Details

analyze1.0s (15.7%)

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)

sample2.2s (33.8%)

Results

695.0ms	5388×	body	128	valid
580.0ms	1151×	body	2048	valid
310.0ms	756×	body	1024	valid
262.0ms	422×	body	4096	valid
134.0ms	1062×	body	128	invalid
119.0ms	369×	body	512	valid
39.0ms	170×	body	256	valid

Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess53.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

795×	`fma-def_binary64`
731×	`div-sub_binary64`
295×	`fma-neg_binary64`
212×	`associate-/l*_binary64`
209×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	104
1	92	88
2	213	88
3	440	88
4	758	88
5	1251	88
6	2221	88
7	4457	88
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 20 to 14 computations (30% saved)

simplify37.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1220×	`fma-neg_binary64`
367×	`fma-def_binary64`
351×	`times-frac_binary64`
266×	`associate-/l*_binary64`
254×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	69	22
3	160	22
4	264	22
5	433	22
6	744	22
7	1341	22
8	2769	22
9	4702	22

Stop Event

1×	node limit

Counts

1 → 2

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

31.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	31.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
▶	31.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 111 to 75 computations (32.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	0.2b	(.f64 (.f64 3 a) c)
✓	0.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
✓	21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series81.0ms (1.3%)

Counts

4 → 100

Calls

33 calls:

6.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))	c	inf
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))	b	0
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))	c	inf
5.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))	b	inf
5.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))	c	-inf

rewrite91.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

704×	`fma-def_binary64`
357×	`fma-neg_binary64`
270×	`egg-rr`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	55
1	275	47
2	3872	47

Stop Event

1×	node limit

Counts

4 → 270

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
278×	`associate-r_binary64`
278×	`associate-/l*_binary64`
254×	`associate-/r*_binary64`
241×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	89	1820
1	275	1752
2	884	1726
3	4841	1726

Stop Event

1×	node limit

Counts

370 → 321

prune254.0ms (4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	313	8	321
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	314	9	323

Error

7.0b

Counts

323 → 9

Alt Table

Status	Error	Program
	32.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))) 3))) (*.f64 3 a))
	46.6b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
▶	31.8b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))) b) (*.f64 3 a))
	31.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
	32.2b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -3))) 1/4) 2)) (*.f64 3 a))
	57.5b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
	40.2b	(/.f64 (fma.f64 3/2 (.f64 a (/.f64 c b)) (.f64 b -2)) (*.f64 3 a))
	39.9b	(/.f64 (.f64 -2 b) (.f64 3 a))
	46.3b	(/.f64 (.f64 (.f64 a (/.f64 c b)) -3/2) (*.f64 3 a))

Compiler

Compiled 9785 to 5777 computations (41% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 c (.f64 a -3))
✓	0.3b	(fma.f64 b b (.f64 c (.f64 a -3)))
✓	0.7b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))) b)
✓	21.4b	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))

series76.0ms (1.2%)

Counts

4 → 100

Calls

33 calls:

6.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))) b)	c	inf
6.0ms	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))	c	-inf
5.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))) b)	c	-inf
5.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))) b)	a	-inf
5.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))) b)	a	inf

rewrite75.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

728×	`prod-diff_binary64`
298×	`fma-def_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`
173×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	47
1	212	45
2	2697	45

Stop Event

1×	node limit

Counts

4 → 151

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
278×	`associate-r_binary64`
278×	`associate-/l*_binary64`
254×	`associate-/r*_binary64`
241×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	89	1820
1	275	1752
2	884	1726
3	4841	1726

Stop Event

1×	node limit

Counts

251 → 202

prune160.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	195	7	202
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	199	12	211

