Details

analyze101.0ms (3.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 20 to 11 computations (45% saved)

sample36.0ms (1.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	6×	pre	128	false

Compiler

Compiled 37 to 21 computations (43.2% saved)

simplify52.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

15.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	15.1b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 42 to 24 computations (42.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 a a) (.f64 b b))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
14.6b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite68.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
11×	`times-frac_binary64`
10×	`fabs-mul_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 75

Calls

3 calls:

6.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
4.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
3.0ms	(-.f64 (.f64 a a) (.f64 b b))

Compiler

Compiled 1557 to 319 computations (79.5% saved)

series62.0ms (2.2%)

Error

1.2b

Counts

3 → 30

Calls

3 calls:

25.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
18.0ms	(-.f64 (.f64 a a) (.f64 b b))
14.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 715 to 564 computations (21.1% saved)

simplify108.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

653×	`times-frac_binary64`
330×	`associate-l_binary64`
306×	`associate-/l*_binary64`
296×	`fma-neg_binary64`
282×	`associate-r_binary64`

Counts

105 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1809
1	285	1640
2	879	1567
3	3871	1555
4	4888	1555
5	4981	1555

prune38.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	4	78

Error

Counts

78 → 4

Alt Table

Status	Error	Program
✓	15.1b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
	0.1b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))) 3))
▶	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))))

Compiler

Compiled 920 to 384 computations (58.3% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 a (*.f64 b (/.f64 b a)))
0.0b	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
0.1b	(*.f64 b (/.f64 b a))

rewrite107.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

45×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
18×	`sqrt-prod_binary64`

Counts

4 → 121

Calls

4 calls:

6.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
5.0ms	(*.f64 b (/.f64 b a))
4.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
3.0ms	(-.f64 a (*.f64 b (/.f64 b a)))

Compiler

Compiled 2330 to 621 computations (73.3% saved)

series73.0ms (2.5%)

Error

Counts

4 → 36

Calls

4 calls:

25.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
18.0ms	(-.f64 a (*.f64 b (/.f64 b a)))
13.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
12.0ms	(*.f64 b (/.f64 b a))

Compiler

Compiled 792 to 590 computations (25.5% saved)

simplify152.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
429×	`associate-/l*_binary64`
310×	`associate-/r*_binary64`
299×	`associate-*l/_binary64`
269×	`associate-*r/_binary64`

Counts

157 → 129

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	2659
1	422	2497
2	1120	2366
3	3371	2338
4	4631	2338
5	4993	2338
6	4875	2338

prune64.0ms (2.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	129	4	133

Error

Counts

133 → 4

Alt Table

Status	Error	Program
✓	15.1b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
	0.1b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))) 3))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
▶	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))))

Compiler

Compiled 1679 to 547 computations (67.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 b a) a)
0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))))
0.0b	(*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))
0.0b	(/.f64 (-.f64 a b) a)

rewrite128.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

69×	`*-un-lft-identity_binary64`
68×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 155

Calls

4 calls:

14.0ms	(*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))
6.0ms	(/.f64 (+.f64 b a) a)
5.0ms	(/.f64 (-.f64 a b) a)
1.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))))

Compiler

Compiled 2938 to 709 computations (75.9% saved)

series75.0ms (2.6%)

Error

Counts

4 → 42

Calls

4 calls:

25.0ms	(*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))
15.0ms	(/.f64 (-.f64 a b) a)
15.0ms	(/.f64 (+.f64 b a) a)
13.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))))

Compiler

Compiled 1027 to 716 computations (30.3% saved)

simplify122.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

581×	`times-frac_binary64`
546×	`distribute-rgt-in_binary64`
522×	`distribute-lft-in_binary64`
275×	`fma-def_binary64`
145×	`associate-*l/_binary64`

Counts

197 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	3207
1	543	2953
2	1754	2947
3	4619	2933
4	4964	2933

prune60.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	128	4	132

Error

Counts

132 → 4

Alt Table

Status	Error	Program
✓	15.1b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	0.1b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))) 3))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
✓	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))))

Compiler

Compiled 1790 to 558 computations (68.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(fma.f64 (/.f64 b a) (/.f64 b a) -1)
0.0b	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
0.0b	(pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))) 3)
0.1b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))) 3))

rewrite95.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

35×	`sqrt-prod_binary64`
28×	`add-sqr-sqrt_binary64`
26×	`cbrt-prod_binary64`
20×	`cube-prod_binary64`
20×	`*-un-lft-identity_binary64`

Counts

4 → 110

Calls

4 calls:

3.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))) 3))
3.0ms	(pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))) 3)
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
1.0ms	(fma.f64 (/.f64 b a) (/.f64 b a) -1)

Compiler

Compiled 1909 to 1082 computations (43.3% saved)

series73.0ms (2.6%)

Error

Counts

4 → 30

Calls

4 calls:

25.0ms	(fma.f64 (/.f64 b a) (/.f64 b a) -1)
22.0ms	(pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))) 3)
12.0ms	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
10.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))) 3))

Compiler

Compiled 832 to 601 computations (27.8% saved)

simplify133.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

437×	`associate-l_binary64`
308×	`associate-r_binary64`
301×	`log-prod_binary64`
299×	`distribute-rgt-in_binary64`
285×	`distribute-lft-in_binary64`

Counts

140 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	2861
1	182	2734
2	407	2642
3	1518	2620
4	4753	2620
5	4910	2620

prune31.0ms (1.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	97	4	101

Error

Counts

101 → 4

Alt Table

Status	Error	Program
	15.1b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
	0.1b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))) 3))
	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))))

Compiler

Compiled 703 to 377 computations (46.4% saved)

regimes239.0ms (8.3%)

Accuracy

Total 0.0b remaining (79%)

Threshold costs 0.0b (79%)

Compiler

Compiled 5181 to 3085 computations (40.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	18	17
2	30	17
3	39	17
4	46	17
5	49	17
6	50	17
7	50	17

end0.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

sample1.0s (35.2%)

Algorithm

1×

intervals

Results

383.0ms	8000×	body	128	valid
265.0ms	8000×	pre	128	true
3.0ms	129×	pre	128	false

Compiler

Compiled 93 to 56 computations (39.8% saved)

Details

analyze101.0ms (3.5%)

sample36.0ms (1.3%)

simplify52.0ms (1.8%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

rewrite68.0ms (2.4%)

series62.0ms (2.2%)

simplify108.0ms (3.8%)

prune38.0ms (1.3%)

localize7.0ms (0.3%)

rewrite107.0ms (3.7%)

series73.0ms (2.5%)

simplify152.0ms (5.3%)

prune64.0ms (2.2%)

localize8.0ms (0.3%)

rewrite128.0ms (4.5%)

series75.0ms (2.6%)

simplify122.0ms (4.3%)

prune60.0ms (2.1%)

localize9.0ms (0.3%)

rewrite95.0ms (3.3%)

series73.0ms (2.6%)

simplify133.0ms (4.6%)

prune31.0ms (1.1%)

regimes239.0ms (8.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.0s (35.2%)

Profiling