Details

analyze1.3s (22.9%)

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
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.1s (20.2%)

Results

1.0s	8256×	body	128	valid
87.0ms	728×	body	128	invalid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess46.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

878×	`div-sub_binary64`
306×	`fma-def_binary64`
304×	`times-frac_binary64`
248×	`fma-neg_binary64`
219×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	176
1	158	176
2	306	176
3	640	176
4	1557	176
5	3631	176
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify25.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-neg_binary64`
663×	`div-sub_binary64`
241×	`cancel-sign-sub-inv_binary64`
213×	`distribute-neg-frac_binary64`
210×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	53	16
3	100	16
4	210	16
5	422	16
6	913	16
7	2616	16

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

10.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.2b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	9.9b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series54.0ms (1%)

Counts

2 → 69

Calls

24 calls:

5.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	a	inf
4.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	z	0
4.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	t	-inf
4.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	a	0
3.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	a	-inf

rewrite64.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

412×	`fma-def_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
195×	`fma-neg_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	253	23
2	3872	23

Stop Event

1×	node limit

Counts

2 → 134

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/r*_binary64`
549×	`fma-def_binary64`
458×	`cancel-sign-sub-inv_binary64`
174×	`sub-neg_binary64`
149×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	2839
1	409	2698
2	1881	2491

Stop Event

1×	node limit

Counts

203 → 174

prune136.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	168	6	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	169	6	175

Error

0.0b

Counts

175 → 6

Alt Table

Status	Error	Program
▶	10.2b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (/.f64 (.f64 y z) (-.f64 t (*.f64 z a)))))
	35.4b	(.f64 (/.f64 y (-.f64 t (.f64 z a))) (neg.f64 z))
	39.5b	(/.f64 (neg.f64 (/.f64 (-.f64 x (*.f64 y z)) z)) a)
	42.7b	(-.f64 (+.f64 (fma.f64 (/.f64 y (pow.f64 a 3)) (.f64 (/.f64 t z) (/.f64 t z)) (/.f64 y a)) (.f64 (/.f64 t (.f64 a a)) (-.f64 (/.f64 y z) (/.f64 (/.f64 x z) z)))) (/.f64 x (.f64 z a)))
	11.1b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)) (/.f64 (fma.f64 y (neg.f64 z) x) (cbrt.f64 (-.f64 t (*.f64 z a)))))
	10.4b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))

Compiler

Compiled 4556 to 1426 computations (68.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.7b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	9.4b	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))

series65.0ms (1.2%)

Counts

2 → 96

Calls

24 calls:

6.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))	y	-inf
6.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))	y	0
4.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))	y	inf
4.0ms	(/.f64 x (-.f64 t (*.f64 z a)))	x	-inf
3.0ms	(/.f64 x (-.f64 t (*.f64 z a)))	x	inf

rewrite59.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

669×	`prod-diff_binary64`
230×	`log1p-udef_binary64`
127×	`add-sqr-sqrt_binary64`
119×	`log1p-expm1-u_binary64`
119×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	242	23
2	3568	23

Stop Event

1×	node limit

Counts

2 → 80

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-/r*_binary64`
500×	`associate-l_binary64`
421×	`fma-def_binary64`
252×	`associate-*l/_binary64`
219×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	105	2777
1	332	2657
2	1431	2478

