Details

analyze717.0ms (15.5%)

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
35.1%	55%	9.9%	9
36.3%	50.9%	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 (42.6%)

Results

619.0ms	5347×	body	128	valid
530.0ms	1183×	body	2048	valid
270.0ms	733×	body	1024	valid
228.0ms	421×	body	4096	valid
118.0ms	1057×	body	128	invalid
112.0ms	375×	body	512	valid
38.0ms	197×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify61.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

518×	`div-sub_binary64`
428×	`fma-neg_binary64`
208×	`associate-/l*_binary64`
205×	`fma-def_binary64`
181×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	27	20
2	57	20
3	126	20
4	216	20
5	392	20
6	662	20
7	1008	20
8	1214	20
9	1599	20
10	3126	20
11	3899	20
12	3997	20
13	4005	20
14	4013	20
15	4013	20
16	4071	20
17	4107	20
18	4137	20
19	4149	20

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

36.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.8b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
✓	1.4b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	22.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series158.0ms (3.4%)

Counts

3 → 60

Calls

3 calls:

78.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
46.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
33.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

rewrite64.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

352×	`fma-neg_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
133×	`add-sqr-sqrt_binary64`
129×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	262	45
2	4018	45

Stop Event

1×	node limit

Counts

3 → 124

Calls

3 calls:

61.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
61.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify38.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
494×	`associate-/l*_binary64`
393×	`associate-/r*_binary64`
361×	`fma-def_binary64`
141×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	1731
1	403	1687
2	1424	1661

Stop Event

1×	node limit

Counts

184 → 194

prune113.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	184	10	194
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	184	11	195

Error

6.7b

Counts

195 → 11

Alt Table

Status	Error	Program
▶	36.8b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
	43.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	49.0b	(/.f64 (.f64 (+.f64 (fma.f64 b_2 b_2 (.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)
	43.7b	(/.f64 (*.f64 -2 b_2) a)
	48.5b	(pow.f64 (/.f64 a (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) -1)
	57.2b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
✓	36.8b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	56.8b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 a)))
	40.2b	(*.f64 -1/2 (/.f64 c b_2))
	48.7b	(.f64 (pow.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) 2) (.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a)))
	55.6b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)) 2)

Compiler

Compiled 4492 to 1575 computations (64.9% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
✓	1.4b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
	22.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series85.0ms (1.8%)

Counts

2 → 40

Calls

2 calls:

47.0ms	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
38.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

rewrite53.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

328×	`fma-neg_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
136×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	292	29
2	4222	29

Stop Event

1×	node limit

Counts

2 → 82

Calls

2 calls:

51.0ms	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
51.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

simplify35.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

692×	`times-frac_binary64`
458×	`associate-/l*_binary64`
372×	`associate-/r*_binary64`
314×	`associate-l_binary64`
238×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1176
1	322	1144
2	1138	1130

Stop Event

1×	node limit

Counts

122 → 130

prune127.0ms (2.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	178	11	189

Error

6.7b

Counts

189 → 11

Alt Table

Status	Error	Program
	56.8b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 a)))
	43.8b	(.f64 (.f64 2 b_2) (/.f64 1 (neg.f64 a)))
✓	36.8b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
	43.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	48.5b	(pow.f64 (/.f64 a (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) -1)
	57.2b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
✓	36.8b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
▶	40.2b	(*.f64 -1/2 (/.f64 c b_2))
	48.7b	(.f64 (pow.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) 2) (.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a)))
	49.0b	(/.f64 (.f64 (+.f64 (fma.f64 b_2 b_2 (.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)
	55.6b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)) 2)

Compiler

Compiled 4365 to 1779 computations (59.2% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 -1/2 (/.f64 c b_2))

series6.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

6.0ms

(*.f64 -1/2 (/.f64 c b_2))

rewrite59.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
317×	`log-prod_binary64`
116×	`expm1-udef_binary64`
116×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	127	7
2	1622	7

Stop Event

1×	node limit

Counts

1 → 25

Calls

1 calls:

59.0ms

(*.f64 -1/2 (/.f64 c b_2))