Error

7.0b

Counts

211 → 12

Alt Table

Status	Error	Program
	35.8b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))))) b) (*.f64 3 a))
	46.6b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
▶	30.6b	(/.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))) (*.f64 3 a))
	32.2b	(/.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 1/4) 2) b) (*.f64 3 a))
	42.4b	(/.f64 (fma.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))) (*.f64 3 a))
	31.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
	30.7b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))) b)) 2) (*.f64 3 a))
	57.5b	(/.f64 (-.f64 b b) (*.f64 3 a))
	40.2b	(/.f64 (fma.f64 3/2 (.f64 a (/.f64 c b)) (.f64 b -2)) (*.f64 3 a))
	39.9b	(/.f64 (.f64 -2 b) (.f64 3 a))
	46.3b	(/.f64 (.f64 (.f64 a (/.f64 c b)) -3/2) (*.f64 3 a))
	32.2b	(/.f64 (-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))) 3)) b) (*.f64 3 a))

Compiler

Compiled 5267 to 3262 computations (38.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))) (*.f64 3 a))
	0.2b	(.f64 c (.f64 a -3))
✓	0.2b	(fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))))
✓	13.6b	(sqrt.f64 (.f64 c (.f64 a -3)))

series273.0ms (4.3%)

Counts

3 → 24

Calls

24 calls:

37.0ms	(/.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))) (*.f64 3 a))	a	-inf
36.0ms	(/.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))) (*.f64 3 a))	c	inf
28.0ms	(/.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))) (*.f64 3 a))	a	inf
26.0ms	(/.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))) (*.f64 3 a))	c	-inf
20.0ms	(fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))))	a	-inf

rewrite60.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

274×	`prod-diff_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`
129×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	287	47
2	3550	47

Stop Event

1×	node limit

Counts

3 → 90

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

720×	`times-frac_binary64`
383×	`associate-/l*_binary64`
336×	`associate-/r*_binary64`
278×	`associate-r_binary64`
251×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	1004
1	328	918
2	1072	861

Stop Event

1×	node limit

Counts

114 → 138

prune127.0ms (2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	144	9	153
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	148	17	165

Error

5.5b

Counts

165 → 17

Alt Table

Status	Error	Program
	47.3b	(/.f64 (.f64 (.f64 c a) -1/2) (*.f64 a b))
	31.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
	55.4b	(.f64 1/6 (/.f64 (pow.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) 2) (.f64 a b)))
▶	30.7b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))) b)) 2) (*.f64 3 a))
	32.2b	(/.f64 (-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))) 3)) b) (*.f64 3 a))
	53.8b	(-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a 3))))) (/.f64 1/3 a)))) 1)
	39.9b	(*.f64 -2/3 (/.f64 b a))
	57.5b	(/.f64 (-.f64 b b) (*.f64 3 a))
	44.6b	(.f64 (/.f64 1/3 a) (sqrt.f64 (.f64 -3 (*.f64 c a))))
	44.6b	(.f64 1/3 (/.f64 (sqrt.f64 (.f64 -3 (*.f64 c a))) a))
	46.6b	(/.f64 (/.f64 (.f64 (.f64 c a) -3/2) b) (*.f64 3 a))
	40.2b	(/.f64 (fma.f64 3/2 (.f64 a (/.f64 c b)) (.f64 b -2)) (*.f64 3 a))
	39.9b	(/.f64 (.f64 -2 b) (.f64 3 a))
	46.3b	(/.f64 (.f64 (.f64 a (/.f64 c b)) -3/2) (*.f64 3 a))
	46.0b	(.f64 (/.f64 (sqrt.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a 3)))))) a) (/.f64 (sqrt.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a 3)))))) 3))
	46.0b	(.f64 (.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a 3))))) 1/3) (/.f64 1 a))
✓	30.6b	(/.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))) (*.f64 3 a))

Compiler

Compiled 4086 to 2807 computations (31.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 c (.f64 a -3))
✓	0.2b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))) b)
✓	0.3b	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))) b)) 2)
	13.6b	(sqrt.f64 (.f64 c (.f64 a -3)))

series327.0ms (5.1%)

Counts

2 → 16

Calls

18 calls:

51.0ms	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))) b)) 2)	c	-inf
47.0ms	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))) b)) 2)	c	inf
42.0ms	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))) b)) 2)	a	-inf
27.0ms	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))) b)) 2)	a	inf
25.0ms	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))) b)) 2)	c	0

rewrite61.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`prod-diff_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
124×	`add-sqr-sqrt_binary64`
120×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	278	30
2	3125	30

