Details

analyze999.0ms (12.7%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	93.6%	6.4%	7
6.2%	87.4%	6.4%	8
10.1%	81.1%	8.7%	9
15.6%	71%	13.4%	10
22%	63%	15%	11
29.1%	52.9%	18.1%	12
33.8%	45.6%	20.5%	13
38.8%	38.9%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.3s (28.8%)

Results

729.0ms	5389×	body	128	valid
610.0ms	1150×	body	2048	valid
317.0ms	757×	body	1024	valid
269.0ms	422×	body	4096	valid
146.0ms	1064×	body	128	invalid
131.0ms	369×	body	512	valid
38.0ms	169×	body	256	valid

Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess45.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

807×	`fma-def_binary64`
679×	`div-sub_binary64`
295×	`fma-neg_binary64`
214×	`associate-/l*_binary64`
209×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	104
1	98	88
2	198	88
3	446	88
4	768	88
5	1261	88
6	2236	88
7	4458	88
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 20 to 14 computations (30% saved)

simplify30.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
619×	`times-frac_binary64`
338×	`fma-def_binary64`
314×	`associate-/l*_binary64`
262×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	69	22
3	161	22
4	259	22
5	417	22
6	734	22
7	1326	22
8	2618	22
9	3877	22

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

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

31.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	31.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	31.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))

Compiler

Compiled 111 to 75 computations (32.4% saved)

localize13.0ms (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))
✓	0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	0.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series117.0ms (1.5%)

Counts

4 → 96

Calls

36 calls:

10.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	a	-inf
9.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	a	inf
7.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	c	-inf
7.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	c	inf
6.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))	c	-inf

rewrite79.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

277×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
161×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	343	62
2	4859	62

Stop Event

1×	node limit

Counts

4 → 158

simplify51.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
432×	`fma-def_binary64`
422×	`associate-/r*_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	402	2164
2	1403	2078

Stop Event

1×	node limit

Counts

254 → 232

prune176.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	224	8	232
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	225	9	234

Error

4.1b

Counts

234 → 9

Alt Table

Status	Error	Program
	47.1b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	43.4b	(/.f64 (neg.f64 c) b)
▶	31.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	40.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	39.8b	(/.f64 (neg.f64 b) a)
	54.6b	(cbrt.f64 (pow.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a)) 3))
	46.8b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) -1)
	57.5b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	46.8b	(.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (/.f64 1/2 a)))

Compiler

Compiled 6110 to 3544 computations (42% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
✓	0.3b	(fma.f64 b b (.f64 a (.f64 c -4)))
✓	0.7b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)
✓	21.4b	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))

series128.0ms (1.6%)

Counts

4 → 96

Calls

36 calls:

13.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))	a	inf
9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))	a	-inf
8.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))	b	inf
7.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)	a	-inf
7.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))	c	-inf

rewrite79.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

737×	`prod-diff_binary64`
158×	`egg-rr`
139×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	281	59
2	3626	59

Stop Event

1×	node limit

Counts

4 → 158

simplify53.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
432×	`fma-def_binary64`
422×	`associate-/r*_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	402	2164
2	1403	2078

Stop Event

1×	node limit

Counts

254 → 232

prune160.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	226	6	232
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	232	9	241

Error

4.1b

Counts

241 → 9

Alt Table

Status	Error	Program
	43.4b	(/.f64 (neg.f64 c) b)
	49.5b	(/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (.f64 (.f64 a 2) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
	39.8b	(/.f64 (neg.f64 b) a)
▶	30.5b	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
	46.8b	(.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (/.f64 1/2 a)))
	40.2b	(.f64 (-.f64 (-.f64 (.f64 2 (*.f64 (/.f64 c b) a)) b) b) (/.f64 1/2 a))
	57.5b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
	46.1b	(.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 1/2 a))
	35.7b	(.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))) b) (/.f64 1/2 a))

Compiler

Compiled 5906 to 3673 computations (37.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
✓	0.2b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
✓	13.6b	(sqrt.f64 (.f64 a (.f64 c -4)))

series235.0ms (3%)

Counts

3 → 24

Calls

24 calls:

28.0ms	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))	a	-inf
26.0ms	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))	c	inf
26.0ms	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))	a	inf
20.0ms	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))	c	-inf
18.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)	c	inf

rewrite194.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

937×	`prod-diff_binary64`
442×	`egg-rr`
143×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`
136×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	287	45
2	3914	45

Stop Event

1×	node limit

Counts

3 → 442

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

728×	`times-frac_binary64`
385×	`associate-/l*_binary64`
360×	`associate-/r*_binary64`
271×	`associate-r_binary64`
249×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	988
1	323	908
2	1054	857

Stop Event

1×	node limit

Counts

466 → 487

prune490.0ms (6.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	485	2	487
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	487	9	496