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

25 → 25

prune24.0ms (0.5%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	21	15	36

Error

6.7b

Counts

36 → 15

Alt Table

Status	Error	Program
	56.8b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 a)))
	43.8b	(.f64 (.f64 2 b_2) (/.f64 1 (neg.f64 a)))
▶	40.3b	(/.f64 -1/2 (/.f64 b_2 c))
✓	36.8b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
	43.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	49.0b	(/.f64 (.f64 (+.f64 (fma.f64 b_2 b_2 (.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)
	52.1b	(pow.f64 (pow.f64 (/.f64 (*.f64 -1/2 c) b_2) 3) 1/3)
	48.5b	(pow.f64 (/.f64 a (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) -1)
	57.2b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
✓	36.8b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
✓	40.2b	(*.f64 -1/2 (/.f64 c b_2))
	48.5b	(exp.f64 (log.f64 (/.f64 (*.f64 -1/2 c) b_2)))
	48.7b	(.f64 (pow.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) 2) (.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a)))
	40.5b	(/.f64 (/.f64 (*.f64 -1/2 c) (pow.f64 (cbrt.f64 b_2) 2)) (cbrt.f64 b_2))
	55.6b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)) 2)

Compiler

Compiled 650 to 426 computations (34.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 -1/2 (/.f64 b_2 c))

series6.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(/.f64 -1/2 (/.f64 b_2 c))

rewrite36.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`log1p-expm1-u_binary64`
650×	`expm1-log1p-u_binary64`
329×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	134	7
2	1782	7

Stop Event

1×	node limit

Counts

1 → 31

Calls

1 calls:

36.0ms

(/.f64 -1/2 (/.f64 b_2 c))

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

55 → 31

prune24.0ms (0.5%)

Pruning

15 alts after pruning (11 fresh and 4 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	11	11
Picked	0	1	1
Done	0	3	3
Total	31	15	46

Error

6.7b

Counts

46 → 15

Alt Table

Status	Error	Program
	56.8b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 a)))
	43.8b	(.f64 (.f64 2 b_2) (/.f64 1 (neg.f64 a)))
✓	40.3b	(/.f64 -1/2 (/.f64 b_2 c))
✓	36.8b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
	43.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	49.0b	(/.f64 (.f64 (+.f64 (fma.f64 b_2 b_2 (.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)
	52.1b	(pow.f64 (pow.f64 (/.f64 (*.f64 -1/2 c) b_2) 3) 1/3)
	48.5b	(pow.f64 (/.f64 a (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) -1)
	57.2b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
✓	36.8b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
✓	40.2b	(*.f64 -1/2 (/.f64 c b_2))
	48.5b	(exp.f64 (log.f64 (/.f64 (*.f64 -1/2 c) b_2)))
	48.7b	(.f64 (pow.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) 2) (.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a)))
	40.5b	(/.f64 (/.f64 (*.f64 -1/2 c) (pow.f64 (cbrt.f64 b_2) 2)) (cbrt.f64 b_2))
	55.6b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)) 2)

Compiler

Compiled 517 to 325 computations (37.1% saved)

regimes780.0ms (16.9%)

Accuracy

Total 4.4b remaining (42.8%)

Threshold costs 0b (0%)

Counts

61 → 3

Compiler

Compiled 4220 to 2658 computations (37% saved)

bsearch50.0ms (1.1%)

Steps

Iters	Range		Point
1	1.1746381004079593e+111	1.2027482700904448e+112	3.8527115384289745e+111
9	-2.7374413680200954e-43	-2.8655546485837628e-49	-9.582839230886112e-49

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	53
1	40	53
2	57	53
3	73	53
4	82	53
5	86	53
6	87	53

Stop Event

1×

saturated

end170.0ms (3.7%)

Compiler: Compiled 314 to 199 computations (36.6% saved)

Details

analyze717.0ms (15.5%)

sample2.0s (42.6%)

simplify61.0ms (1.3%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series158.0ms (3.4%)

rewrite64.0ms (1.4%)

simplify38.0ms (0.8%)

prune113.0ms (2.5%)

localize10.0ms (0.2%)

series85.0ms (1.8%)

rewrite53.0ms (1.1%)

simplify35.0ms (0.7%)

prune127.0ms (2.8%)

localize3.0ms (0.1%)

series6.0ms (0.1%)

rewrite59.0ms (1.3%)

simplify7.0ms (0.2%)

prune24.0ms (0.5%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite36.0ms (0.8%)

simplify10.0ms (0.2%)

prune24.0ms (0.5%)

regimes780.0ms (16.9%)

bsearch50.0ms (1.1%)

simplify3.0ms (0.1%)

end170.0ms (3.7%)

Profiling