)

Counts

3 → 120

Calls

3 calls:

35.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
16.0ms	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
8.0ms	(/.f64 1 (-.f64 a t))

rewrite71.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

268×	`expm1-udef_binary64`
268×	`log1p-udef_binary64`
253×	`fma-neg_binary64`
150×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`

Counts

3 → 93

Calls

3 calls:

69.0ms	(/.f64 1 (-.f64 a t))
69.0ms	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
69.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	34
1	290	34
2	3877	34
3	4947	34
0	0	0
1	0	0

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

656×	`times-frac_binary64`
556×	`associate-/l*_binary64`
515×	`cancel-sign-sub-inv_binary64`
372×	`sub-neg_binary64`
197×	`fma-neg_binary64`

Counts

213 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	3518
1	577	3479
2	2099	2838
3	5004	2838

prune133.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	184	7	191

Error

0.0b

Counts

191 → 7

Alt Table

Status	Error	Program
▶	12.0b	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
✓	11.3b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	33.7b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
	47.5b	(/.f64 (+.f64 (pow.f64 (.f64 y (/.f64 (-.f64 t z) (-.f64 a t))) 3) (pow.f64 (+.f64 y x) 3)) (fma.f64 (.f64 y (/.f64 (-.f64 t z) (-.f64 a t))) (.f64 y (/.f64 (-.f64 t z) (-.f64 a t))) (-.f64 (pow.f64 (+.f64 y x) 2) (.f64 (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))) (+.f64 y x)))))
	45.0b	(fma.f64 y (pow.f64 (sqrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) 2) (+.f64 x y))
	27.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	37.0b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 4502 to 1632 computations (63.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z)))
✓	0.0b	(/.f64 y (-.f64 a t))
✓	4.5b	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
✓	12.8b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))

series137.0ms (2.1%)

Counts

4 → 192

Calls

4 calls:

47.0ms	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
46.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z)))
29.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))
15.0ms	(/.f64 y (-.f64 a t))

rewrite93.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

282×	`expm1-udef_binary64`
282×	`log1p-udef_binary64`
153×	`egg-rr`
153×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`

Counts

4 → 153

Calls

4 calls:

87.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z)))
87.0ms	(/.f64 y (-.f64 a t))
87.0ms	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
87.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	55
1	287	51
2	4341	51
3	5203	51
0	0	0
1	0	0

simplify110.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

926×	`cancel-sign-sub-inv_binary64`
711×	`times-frac_binary64`
583×	`sub-neg_binary64`
277×	`associate--r+_binary64`
267×	`fma-neg_binary64`

Counts

345 → 286

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	248	5889
1	709	5739
2	2533	5184
3	5094	5184

prune193.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	2	3	5
Picked	0	1	1
Done	1	0	1
Total	287	6	293

Error

0.0b

Counts

293 → 6

Alt Table

Status	Error	Program
✓	12.0b	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
	33.7b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
	11.8b	(+.f64 y (+.f64 x (/.f64 (-.f64 t z) (/.f64 (-.f64 a t) y))))
▶	11.3b	(+.f64 y (+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))))
	27.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	37.0b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 7767 to 2380 computations (69.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z))))
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 t z))
✓	2.7b	(/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))
✓	3.3b	(+.f64 y (+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))))

series136.0ms (2%)

Counts

4 → 204

Calls

4 calls:

42.0ms	(+.f64 y (+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))))
40.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z))))
31.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))
22.0ms	(/.f64 (-.f64 a t) (-.f64 t z))

rewrite103.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

292×	`log1p-udef_binary64`
159×	`add-sqr-sqrt_binary64`
158×	`egg-rr`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`

Counts

4 → 158

Calls

4 calls:

97.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z))))
97.0ms	(/.f64 (-.f64 a t) (-.f64 t z))
97.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))
97.0ms	(+.f64 y (+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	58
1	296	54
2	4689	54
3	5183	54
0	0	0
1	0	0

simplify150.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

907×	`fma-neg_binary64`
861×	`times-frac_binary64`
731×	`sub-neg_binary64`
342×	`associate--r+_binary64`
281×	`associate--l+_binary64`

Counts

362 → 312

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	6380
1	803	6176
2	2952	5591
3	4971	5591
4	5527	5591

prune207.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	312	0	312
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	312	6	318

Error

0.0b

Counts

318 → 6

Alt Table

Status	Error	Program
✓	12.0b	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
	33.7b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
	11.8b	(+.f64 y (+.f64 x (/.f64 (-.f64 t z) (/.f64 (-.f64 a t) y))))
✓	11.3b	(+.f64 y (+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))))
	27.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	37.0b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 8294 to 2550 computations (69.3% saved)

regimes1.6s (24.3%)

Accuracy

Total 6.8b remaining (99.1%)

Threshold costs 0b (0%)

Counts

131 → 4

Compiler

Compiled 16068 to 9660 computations (39.9% saved)

bsearch90.0ms (1.4%)

Steps

Iters	Range		Point
8	1.001585356213362e+229	4.18766107965653e+231	2.3034710670409075e+230
10	5.387703369790426e-288	9.868680093565099e-278	5.542187589704571e-282
10	-1.998910459795362e+63	-2.7816405878360242e+53	-3.137181392971283e+60

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`+-commutative_binary64`
10×	`*-commutative_binary64`
10×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	91
1	50	91
2	66	91
3	81	91
4	89	91
5	92	91
6	93	91
7	93	91

end96.0ms (1.4%)

Compiler: Compiled 262 to 135 computations (48.5% saved)

Details

analyze1.4s (20.5%)

sample1.5s (22.1%)

simplify138.0ms (2.1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series58.0ms (0.9%)

rewrite73.0ms (1.1%)

simplify94.0ms (1.4%)

prune140.0ms (2.1%)

localize9.0ms (0.1%)

series60.0ms (0.9%)

rewrite71.0ms (1.1%)

simplify75.0ms (1.1%)

prune133.0ms (2%)

localize12.0ms (0.2%)

series137.0ms (2.1%)

rewrite93.0ms (1.4%)

simplify110.0ms (1.7%)

prune193.0ms (2.9%)

localize11.0ms (0.2%)

series136.0ms (2%)

rewrite103.0ms (1.5%)

simplify150.0ms (2.3%)

prune207.0ms (3.1%)

regimes1.6s (24.3%)

bsearch90.0ms (1.4%)

simplify5.0ms (0.1%)

end96.0ms (1.4%)

Profiling