Stop Event

1×	node limit

Counts

2 → 107

simplify35.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
590×	`cancel-sign-sub-inv_binary64`
462×	`fma-neg_binary64`
304×	`distribute-neg-frac_binary64`
253×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	559
1	174	508
2	507	481
3	2567	477

Stop Event

1×	node limit

Counts

123 → 82

prune105.0ms (1.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	124	17	141

Error

5.5b

Counts

141 → 17

Alt Table

Status	Error	Program
	47.3b	(/.f64 (.f64 (.f64 c a) -1/2) (*.f64 a b))
	31.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
	55.4b	(.f64 1/6 (/.f64 (pow.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) 2) (.f64 a b)))
✓	30.7b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))) b)) 2) (*.f64 3 a))
	32.2b	(/.f64 (-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))) 3)) b) (*.f64 3 a))
	53.8b	(-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a 3))))) (/.f64 1/3 a)))) 1)
	39.9b	(*.f64 -2/3 (/.f64 b a))
	57.5b	(/.f64 (-.f64 b b) (*.f64 3 a))
	44.6b	(.f64 (/.f64 1/3 a) (sqrt.f64 (.f64 -3 (*.f64 c a))))
	44.6b	(.f64 1/3 (/.f64 (sqrt.f64 (.f64 -3 (*.f64 c a))) a))
	46.6b	(/.f64 (/.f64 (.f64 (.f64 c a) -3/2) b) (*.f64 3 a))
	40.2b	(/.f64 (fma.f64 3/2 (.f64 a (/.f64 c b)) (.f64 b -2)) (*.f64 3 a))
	39.9b	(/.f64 (.f64 -2 b) (.f64 3 a))
	46.3b	(/.f64 (.f64 (.f64 a (/.f64 c b)) -3/2) (*.f64 3 a))
	46.0b	(.f64 (/.f64 (sqrt.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a 3)))))) a) (/.f64 (sqrt.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a 3)))))) 3))
	46.0b	(.f64 (.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a 3))))) 1/3) (/.f64 1 a))
✓	30.6b	(/.f64 (fma.f64 -1 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))) (*.f64 3 a))

Compiler

Compiled 3384 to 2317 computations (31.5% saved)

regimes893.0ms (14%)

Accuracy

Total 5.7b remaining (43.1%)

Threshold costs 0b (0%)

Counts

77 → 4

Compiler

Compiled 7505 to 5428 computations (27.7% saved)

bsearch101.0ms (1.6%)

Algorithm

3×	binary-search

Calls

3 calls:

55.0ms	b
25.0ms	b
17.0ms	b

Steps

Iters

Point

Range

2.634688304178707e-39

∈ [

8.600532443318868e-50

7.975834508293734e-38

]

-1.4196138185551953e-103

∈ [

-4.598494536205818e-103

-1.3884645000775056e-103

]

-4.895509654010244e+141

∈ [

-1.8024645124625e+146

-4.066473418815342e+141

]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	85
1	44	85
2	48	85
3	50	85
4	51	85

Stop Event

1×

saturated

end203.0ms (3.2%)

Stop Event

1×

fuel

Compiler

Compiled 401 to 286 computations (28.7% saved)

Details

analyze1.0s (15.7%)

sample2.2s (33.8%)

preprocess53.0ms (0.8%)

simplify37.0ms (0.6%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series81.0ms (1.3%)

rewrite91.0ms (1.4%)

simplify67.0ms (1%)

prune254.0ms (4%)

localize9.0ms (0.1%)

series76.0ms (1.2%)

rewrite75.0ms (1.2%)

simplify65.0ms (1%)

prune160.0ms (2.5%)

localize10.0ms (0.2%)

series273.0ms (4.3%)

rewrite60.0ms (0.9%)

simplify30.0ms (0.5%)

prune127.0ms (2%)

localize11.0ms (0.2%)

series327.0ms (5.1%)

rewrite61.0ms (1%)

simplify35.0ms (0.5%)

prune105.0ms (1.6%)

regimes893.0ms (14%)

bsearch101.0ms (1.6%)

simplify4.0ms (0.1%)

end203.0ms (3.2%)

Profiling