Details

analyze616.0ms (9.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.3s (34.4%)

Results

752.0ms	5400×	body	128	valid
616.0ms	1186×	body	2048	valid
294.0ms	714×	body	1024	valid
274.0ms	426×	body	4096	valid
142.0ms	1101×	body	128	invalid
131.0ms	361×	body	512	valid
38.0ms	169×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

993×	`fma-def_binary64`
557×	`rules-5-rev_binary64`
372×	`rules-4-rev_binary64`
342×	`rules-20_binary64`
321×	`rules-33_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	35	26
2	78	24
3	252	24
4	1063	22
5	3653	22
6	4537	22
7	5169	22

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

34.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	34.4b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (*.f64 a -2))
	34.4b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.4b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (*.f64 a -2))
✓	0.8b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	26.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series120.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

50.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (*.f64 a -2))
33.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
28.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
9.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite112.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

840×	`prod-diff_binary64`
158×	`egg-rr`
133×	`add-sqr-sqrt_binary64`
127×	`log1p-expm1-u_binary64`
127×	`expm1-log1p-u_binary64`

Counts

4 → 158

Calls

4 calls:

108.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
108.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (*.f64 a -2))
108.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
108.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	309	62
2	3762	62
3	5261	62
0	0	0
1	0	0

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-def_binary64`
475×	`rules-13_binary64`
452×	`rules-20_binary64`
339×	`rules-14-rev_binary64`
282×	`fma-neg_binary64`

Counts

254 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	2110
1	400	1921
2	1671	1909
3	5201	1909

prune171.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	220	9	229
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	221	10	231

Error

8.4b

Counts

231 → 10

Alt Table

Status	Error	Program
	47.8b	(neg.f64 (fma.f64 a (/.f64 (*.f64 c c) (pow.f64 b 3)) (/.f64 c b)))
✓	34.4b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (*.f64 a -2))
	46.7b	(/.f64 (+.f64 b (/.f64 (fma.f64 b (.f64 b 1/2) (.f64 c (.f64 a -4))) (sqrt.f64 (.f64 c (.f64 a -4))))) (.f64 a -2))
	42.7b	(/.f64 c (neg.f64 b))
	45.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	44.9b	(/.f64 (neg.f64 b) a)
	34.9b	(.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) 2) (/.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (.f64 a -2)))
▶	34.4b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 (.f64 a -2)))
	35.2b	(/.f64 (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2)) (*.f64 a -2))
	56.3b	(/.f64 (+.f64 b (neg.f64 b)) (*.f64 a -2))

Compiler

Compiled 6135 to 3657 computations (40.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (*.f64 a -2))
✓	0.2b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 (.f64 a -2)))
	0.8b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	26.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series55.0ms (0.8%)

Counts

2 → 32

Calls

2 calls:

54.0ms	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 (.f64 a -2)))
1.0ms	(/.f64 1 (*.f64 a -2))

rewrite90.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

899×	`prod-diff_binary64`
148×	`add-sqr-sqrt_binary64`
140×	`log1p-expm1-u_binary64`
140×	`expm1-log1p-u_binary64`
138×	`add-cbrt-cube_binary64`

Counts

2 → 115

Calls

2 calls:

87.0ms	(/.f64 1 (*.f64 a -2))
87.0ms	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 (.f64 a -2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	352	26
2	4240	26
3	5843	26
0	0	0
1	0	0

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
280×	`fma-def_binary64`
198×	`rules-20_binary64`
184×	`rules-13_binary64`
173×	`rules-4_binary64`

Counts

147 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	597
1	216	561
2	759	555
3	4311	555
4	5249	555

prune264.0ms (3.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	255	11	266

Error

8.4b

Counts

266 → 11

Alt Table

Status	Error	Program
	47.8b	(neg.f64 (fma.f64 a (/.f64 (*.f64 c c) (pow.f64 b 3)) (/.f64 c b)))
✓	34.4b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (*.f64 a -2))
	46.7b	(/.f64 (+.f64 b (/.f64 (fma.f64 b (.f64 b 1/2) (.f64 c (.f64 a -4))) (sqrt.f64 (.f64 c (.f64 a -4))))) (.f64 a -2))
	45.2b	(.f64 (+.f64 b b) (/.f64 1 (.f64 a -2)))
	42.7b	(/.f64 c (neg.f64 b))
	45.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	44.9b	(/.f64 (neg.f64 b) a)
▶	34.9b	(.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) 2) (/.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (.f64 a -2)))
✓	34.4b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 (.f64 a -2)))
	35.2b	(/.f64 (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2)) (*.f64 a -2))
	56.3b	(/.f64 (+.f64 b (neg.f64 b)) (*.f64 a -2))

Compiler

Compiled 7521 to 4644 computations (38.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
✓	0.5b	(/.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (*.f64 a -2))
	0.8b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	26.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series501.0ms (7.4%)

Counts

2 → 40

Calls

2 calls:

327.0ms	(/.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (*.f64 a -2))
173.0ms	(cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))

rewrite76.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

868×	`prod-diff_binary64`
141×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`
134×	`expm1-log1p-u_binary64`
132×	`add-cbrt-cube_binary64`

Counts

2 → 61

Calls

2 calls:

74.0ms	(cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
74.0ms	(/.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (*.f64 a -2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	329	42
2	3988	42
3	5527	42
0	0	0
1	0	0

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

961×	`rules-13_binary64`
400×	`fma-neg_binary64`
399×	`rules-14-rev_binary64`
325×	`rules-21_binary64`
232×	`rules-20_binary64`

