Details

analyze709.0ms (8.6%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
34.7%	55.4%	9.9%	9
36.1%	51.1%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.0s (24.8%)

Results

640.0ms	5306×	body	128	valid
545.0ms	1168×	body	2048	valid
294.0ms	781×	body	1024	valid
227.0ms	412×	body	4096	valid
132.0ms	1114×	body	128	invalid
107.0ms	382×	body	512	valid
43.0ms	207×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
361×	`div-sub_binary64`
341×	`fma-def_binary64`
313×	`associate-/l*_binary64`
224×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	23	18
2	42	18
3	77	18
4	123	18
5	218	18
6	370	18
7	586	18
8	948	18
9	1471	18
10	2000	18
11	3220	18
12	4095	18
13	4427	18
14	4435	18
15	4443	18
16	4469	18
17	4485	18
18	4521	18
19	4553	18
20	4565	18

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

33.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	33.9b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Compiler

Compiled 58 to 30 computations (48.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	24.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series211.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

124.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
45.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
33.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite102.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
338×	`fma-neg_binary64`
313×	`egg-rr`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	55
1	239	55
2	3605	55

Stop Event

1×	node limit

Counts

4 → 313

Calls

4 calls:

95.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
95.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
95.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
95.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

738×	`times-frac_binary64`
490×	`associate-/l*_binary64`
401×	`associate-/r*_binary64`
360×	`fma-def_binary64`
133×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2203
1	392	2175
2	1383	2133

Stop Event

1×	node limit

Counts

409 → 388

prune263.0ms (3.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	377	11	388
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	378	11	389

Error

5.0b

Counts

389 → 11

Alt Table

Status	Error	Program
	35.4b	(fma.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a) (neg.f64 (/.f64 b_2 a)))
	34.1b	(.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 1 a)))
▶	33.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	42.1b	(/.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3/2) (pow.f64 b_2 3)) (fma.f64 b_2 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	46.3b	(/.f64 (.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (/.f64 1 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))) a)
	33.9b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	40.9b	(/.f64 (*.f64 -2 b_2) a)
	40.9b	(-.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 2 (/.f64 b_2 a)))
	40.9b	(*.f64 (/.f64 -2 a) b_2)
	41.7b	(/.f64 (*.f64 c -1/2) b_2)
	56.5b	(/.f64 (-.f64 b_2 b_2) a)

Compiler

Compiled 9647 to 2970 computations (69.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	24.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series67.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

66.0ms

(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

rewrite52.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

699×	`fma-def_binary64`
320×	`fma-neg_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	272	18
2	3795	18

Stop Event

1×	node limit

Counts

1 → 43

Calls

1 calls:

51.0ms

(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-neg_binary64`
363×	`times-frac_binary64`
238×	`associate-/l*_binary64`
212×	`associate-r_binary64`
204×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	654
1	207	642
2	703	624
3	3903	624

Stop Event

1×	node limit

Counts

63 → 66

prune274.0ms (3.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	379	4	383
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	383	11	394

Error

5.0b

Counts

394 → 11

Alt Table

Status	Error	Program
	41.7b	(/.f64 (*.f64 c -1/2) b_2)
	46.3b	(.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) (/.f64 1 a))
	56.5b	(/.f64 (-.f64 b_2 b_2) a)
	40.9b	(fma.f64 1/2 (/.f64 c b_2) (/.f64 b_2 (/.f64 a -2)))
	34.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 (.f64 (neg.f64 a) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b_2 b_2))) b_2) (/.f64 1 a))
	46.6b	(/.f64 (sqrt.f64 (*.f64 a (neg.f64 c))) a)
✓	33.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
▶	33.9b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	40.9b	(/.f64 (*.f64 -2 b_2) a)
	40.9b	(*.f64 (/.f64 -2 a) b_2)
	35.4b	(fma.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a) (neg.f64 (/.f64 b_2 a)))

Compiler

Compiled 10086 to 3582 computations (64.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	24.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series662.0ms (8%)

Counts

1 → 20

Calls

1 calls:

662.0ms

(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) -1)

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

323×	`fma-neg_binary64`
238×	`expm1-udef_binary64`
238×	`log1p-udef_binary64`
137×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	277	18
2	3912	18

Stop Event

1×	node limit

Counts

1 → 46

Calls

1 calls:

49.0ms

(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) -1)

simplify36.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-neg_binary64`
363×	`times-frac_binary64`
239×	`associate-/l*_binary64`
212×	`associate-r_binary64`
206×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	654
1	207	642
2	703	624
3	3907	624

Stop Event

1×	node limit

Counts

66 → 69

prune245.0ms (3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	385	1	386
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	385	12	397

Error

5.0b

Counts

397 → 12

Alt Table

Status	Error	Program
	41.7b	(/.f64 (*.f64 c -1/2) b_2)
	46.3b	(.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) (/.f64 1 a))
	56.5b	(/.f64 (-.f64 b_2 b_2) a)
	40.9b	(fma.f64 1/2 (/.f64 c b_2) (/.f64 b_2 (/.f64 a -2)))
▶	34.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 (.f64 (neg.f64 a) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b_2 b_2))) b_2) (/.f64 1 a))
	46.6b	(/.f64 (sqrt.f64 (*.f64 a (neg.f64 c))) a)
✓	33.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
✓	33.9b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	40.9b	(/.f64 (*.f64 -2 b_2) a)
	44.8b	(pow.f64 (/.f64 a (.f64 (/.f64 (.f64 c -1/2) b_2) a)) -1)
	40.9b	(*.f64 (/.f64 -2 a) b_2)
	35.4b	(fma.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a) (neg.f64 (/.f64 b_2 a)))