Stop Event

1×	node limit

Counts

176 → 120

prune102.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	118	8	126

Error

0.0b

Counts

126 → 8

Alt Table

Status	Error	Program
	9.0b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (.f64 (/.f64 y (-.f64 t (*.f64 z a))) z)))
	10.4b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))
✓	10.2b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (/.f64 (.f64 y z) (-.f64 t (*.f64 z a)))))
	7.9b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (.f64 y (.f64 z (/.f64 1 (-.f64 t (.f64 z a)))))))
▶	7.8b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (.f64 y (/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) z)))))
	39.5b	(/.f64 (neg.f64 (/.f64 (-.f64 x (*.f64 y z)) z)) a)
	42.7b	(-.f64 (+.f64 (fma.f64 (/.f64 y (pow.f64 a 3)) (.f64 (/.f64 t z) (/.f64 t z)) (/.f64 y a)) (.f64 (/.f64 t (.f64 a a)) (-.f64 (/.f64 y z) (/.f64 (/.f64 x z) z)))) (/.f64 x (.f64 z a)))
	11.1b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)) (/.f64 (fma.f64 y (neg.f64 z) x) (cbrt.f64 (-.f64 t (*.f64 z a)))))

Compiler

Compiled 3612 to 1140 computations (68.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) z))
	2.7b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	3.0b	(.f64 y (/.f64 1 (/.f64 (-.f64 t (.f64 z a)) z)))
✓	7.6b	(/.f64 (-.f64 t (*.f64 z a)) z)

series55.0ms (1%)

Counts

3 → 120

Calls

30 calls:

5.0ms	(.f64 y (/.f64 1 (/.f64 (-.f64 t (.f64 z a)) z)))	y	inf
4.0ms	(.f64 y (/.f64 1 (/.f64 (-.f64 t (.f64 z a)) z)))	y	-inf
3.0ms	(.f64 y (/.f64 1 (/.f64 (-.f64 t (.f64 z a)) z)))	y	0
3.0ms	(/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) z))	t	-inf
2.0ms	(.f64 y (/.f64 1 (/.f64 (-.f64 t (.f64 z a)) z)))	t	-inf

rewrite119.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

887×	`prod-diff_binary64`
321×	`egg-rr`
124×	`add-sqr-sqrt_binary64`
116×	`add-cbrt-cube_binary64`
116×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	243	33
2	3516	33

Stop Event

1×	node limit

Counts

3 → 321

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

725×	`associate-/l*_binary64`
489×	`associate-/r*_binary64`
342×	`fma-def_binary64`
323×	`associate-l_binary64`
190×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	94	2636
1	283	2566
2	1148	2346

Stop Event

1×	node limit

Counts

441 → 362

prune383.0ms (6.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	412	2	414
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	415	7	422

Error

0.0b

Counts

422 → 7

Alt Table

Status	Error	Program
▶	7.9b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (/.f64 1 (/.f64 (/.f64 (-.f64 t (.f64 z a)) z) y))))
	40.5b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (neg.f64 (fma.f64 (.f64 (/.f64 t (pow.f64 a 3)) t) (/.f64 y (*.f64 z z)) (fma.f64 (/.f64 (/.f64 t a) a) (/.f64 y z) (/.f64 y a))))))
	9.0b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (.f64 (/.f64 y (-.f64 t (*.f64 z a))) z)))
	10.4b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))
✓	10.2b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (/.f64 (.f64 y z) (-.f64 t (*.f64 z a)))))
	39.5b	(/.f64 (neg.f64 (/.f64 (-.f64 x (*.f64 y z)) z)) a)
	11.1b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)) (/.f64 (fma.f64 y (neg.f64 z) x) (cbrt.f64 (-.f64 t (*.f64 z a)))))

Compiler

Compiled 18657 to 5974 computations (68% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 1 (/.f64 (/.f64 (-.f64 t (*.f64 z a)) z) y))
	2.7b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	3.1b	(/.f64 (/.f64 (-.f64 t (*.f64 z a)) z) y)
	7.6b	(/.f64 (-.f64 t (*.f64 z a)) z)

series56.0ms (1%)

Counts

2 → 96

Calls

24 calls:

6.0ms	(/.f64 (/.f64 (-.f64 t (*.f64 z a)) z) y)	y	inf
5.0ms	(/.f64 1 (/.f64 (/.f64 (-.f64 t (*.f64 z a)) z) y))	y	-inf
4.0ms	(/.f64 1 (/.f64 (/.f64 (-.f64 t (*.f64 z a)) z) y))	y	inf
3.0ms	(/.f64 1 (/.f64 (/.f64 (-.f64 t (*.f64 z a)) z) y))	y	0
3.0ms	(/.f64 (/.f64 (-.f64 t (*.f64 z a)) z) y)	y	-inf

rewrite60.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

896×	`prod-diff_binary64`
128×	`add-sqr-sqrt_binary64`
120×	`add-cbrt-cube_binary64`
120×	`log1p-expm1-u_binary64`
120×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	248	26
2	3755	26

Stop Event

1×	node limit

Counts

2 → 89

simplify41.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1003×	`times-frac_binary64`
640×	`associate-/l*_binary64`
391×	`associate-/r*_binary64`
307×	`associate-l_binary64`
229×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	1961
1	232	1901
2	934	1782

Stop Event

1×	node limit

Counts

185 → 117

prune383.0ms (6.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	424	1	425
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	425	7	432

Error

0.0b

Counts

432 → 7

Alt Table

Status	Error	Program
✓	10.2b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (/.f64 (.f64 y z) (-.f64 t (*.f64 z a)))))
	3.7b	(+.f64 (/.f64 x (-.f64 t (*.f64 z a))) (neg.f64 (/.f64 y (-.f64 (/.f64 t z) (/.f64 a 1)))))
	9.0b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (.f64 (/.f64 y (-.f64 t (*.f64 z a))) z)))
	10.4b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))
✓	7.9b	(+.f64 (/.f64 x (-.f64 t (.f64 z a))) (neg.f64 (/.f64 1 (/.f64 (/.f64 (-.f64 t (.f64 z a)) z) y))))
	39.5b	(/.f64 (neg.f64 (/.f64 (-.f64 x (*.f64 y z)) z)) a)
	11.1b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)) (/.f64 (fma.f64 y (neg.f64 z) x) (cbrt.f64 (-.f64 t (*.f64 z a)))))

Compiler

Compiled 18753 to 5811 computations (69% saved)

regimes1.1s (20.6%)

Accuracy

Total 2.2b remaining (98.8%)

Threshold costs 0b (0%)

Counts

123 → 3

Compiler

Compiled 17066 to 10462 computations (38.7% saved)

bsearch34.0ms (0.6%)

Algorithm

2×	binary-search

Calls

2 calls:

24.0ms	z
2.0ms	z

Steps

Iters	Point		Range
3.163945609906825e-168	∈ [	3.662928062609174e-172	,	2.725659075317117e-164	]
-1.22074817042731e+59	∈ [	-3.1284530037794014e+72	,	-1.1988877074612637e+59	]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	84
1	52	84
2	71	84
3	81	84
4	85	84

Stop Event

1×

saturated

end102.0ms (1.8%)

Stop Event

1×

fuel

Compiler

Compiled 279 to 137 computations (50.9% saved)

Details

analyze1.3s (22.9%)

sample1.1s (20.2%)

preprocess46.0ms (0.8%)

simplify25.0ms (0.4%)

prune2.0ms (0%)

localize9.0ms (0.2%)

series54.0ms (1%)

rewrite64.0ms (1.2%)

simplify58.0ms (1.1%)

prune136.0ms (2.5%)

localize9.0ms (0.2%)

series65.0ms (1.2%)

rewrite59.0ms (1.1%)

simplify53.0ms (1%)

prune102.0ms (1.8%)

localize10.0ms (0.2%)

series55.0ms (1%)

rewrite119.0ms (2.2%)

simplify58.0ms (1.1%)

prune383.0ms (6.9%)

localize11.0ms (0.2%)

series56.0ms (1%)

rewrite60.0ms (1.1%)

simplify41.0ms (0.7%)

prune383.0ms (6.9%)

regimes1.1s (20.6%)

bsearch34.0ms (0.6%)

simplify9.0ms (0.2%)

end102.0ms (1.8%)

Profiling