Counts

101 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	2408
1	700	2252
2	2975	2132
3	6787	2132

prune372.0ms (5.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	422	1	423
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	423	11	434

Error

8.4b

Counts

434 → 11

Alt Table

Status	Error	Program
	47.8b	(neg.f64 (fma.f64 a (/.f64 (*.f64 c c) (pow.f64 b 3)) (/.f64 c b)))
✓	34.4b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (*.f64 a -2))
	46.7b	(/.f64 (+.f64 b (/.f64 (fma.f64 b (.f64 b 1/2) (.f64 c (.f64 a -4))) (sqrt.f64 (.f64 c (.f64 a -4))))) (.f64 a -2))
	45.2b	(.f64 (+.f64 b b) (/.f64 1 (.f64 a -2)))
	42.7b	(/.f64 c (neg.f64 b))
	45.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	44.9b	(/.f64 (neg.f64 b) a)
✓	34.4b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 (.f64 a -2)))
▶	35.2b	(/.f64 (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2)) (*.f64 a -2))
	46.6b	(.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) 2) (.f64 -1/2 (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 a c) -4))) a)))
	56.3b	(/.f64 (+.f64 b (neg.f64 b)) (*.f64 a -2))

Compiler

Compiled 18960 to 11986 computations (36.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2)) (*.f64 a -2))
✓	0.5b	(pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2)
✓	9.3b	(+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2))
✓	26.7b	(pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4)

series187.0ms (2.8%)

Counts

4 → 112

Calls

4 calls:

58.0ms	(pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2)
53.0ms	(/.f64 (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2)) (*.f64 a -2))
42.0ms	(pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4)
33.0ms	(+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2))

rewrite96.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

598×	`prod-diff_binary64`
154×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`
147×	`egg-rr`

Counts

4 → 147

Calls

4 calls:

92.0ms	(/.f64 (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2)) (*.f64 a -2))
92.0ms	(pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2)
92.0ms	(+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2))
92.0ms	(pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	68
1	384	65
2	4287	65
3	5237	65
0	0	0
1	0	0

simplify118.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

330×	`fma-def_binary64`
306×	`rules-4_binary64`
297×	`rules-20_binary64`
245×	`rules-13_binary64`
234×	`rules-6_binary64`

Counts

259 → 299

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	348	5061
1	1191	4852
2	4997	4852
3	5018	4852

prune233.0ms (3.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	296	3	299
Fresh	3	5	8
Picked	0	1	1
Done	0	2	2
Total	299	11	310

Error

1.2b

Counts

310 → 11

Alt Table

Status	Error	Program
	47.8b	(neg.f64 (fma.f64 a (/.f64 (*.f64 c c) (pow.f64 b 3)) (/.f64 c b)))
✓	34.4b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (*.f64 a -2))
	42.7b	(/.f64 c (neg.f64 b))
	51.4b	(/.f64 (+.f64 b (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 4 c))) (log.f64 (/.f64 1 a))))) 2)) (*.f64 a -2))
	46.7b	(/.f64 (+.f64 b (/.f64 (fma.f64 b (.f64 b 1/2) (.f64 c (.f64 a -4))) (sqrt.f64 (.f64 c (.f64 a -4))))) (.f64 a -2))
	52.1b	(/.f64 (+.f64 b (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 a -2))
	45.0b	(-.f64 (/.f64 c b) (/.f64 b a))
✓	34.4b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 (.f64 a -2)))
✓	35.2b	(/.f64 (+.f64 b (pow.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) 2)) (*.f64 a -2))
	46.6b	(.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) 2) (.f64 -1/2 (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 a c) -4))) a)))
	52.5b	(/.f64 (+.f64 b (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 a -4)) (neg.f64 (log.f64 c)))) 2)) (.f64 a -2))

Compiler

Compiled 10481 to 6849 computations (34.7% saved)

regimes870.0ms (12.9%)

Accuracy

Total 9.6b remaining (91.6%)

Threshold costs 0b (0%)

Counts

72 → 3

Compiler

Compiled 5680 to 4110 computations (27.6% saved)

bsearch81.0ms (1.2%)

Steps

Iters	Range		Point
9	5.329808561740872e+92	4.6543464877957586e+98	2.1532958080945476e+95
8	-1.4483942438908369e-12	-3.56303397615803e-15	-3.62263644777804e-15

Compiler

Compiled 4 to 3 computations (25% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	52
1	26	52

end156.0ms (2.3%)

Compiler: Compiled 292 to 206 computations (29.5% saved)

Details

analyze616.0ms (9.1%)

sample2.3s (34.4%)

simplify61.0ms (0.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series120.0ms (1.8%)

rewrite112.0ms (1.7%)

simplify71.0ms (1.1%)

prune171.0ms (2.5%)

localize10.0ms (0.2%)

series55.0ms (0.8%)

rewrite90.0ms (1.3%)

simplify59.0ms (0.9%)

prune264.0ms (3.9%)

localize13.0ms (0.2%)

series501.0ms (7.4%)

rewrite76.0ms (1.1%)

simplify72.0ms (1.1%)

prune372.0ms (5.5%)

localize14.0ms (0.2%)

series187.0ms (2.8%)

rewrite96.0ms (1.4%)

simplify118.0ms (1.7%)

prune233.0ms (3.5%)

regimes870.0ms (12.9%)

bsearch81.0ms (1.2%)

simplify1.0ms (0%)

end156.0ms (2.3%)

Profiling