Error

2.5b

Counts

496 → 9

Alt Table

Status	Error	Program
	43.4b	(/.f64 (neg.f64 c) b)
	49.5b	(/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (.f64 (.f64 a 2) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
	46.4b	(/.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (.f64 c -4)) (sqrt.f64 a))) b) (*.f64 a 2))
✓	30.5b	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
	39.8b	(/.f64 (neg.f64 b) a)
▶	30.8b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))) b)) (.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))) b)) (/.f64 1/2 a)))
	40.2b	(.f64 (-.f64 (-.f64 (.f64 2 (*.f64 (/.f64 c b) a)) b) b) (/.f64 1/2 a))
	57.5b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
	46.1b	(.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 1/2 a))

Compiler

Compiled 23618 to 15206 computations (35.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))) b)) (.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))) b)) (/.f64 1/2 a)))
✓	0.2b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 a c)))) b)) (/.f64 1/2 a))
✓	0.2b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))) b)
✓	13.6b	(sqrt.f64 (.f64 -4 (.f64 a c)))

series547.0ms (7%)

Counts

4 → 28

Calls

33 calls:

67.0ms	(.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 a c)))) b)) (/.f64 1/2 a))	a	inf
63.0ms	(.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 a c)))) b)) (/.f64 1/2 a))	c	inf
62.0ms	(.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 a c)))) b)) (/.f64 1/2 a))	a	-inf
46.0ms	(.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 a c)))) b)) (/.f64 1/2 a))	c	-inf
29.0ms	(.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))) b)) (.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))) b)) (/.f64 1/2 a)))	a	-inf

rewrite72.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

568×	`prod-diff_binary64`
157×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`
148×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	68
1	324	68
2	4087	68

Stop Event

1×	node limit

Counts

4 → 134

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

728×	`times-frac_binary64`
421×	`associate-/l*_binary64`
386×	`associate-/r*_binary64`
369×	`fma-def_binary64`
202×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1230
1	397	1134
2	1286	1109

Stop Event

1×	node limit

Counts

162 → 190

prune269.0ms (3.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	295	9	304

Error

2.5b

Counts

304 → 9

Alt Table

Status	Error	Program
	43.4b	(/.f64 (neg.f64 c) b)
	49.5b	(/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (.f64 (.f64 a 2) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
	46.4b	(/.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (.f64 c -4)) (sqrt.f64 a))) b) (*.f64 a 2))
✓	30.5b	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
	39.8b	(/.f64 (neg.f64 b) a)
✓	30.8b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))) b)) (.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))) b)) (/.f64 1/2 a)))
	40.2b	(.f64 (-.f64 (-.f64 (.f64 2 (*.f64 (/.f64 c b) a)) b) b) (/.f64 1/2 a))
	57.5b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
	46.1b	(.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 1/2 a))

Compiler

Compiled 10462 to 6741 computations (35.6% saved)

regimes1.5s (18.7%)

Accuracy

Total 6.9b remaining (69.2%)

Threshold costs 0b (0%)

Counts

148 → 4

Compiler

Compiled 13152 to 9226 computations (29.9% saved)

bsearch114.0ms (1.5%)

Algorithm

3×	binary-search

Calls

3 calls:

60.0ms	b
29.0ms	b
20.0ms	b

Steps

Iters

Point

Range

1.648410596510835e-47

∈ [

8.600532443318868e-50

7.975834508293734e-38

]

-1.4196138185551953e-103

∈ [

-4.598494536205818e-103

-1.3884645000775056e-103

]

-1.2624005950379626e+150

∈ [

-1.1719631462360283e+151

-5.881653300789134e+149

]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	73
1	51	73
2	61	73
3	67	73
4	69	73

Stop Event

1×

saturated

end133.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 271 to 180 computations (33.6% saved)

Details

analyze999.0ms (12.7%)

sample2.3s (28.8%)

preprocess45.0ms (0.6%)

simplify30.0ms (0.4%)

prune4.0ms (0%)

localize13.0ms (0.2%)

series117.0ms (1.5%)

rewrite79.0ms (1%)

simplify51.0ms (0.6%)

prune176.0ms (2.2%)

localize10.0ms (0.1%)

series128.0ms (1.6%)

rewrite79.0ms (1%)

simplify53.0ms (0.7%)

prune160.0ms (2%)

localize10.0ms (0.1%)

series235.0ms (3%)

rewrite194.0ms (2.5%)

simplify54.0ms (0.7%)

prune490.0ms (6.2%)

localize13.0ms (0.2%)

series547.0ms (7%)

rewrite72.0ms (0.9%)

simplify40.0ms (0.5%)

prune269.0ms (3.4%)

regimes1.5s (18.7%)

bsearch114.0ms (1.5%)

simplify4.0ms (0%)

end133.0ms (1.7%)

Profiling