Compiler

Compiled 10159 to 3571 computations (64.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 c) 2)
✓	0.5b	(cbrt.f64 c)
✓	1.2b	(-.f64 (sqrt.f64 (fma.f64 (.f64 (neg.f64 a) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (.f64 b_2 b_2))) b_2)
✓	24.5b	(sqrt.f64 (fma.f64 (.f64 (neg.f64 a) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (.f64 b_2 b_2)))

series329.0ms (4%)

Counts

4 → 80

Calls

4 calls:

133.0ms	(sqrt.f64 (fma.f64 (.f64 (neg.f64 a) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (.f64 b_2 b_2)))
123.0ms	(-.f64 (sqrt.f64 (fma.f64 (.f64 (neg.f64 a) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (.f64 b_2 b_2))) b_2)
43.0ms	(pow.f64 (cbrt.f64 c) 2)
30.0ms	(cbrt.f64 c)

rewrite62.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

772×	`prod-diff_binary64`
211×	`log1p-udef_binary64`
136×	`egg-rr`
133×	`add-sqr-sqrt_binary64`
128×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	56
1	275	36
2	3494	36

Stop Event

1×	node limit

Counts

4 → 136

Calls

4 calls:

59.0ms	(pow.f64 (cbrt.f64 c) 2)
59.0ms	(cbrt.f64 c)
59.0ms	(-.f64 (sqrt.f64 (fma.f64 (.f64 (neg.f64 a) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (.f64 b_2 b_2))) b_2)
59.0ms	(sqrt.f64 (fma.f64 (.f64 (neg.f64 a) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (.f64 b_2 b_2)))

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

409×	`times-frac_binary64`
286×	`associate-r_binary64`
278×	`associate-/l*_binary64`
237×	`associate-l_binary64`
226×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	94	1472
1	299	1452
2	936	1410
3	4756	1410

Stop Event

1×	node limit

Counts

216 → 191

prune133.0ms (1.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	1	8	9
Picked	0	1	1
Done	1	1	2
Total	218	11	229

Error

5.0b

Counts

229 → 11

Alt Table

Status	Error	Program
	41.7b	(/.f64 (*.f64 c -1/2) b_2)
	46.3b	(.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) (/.f64 1 a))
	56.5b	(/.f64 (-.f64 b_2 b_2) a)
	40.9b	(fma.f64 1/2 (/.f64 c b_2) (/.f64 b_2 (/.f64 a -2)))
✓	34.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 (.f64 (neg.f64 a) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b_2 b_2))) b_2) (/.f64 1 a))
	46.6b	(/.f64 (sqrt.f64 (*.f64 a (neg.f64 c))) a)
	34.1b	(.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (.f64 c (neg.f64 a)))) b_2) (/.f64 1 a))
✓	33.9b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
	40.9b	(/.f64 (*.f64 -2 b_2) a)
	44.8b	(pow.f64 (/.f64 a (.f64 (/.f64 (.f64 c -1/2) b_2) a)) -1)
	35.4b	(fma.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a) (neg.f64 (/.f64 b_2 a)))

Compiler

Compiled 5688 to 2578 computations (54.7% saved)

regimes2.6s (31.3%)

Accuracy

Total 4.8b remaining (45.2%)

Threshold costs 0b (0%)

Counts

203 → 3

Compiler

Compiled 19168 to 10758 computations (43.9% saved)

bsearch47.0ms (0.6%)

Steps

Iters	Range		Point
4	2.3830180217927396e-41	3.6143573520012696e-41	2.498456083999789e-41
4	-6.13913964654954e+110	-1.3790581557581322e+105	-5.6088049906029185e+109

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`cancel-sign-sub-inv_binary64`
18×	`neg-sub0_binary64`
18×	`neg-mul-1_binary64`
17×	`distribute-rgt-neg-in_binary64`
17×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	48
1	42	48
2	62	48
3	82	46
4	112	46
5	147	46
6	170	46
7	197	46
8	216	46
9	220	46

Stop Event

1×

saturated

end128.0ms (1.5%)

Compiler: Compiled 242 to 153 computations (36.8% saved)

Details

analyze709.0ms (8.6%)

sample2.0s (24.8%)

simplify62.0ms (0.8%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series211.0ms (2.6%)

rewrite102.0ms (1.2%)

simplify50.0ms (0.6%)

prune263.0ms (3.2%)

localize9.0ms (0.1%)

series67.0ms (0.8%)

rewrite52.0ms (0.6%)

simplify37.0ms (0.4%)

prune274.0ms (3.3%)

localize18.0ms (0.2%)

series662.0ms (8%)

rewrite50.0ms (0.6%)

simplify36.0ms (0.4%)

prune245.0ms (3%)

localize14.0ms (0.2%)

series329.0ms (4%)

rewrite62.0ms (0.8%)

simplify59.0ms (0.7%)

prune133.0ms (1.6%)

regimes2.6s (31.3%)

bsearch47.0ms (0.6%)

simplify5.0ms (0.1%)

end128.0ms (1.5%)

Profiling