Details

analyze663.0ms (10.1%)

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)

sample2.4s (37.4%)

Results

653.0ms	5321×	body	128	valid
558.0ms	1193×	body	2048	valid
407.0ms	781×	body	1024	valid
201.0ms	350×	body	4096	valid
124.0ms	1074×	body	128	invalid
120.0ms	405×	body	512	valid
42.0ms	206×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify306.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	27	20
2	54	20
3	115	20
4	179	20
5	291	20
6	417	20
7	528	20
8	602	20
9	854	20
10	1802	20
11	1043	20
12	1027	20
13	1035	20
14	1043	20
15	1043	20
16	1101	20
17	1137	20
18	1139	20
19	1151	20
20	1046	20

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

36.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.5b	(/.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 (0.1%)

Local error

Found 4 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)
✓	0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	25.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series173.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

78.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
52.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
36.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite96.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

694×	`fma-def_binary64`
352×	`fma-neg_binary64`
337×	`egg-rr`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`

Counts

4 → 337

Calls

4 calls:

87.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
87.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
87.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
87.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	59
1	257	55
2	3373	55
3	4972	55
0	0	0
1	0	0

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
497×	`associate-/l*_binary64`
494×	`fma-neg_binary64`
404×	`associate-/r*_binary64`
370×	`fma-def_binary64`

Counts

433 → 410

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	2047
1	405	2003
2	1350	1977
3	4891	1977
4	5208	1977

prune253.0ms (3.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	401	9	410
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	401	10	411

Error

6.1b

Counts

411 → 10

Alt Table

Status	Error	Program
▶	37.3b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)) a)
	57.4b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	41.2b	(*.f64 -1/2 (/.f64 c b_2))
	55.8b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 a)))
	41.3b	(/.f64 (*.f64 -2 b_2) a)
✓	36.5b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	49.2b	(.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	49.7b	(/.f64 (/.f64 1 (/.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (+.f64 (fma.f64 b_2 b_2 (.f64 b_2 b_2)) (.f64 a c)))) a)
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	53.2b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)))) a)

Compiler

Compiled 10539 to 2953 computations (72% saved)

localize35.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)
	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	10.3b	(-.f64 (neg.f64 b_2) (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2))
✓	26.6b	(pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4)

series174.0ms (2.7%)

Counts

3 → 92

Calls

3 calls:

72.0ms	(-.f64 (neg.f64 b_2) (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2))
59.0ms	(pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)
42.0ms	(pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4)

rewrite96.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

614×	`fma-def_binary64`
291×	`fma-neg_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
147×	`egg-rr`

Counts

3 → 147

Calls

3 calls:

91.0ms	(pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)
91.0ms	(-.f64 (neg.f64 b_2) (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2))
91.0ms	(pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	301	40
2	3285	38
3	4987	38
4	4848	38
0	0	0
1	0	0

simplify105.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

286×	`times-frac_binary64`
278×	`fma-neg_binary64`
268×	`associate-/r*_binary64`
266×	`sub-neg_binary64`
237×	`associate-r_binary64`

Counts

239 → 275

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	331	4288
1	1081	4192
2	4347	4188
3	5025	4188

prune370.0ms (5.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	443	2	445
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	445	10	455

Error

0.8b

Counts

455 → 10

Alt Table

Status	Error	Program
	49.7b	(/.f64 (/.f64 1 (/.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (+.f64 (fma.f64 b_2 b_2 (.f64 b_2 b_2)) (.f64 a c)))) a)
	52.4b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 a) (log.f64 (/.f64 -1 c))))) 2)) a)
▶	41.2b	(*.f64 -1/2 (/.f64 c b_2))
	55.8b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 a)))
✓	37.3b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)) a)
	49.2b	(.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	55.2b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 c) (log.f64 (neg.f64 a))))) 2)) a)
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	53.2b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)))) a)
✓	36.5b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 14135 to 5908 computations (58.2% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

7.0ms

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

rewrite37.0ms (0.6%)

Algorithm

2×	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`

Counts

1 → 27

Calls

1 calls:

37.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	127	7
2	1573	7
3	4969	7
0	0	0
1	0	0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune22.0ms (0.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	26	11	37

Error

0.8b

Counts

37 → 11

Alt Table

Status	Error	Program
	50.1b	(pow.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 c b_2))) 2)
	49.2b	(.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	49.7b	(/.f64 (/.f64 1 (/.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (+.f64 (fma.f64 b_2 b_2 (.f64 b_2 b_2)) (.f64 a c)))) a)
	52.4b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 a) (log.f64 (/.f64 -1 c))))) 2)) a)
✓	37.3b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)) a)
▶	41.2b	(/.f64 (*.f64 -1/2 c) b_2)
	55.2b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 c) (log.f64 (neg.f64 a))))) 2)) a)
	55.8b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 a)))
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	53.2b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)))) a)
✓	36.5b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 579 to 381 computations (34.2% saved)

localize3.0ms (0%)

prune8.0ms (0.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	2	2
Total	11	11

Error

0.8b

Counts

11 → 11

Alt Table

Status	Error	Program
	50.1b	(pow.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 c b_2))) 2)
	49.2b	(.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	49.7b	(/.f64 (/.f64 1 (/.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (+.f64 (fma.f64 b_2 b_2 (.f64 b_2 b_2)) (.f64 a c)))) a)
	52.4b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 a) (log.f64 (/.f64 -1 c))))) 2)) a)
✓	37.3b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)) a)
✓	41.2b	(/.f64 (*.f64 -1/2 c) b_2)
	55.2b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 c) (log.f64 (neg.f64 a))))) 2)) a)
	55.8b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 a)))
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	53.2b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)))) a)
✓	36.5b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 191 to 129 computations (32.5% saved)

regimes1.4s (21.2%)

Accuracy

Total 9.3b remaining (91.9%)

Threshold costs 0b (0%)

Counts

75 → 3

Compiler

Compiled 5700 to 3554 computations (37.6% saved)

bsearch93.0ms (1.4%)

Steps

Iters	Range		Point
7	3.51924356345418e+85	1.9056159869820554e+87	9.108292722462307e+85
11	-7.078853247986652e-57	-3.7037813862544596e-82	-1.102385277532225e-63

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	63
1	40	63
2	49	63
3	59	63
4	64	63
5	67	63
6	68	63
7	68	63

end164.0ms (2.5%)

Compiler: Compiled 283 to 183 computations (35.3% saved)

Details

analyze663.0ms (10.1%)

sample2.4s (37.4%)

simplify306.0ms (4.7%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series173.0ms (2.7%)

rewrite96.0ms (1.5%)

simplify80.0ms (1.2%)

prune253.0ms (3.9%)

localize35.0ms (0.5%)

series174.0ms (2.7%)

rewrite96.0ms (1.5%)

simplify105.0ms (1.6%)

prune370.0ms (5.7%)

localize3.0ms (0%)

series7.0ms (0.1%)

rewrite37.0ms (0.6%)

simplify6.0ms (0.1%)

prune22.0ms (0.3%)

localize3.0ms (0%)

prune8.0ms (0.1%)

regimes1.4s (21.2%)

bsearch93.0ms (1.4%)

simplify4.0ms (0.1%)

end164.0ms (2.5%)

Profiling