Details

analyze632.0ms (8.2%)

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)

sample2.4s (31.6%)

Results

767.0ms	5399×	body	128	valid
643.0ms	1193×	body	2048	valid
383.0ms	743×	body	1024	valid
246.0ms	401×	body	4096	valid
162.0ms	1145×	body	128	invalid
141.0ms	370×	body	512	valid
35.0ms	150×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

648×	`rules-33_binary64`
343×	`rules-1_binary64`
333×	`rules-6-rev_binary64`
291×	`rules-5-rev_binary64`
260×	`rules-1-rev_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	32	25
2	77	25
3	214	22
4	822	22
5	3625	22
6	4688	22
7	5867	22

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

34.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 75 to 50 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 4 a) c)
✓	0.5b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series77.0ms (1%)

Counts

4 → 100

Calls

4 calls:

34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
28.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(.f64 (.f64 4 a) c)

rewrite90.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

231×	`expm1-udef_binary64`
231×	`log1p-udef_binary64`
204×	`log-pow_binary64`
202×	`log-div_binary64`
193×	`egg-rr`

Counts

4 → 193

Calls

4 calls:

84.0ms	(.f64 (.f64 4 a) c)
84.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
84.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
84.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	55
1	300	53
2	3880	51
3	5046	51
0	0	0
1	0	0

simplify96.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

467×	`fma-def_binary64`
371×	`rules-11_binary64`
311×	`fma-neg_binary64`
304×	`rules-20_binary64`
277×	`rules-13_binary64`

Counts

293 → 243

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1835
1	257	1694
2	1111	1675
3	4880	1675
4	4997	1675
5	4941	1675

prune185.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	233	10	243
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	234	10	244

Error

8.4b

Counts

244 → 10

Alt Table

Status	Error	Program
	37.8b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 (neg.f64 b)) 2) (cbrt.f64 (neg.f64 b)) (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) (*.f64 2 a))
	56.0b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
▶	35.9b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b))) (*.f64 2 a))
	37.2b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) 3)) (*.f64 2 a))
	36.4b	(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b)) (*.f64 2 a))
	46.6b	(/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a))
	47.2b	(/.f64 (.f64 -2 b) (.f64 2 a))
	53.7b	(/.f64 (.f64 -2 (fma.f64 c (/.f64 a b) (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)))) (*.f64 2 a))
	44.4b	(/.f64 (.f64 -2 (/.f64 (.f64 c a) b)) (*.f64 2 a))
	46.1b	(/.f64 (-.f64 (/.f64 (fma.f64 1/2 (.f64 b b) (.f64 c (.f64 a -4))) (sqrt.f64 (.f64 c (.f64 a -4)))) b) (.f64 2 a))

Compiler

Compiled 6537 to 4106 computations (37.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 4 a) c)
✓	0.2b	(-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b)
✓	2.8b	(exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b)))
✓	12.2b	(sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))

series283.0ms (3.7%)

Counts

3 → 24

Calls

3 calls:

149.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b)
121.0ms	(exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b)))
13.0ms	(sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))

rewrite84.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

627×	`prod-diff_binary64`
215×	`log1p-udef_binary64`
139×	`egg-rr`
120×	`add-sqr-sqrt_binary64`
117×	`log1p-expm1-u_binary64`

Counts

3 → 139

Calls

3 calls:

80.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b)
80.0ms	(exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b)))
80.0ms	(sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	282	45
2	3499	45
3	4993	45
0	0	0
1	0	0

simplify53.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

585×	`rules-14-rev_binary64`
237×	`rules-4_binary64`
201×	`rules-21_binary64`
189×	`fma-neg_binary64`
187×	`rules-11_binary64`

Counts

163 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	59	982
1	160	820
2	660	770
3	3992	770
4	5766	770

prune123.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	145	11	156

Error

8.4b

Counts

156 → 11

Alt Table

Status	Error	Program
	55.2b	(/.f64 (+.f64 (-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (*.f64 2 a))
	37.2b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) 3)) (*.f64 2 a))
	37.0b	(/.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b))) 2)) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b)))) (*.f64 2 a))
	56.0b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
▶	36.4b	(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b)) (*.f64 2 a))
	46.6b	(/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a))
	39.0b	(/.f64 (.f64 (cbrt.f64 b) (-.f64 (/.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (cbrt.f64 b)) (cbrt.f64 (.f64 b b)))) (*.f64 2 a))
	47.2b	(/.f64 (.f64 -2 b) (.f64 2 a))
	53.7b	(/.f64 (.f64 -2 (fma.f64 c (/.f64 a b) (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)))) (*.f64 2 a))
	44.4b	(/.f64 (.f64 -2 (/.f64 (.f64 c a) b)) (*.f64 2 a))
	46.1b	(/.f64 (-.f64 (/.f64 (fma.f64 1/2 (.f64 b b) (.f64 c (.f64 a -4))) (sqrt.f64 (.f64 c (.f64 a -4)))) b) (.f64 2 a))

Compiler

Compiled 4037 to 2824 computations (30% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 4 a) c)
	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	22.8b	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4)
✓	23.1b	(fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b))

series121.0ms (1.6%)

Counts

2 → 72

Calls

2 calls:

80.0ms	(fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b))
41.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4)

rewrite71.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
210×	`log-pow_binary64`
191×	`log-div_binary64`
134×	`add-sqr-sqrt_binary64`

Counts

2 → 67

Calls

2 calls:

69.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4)
69.0ms	(fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	53
1	320	36
2	3910	35
3	4980	35
0	0	0
1	0	0

simplify95.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

406×	`fma-neg_binary64`
300×	`fma-def_binary64`
257×	`rules-4_binary64`
238×	`rules-20_binary64`
219×	`rules-13_binary64`

Counts

139 → 176

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	303	3930
1	1003	3671
2	4695	3671
3	5183	3671

prune422.0ms (5.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	462	5	467
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	467	11	478

Error

4.2b

Counts

478 → 11

Alt Table

Status	Error	Program
✓	36.4b	(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b)) (*.f64 2 a))
	52.8b	(/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 4 c))) (log.f64 (/.f64 1 a))))) 2) b) (*.f64 2 a))
	46.6b	(/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a))
	46.2b	(/.f64 (.f64 c (/.f64 a (/.f64 b -2))) (.f64 2 a))
	51.4b	(/.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 c) (log.f64 (.f64 -4 a)))) 2) b) (.f64 2 a))
	52.8b	(/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2) b) (*.f64 2 a))
	37.2b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) 3)) (*.f64 2 a))
▶	34.0b	(/.f64 (+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (neg.f64 b)) (*.f64 2 a))
	47.2b	(/.f64 (.f64 -2 b) (.f64 2 a))
	44.4b	(/.f64 (.f64 -2 (/.f64 (.f64 c a) b)) (*.f64 2 a))
	46.1b	(/.f64 (-.f64 (/.f64 (fma.f64 1/2 (.f64 b b) (.f64 c (.f64 a -4))) (sqrt.f64 (.f64 c (.f64 a -4)))) b) (.f64 2 a))

Compiler

Compiled 19790 to 12475 computations (37% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (neg.f64 b)) (*.f64 2 a))
	0.2b	(.f64 (.f64 4 a) c)
✓	0.2b	(+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (neg.f64 b))
	12.2b	(sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))

series232.0ms (3%)

Counts

2 → 24

Calls

2 calls:

142.0ms	(/.f64 (+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (neg.f64 b)) (*.f64 2 a))
90.0ms	(+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (neg.f64 b))

rewrite93.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

976×	`prod-diff_binary64`
150×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`
144×	`expm1-log1p-u_binary64`
141×	`add-cbrt-cube_binary64`

Counts

2 → 76

Calls

2 calls:

88.0ms	(/.f64 (+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (neg.f64 b)) (*.f64 2 a))
88.0ms	(+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (neg.f64 b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	44
1	357	40
2	4394	40
3	6209	40
0	0	0
1	0	0

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

418×	`rules-15-rev_binary64`
404×	`rules-12-rev_binary64`
400×	`fma-neg_binary64`
378×	`rules-20_binary64`
255×	`fma-def_binary64`

Counts

100 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1084
1	333	917
2	1483	906
3	5064	906

prune145.0ms (1.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	188	3	191
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	190	12	202

Error

2.2b

Counts

202 → 12

Alt Table

Status	Error	Program
✓	36.4b	(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b)) (*.f64 2 a))
	52.8b	(/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 4 c))) (log.f64 (/.f64 1 a))))) 2) b) (*.f64 2 a))
	46.6b	(/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a))
	46.2b	(/.f64 (.f64 c (/.f64 a (/.f64 b -2))) (.f64 2 a))
	44.4b	(/.f64 (.f64 -2 (/.f64 (.f64 c a) b)) (*.f64 2 a))
	34.1b	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b) (/.f64 1 (.f64 a 2)))
	51.4b	(/.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 c) (log.f64 (.f64 -4 a)))) 2) b) (.f64 2 a))
	52.8b	(/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2) b) (*.f64 2 a))
	44.4b	(.f64 1/4 (/.f64 (.f64 (.f64 c a) -4) (.f64 a b)))
✓	34.0b	(/.f64 (+.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) (neg.f64 b)) (*.f64 2 a))
	47.2b	(/.f64 (.f64 -2 b) (.f64 2 a))
	34.5b	(.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b)) 2) (/.f64 (cbrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c)))) b)) (.f64 a 2)))

Compiler

Compiled 4860 to 3304 computations (32% saved)

regimes2.1s (27.1%)

Accuracy

Total 11.5b remaining (82.4%)

Threshold costs 0b (0%)

Counts

169 → 3

Compiler

Compiled 14936 to 10946 computations (26.7% saved)

bsearch61.0ms (0.8%)

Steps

Iters	Range		Point
5	3.547526034174891e-7	7.910935688616029e-7	5.206062075003178e-7
8	-1.761622937979916e+128	-7.291574701407998e+119	-1.3104263752164671e+126

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	63
1	35	63
2	34	63

end169.0ms (2.2%)

Compiler: Compiled 338 to 247 computations (26.9% saved)

Details

analyze632.0ms (8.2%)

sample2.4s (31.6%)

simplify64.0ms (0.8%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series77.0ms (1%)

rewrite90.0ms (1.2%)

simplify96.0ms (1.2%)

prune185.0ms (2.4%)

localize13.0ms (0.2%)

series283.0ms (3.7%)

rewrite84.0ms (1.1%)

simplify53.0ms (0.7%)

prune123.0ms (1.6%)

localize14.0ms (0.2%)

series121.0ms (1.6%)

rewrite71.0ms (0.9%)

simplify95.0ms (1.2%)

prune422.0ms (5.5%)

localize11.0ms (0.1%)

series232.0ms (3%)

rewrite93.0ms (1.2%)

simplify40.0ms (0.5%)

prune145.0ms (1.9%)

regimes2.1s (27.1%)

bsearch61.0ms (0.8%)

simplify2.0ms (0%)

end169.0ms (2.2%)

Profiling