Details

analyze623.0ms (10.3%)

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 (38.9%)

Results

698.0ms	5306×	body	128	valid
668.0ms	1187×	body	2048	valid
318.0ms	731×	body	1024	valid
299.0ms	446×	body	4096	valid
137.0ms	1076×	body	128	invalid
128.0ms	388×	body	512	valid
43.0ms	198×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify38.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
544×	`div-sub_binary64`
489×	`fma-neg_binary64`
405×	`times-frac_binary64`
262×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	100	24
3	259	22
4	460	22
5	840	22
6	1790	22
7	2999	22
8	3682	22
9	4742	22

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

34.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	34.9b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
▶	34.9b	(/.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
✓	0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.2b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	21.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series125.0ms (2.1%)

Counts

4 → 96

Calls

4 calls:

51.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
36.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
29.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite46.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

169×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`
164×	`add-cbrt-cube_binary64`
160×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	347	62

Stop Event

1×	node limit

Counts

4 → 160

Calls

4 calls:

43.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
43.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
43.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
43.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify47.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

743×	`times-frac_binary64`
469×	`associate-/l*_binary64`
434×	`fma-def_binary64`
425×	`associate-/r*_binary64`
158×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	2060
1	415	1984
2	1475	1904

Stop Event

1×	node limit

Counts

256 → 236

prune172.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	227	9	236
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	229	9	238

Error

5.0b

Counts

238 → 9

Alt Table

Status	Error	Program
	38.9b	(/.f64 (neg.f64 c) b)
	56.3b	(/.f64 (-.f64 (neg.f64 b) (neg.f64 b)) (*.f64 2 a))
	55.5b	(pow.f64 (sqrt.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 2)
▶	35.5b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
	35.8b	(/.f64 (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))) (.f64 2 a))
	43.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.2b	(neg.f64 (/.f64 b a))
	57.5b	(cbrt.f64 (pow.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a)) 3))
	48.3b	(pow.f64 (/.f64 a (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) 1/2)) -1)

Compiler

Compiled 6257 to 3647 computations (41.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)
✓	1.0b	(fma.f64 b b (.f64 (.f64 a c) -4))
✓	13.8b	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2))
✓	22.2b	(pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4)

series149.0ms (2.5%)

Counts

4 → 128

Calls

4 calls:

55.0ms	(pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)
42.0ms	(pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4)
38.0ms	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2))
11.0ms	(fma.f64 b b (.f64 (.f64 a c) -4))

rewrite111.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

812×	`prod-diff_binary64`
249×	`egg-rr`
143×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	307	52
2	3729	52

Stop Event

1×	node limit

Counts

4 → 249

Calls

4 calls:

99.0ms	(pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)
99.0ms	(fma.f64 b b (.f64 (.f64 a c) -4))
99.0ms	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2))
99.0ms	(pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4)

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

301×	`times-frac_binary64`
272×	`associate-/r*_binary64`
238×	`fma-neg_binary64`
233×	`associate-/l*_binary64`
231×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	320	4810
1	1115	4654
2	4578	4654

Stop Event

1×	node limit

Counts

377 → 389

prune419.0ms (6.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	386	3	389
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	389	9	398

Error

0.6b

Counts

398 → 9

Alt Table

Status	Error	Program
	55.5b	(pow.f64 (sqrt.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 2)
	53.1b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 2 a))
	48.3b	(pow.f64 (/.f64 a (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) 1/2)) -1)
	54.2b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2)) (*.f64 2 a))
▶	32.9b	(/.f64 (neg.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (*.f64 2 a))
✓	35.5b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
	38.9b	(/.f64 (neg.f64 c) b)
	43.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	57.5b	(cbrt.f64 (pow.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a)) 3))

Compiler

Compiled 19678 to 13028 computations (33.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (neg.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (*.f64 2 a))
✓	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	12.6b	(sqrt.f64 (.f64 a (.f64 c -4)))

series231.0ms (3.8%)

Counts

3 → 28

Calls

3 calls:

140.0ms	(/.f64 (neg.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (*.f64 2 a))
78.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
12.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite70.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

826×	`prod-diff_binary64`
155×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`
146×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	311	45
2	4304	45

Stop Event

1×	node limit

Counts

3 → 129

Calls

3 calls:

67.0ms	(/.f64 (neg.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (*.f64 2 a))
67.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
67.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

734×	`times-frac_binary64`
388×	`associate-/l*_binary64`
364×	`associate-/r*_binary64`
282×	`associate-r_binary64`
259×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	1010
1	323	930
2	1061	870

Stop Event

1×	node limit

Counts

157 → 176

prune118.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	176	9	185

Error

0.3b

Counts

185 → 9

Alt Table

Status	Error	Program
	55.5b	(pow.f64 (sqrt.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 2)
	53.1b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 2 a))
✓	32.9b	(/.f64 (neg.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (*.f64 2 a))
✓	35.5b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
	47.9b	(/.f64 (neg.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 (.f64 c -4)) (sqrt.f64 a))))) (*.f64 2 a))
	43.2b	(/.f64 (neg.f64 b) a)
▶	38.9b	(/.f64 (neg.f64 c) b)
	57.5b	(cbrt.f64 (pow.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a)) 3))
	48.3b	(pow.f64 (/.f64 a (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) 1/2)) -1)

Compiler

Compiled 4631 to 3105 computations (33% saved)

localize3.0ms (0%)

prune7.0ms (0.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	2	2
Total	9	9

Error

0.3b

Counts

9 → 9

Alt Table

Status	Error	Program
	55.5b	(pow.f64 (sqrt.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 2)
	53.1b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 2 a))
✓	32.9b	(/.f64 (neg.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (*.f64 2 a))
✓	35.5b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
	47.9b	(/.f64 (neg.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 (.f64 c -4)) (sqrt.f64 a))))) (*.f64 2 a))
	43.2b	(/.f64 (neg.f64 b) a)
✓	38.9b	(/.f64 (neg.f64 c) b)
	57.5b	(cbrt.f64 (pow.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a)) 3))
	48.3b	(pow.f64 (/.f64 a (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) 1/2)) -1)

Compiler

Compiled 159 to 117 computations (26.4% saved)

regimes1.2s (19.3%)

Accuracy

Total 9.4b remaining (94.8%)

Threshold costs 0b (0%)

Counts

97 → 3

Compiler

Compiled 7696 to 5522 computations (28.2% saved)

bsearch66.0ms (1.1%)

Steps

Iters	Range		Point
9	1.085993431515551e+74	1.2980207237616743e+79	7.07453807142745e+77
6	-6.839379831418975e-60	-7.250081439596686e-61	-1.0838115433463801e-60

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
13×	`*-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	50
1	46	50
2	67	50
3	91	50
4	103	50
5	109	50
6	111	50

Stop Event

1×

saturated

end124.0ms (2.1%)

Compiler: Compiled 231 to 165 computations (28.6% saved)

Details

analyze623.0ms (10.3%)

sample2.3s (38.9%)

simplify38.0ms (0.6%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series125.0ms (2.1%)

rewrite46.0ms (0.8%)

simplify47.0ms (0.8%)

prune172.0ms (2.8%)

localize14.0ms (0.2%)

series149.0ms (2.5%)

rewrite111.0ms (1.8%)

simplify95.0ms (1.6%)

prune419.0ms (6.9%)

localize10.0ms (0.2%)

series231.0ms (3.8%)

rewrite70.0ms (1.2%)

simplify30.0ms (0.5%)

prune118.0ms (2%)

localize3.0ms (0%)

prune7.0ms (0.1%)

regimes1.2s (19.3%)

bsearch66.0ms (1.1%)

simplify4.0ms (0.1%)

end124.0ms (2.1%)

Profiling