Details

analyze1.4s (20.5%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
5.5%	94.4%	0.1%	8
14%	85.9%	0.1%	9
18%	80.4%	1.7%	10
22.6%	74.1%	3.2%	11
24.8%	71%	4.2%	12
27.7%	66.8%	5.6%	13
28.5%	65.4%	6.1%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample2.0s (29.9%)

Results

1.2s	8256×	body	128	valid
767.0ms	835×	body	8192	exit
32.0ms	195×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify37.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

693×	`div-sub_binary64`
599×	`times-frac_binary64`
519×	`associate-/l*_binary64`
357×	`associate-/l/_binary64`
274×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	37	29
2	94	29
3	345	29
4	1207	28
5	3468	28
6	5020	28

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
	12.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Status

Error

Program

▶

0.2b

(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

12.6b

(*.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (*.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Compiler

Compiled 127 to 87 computations (31.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
✓	0.2b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
✓	0.2b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
✓	0.3b	(/.f64 (PI.f64) a)

series55.0ms (0.8%)

Counts

4 → 72

Calls

4 calls:

22.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
18.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
12.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
2.0ms	(/.f64 (PI.f64) a)

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
55×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

4 → 143

Calls

4 calls:

13.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
4.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
2.0ms	(/.f64 (PI.f64) a)
0.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))

simplify320.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

425×	`times-frac_binary64`
380×	`associate-/l/_binary64`
318×	`fma-neg_binary64`
291×	`fma-def_binary64`
232×	`distribute-rgt-in_binary64`

Counts

215 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	5404
1	676	4819
2	2133	4749
3	4629	4748
4	4989	4748
5	4998	4748
6	4972	4748

prune237.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	231	6	237
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	232	7	239

Error

Counts

239 → 7

Alt Table

Status	Error	Program
	12.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	34.4b	(.f64 (sqrt.f64 (/.f64 1/2 (+.f64 b a))) (.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (sqrt.f64 (/.f64 1/2 (+.f64 a b)))))
	0.3b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (/.f64 (-.f64 b a) (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)))))
	0.5b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
▶	0.2b	(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))
	0.9b	(.f64 (/.f64 1/2 (+.f64 b a)) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))) (.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (/.f64 (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (cbrt.f64 (-.f64 b a)))))

Compiler

Compiled 6998 to 2666 computations (61.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
✓	0.2b	(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))
	0.2b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
	0.3b	(/.f64 (PI.f64) a)

series19.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

19.0ms

(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
4×	`associate-/r*_binary64`
4×	`times-frac_binary64`

Counts

1 → 30

Calls

1 calls:

8.0ms

(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

567×	`times-frac_binary64`
544×	`associate-/l*_binary64`
318×	`associate-/r*_binary64`
307×	`associate-/l/_binary64`
301×	`fma-neg_binary64`

Counts

54 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1928
1	362	1664
2	1254	1598
3	4746	1598
4	4962	1598

prune217.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	180	7	187

Error

Counts

187 → 7

Alt Table

Status	Error	Program
	12.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
▶	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	34.4b	(.f64 (sqrt.f64 (/.f64 1/2 (+.f64 b a))) (.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (sqrt.f64 (/.f64 1/2 (+.f64 a b)))))
	0.5b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
✓	0.2b	(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))
	0.3b	(/.f64 (*.f64 1/2 (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))) (+.f64 b a))
	0.9b	(.f64 (/.f64 1/2 (+.f64 b a)) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))) (.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (/.f64 (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (cbrt.f64 (-.f64 b a)))))

Compiler

Compiled 5035 to 2033 computations (59.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
✓	0.7b	(/.f64 (PI.f64) (*.f64 a b))

series31.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

19.0ms	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
12.0ms	(/.f64 (PI.f64) (*.f64 a b))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cbrt-cube_binary64`
28×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`

Counts

2 → 76

Calls

2 calls:

11.0ms	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
3.0ms	(/.f64 (PI.f64) (*.f64 a b))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

841×	`associate-/r*_binary64`
827×	`associate-/l*_binary64`
338×	`associate-/l/_binary64`
267×	`fma-def_binary64`
181×	`associate-/r/_binary64`

Counts

100 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	2370
1	509	2035
2	1807	1969
3	5391	1969

prune113.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	126	6	132

Error

Counts

132 → 6

Alt Table

Status	Error	Program
	0.3b	(/.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64)) (.f64 a b))
	0.5b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
	0.5b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 (.f64 a b) (sqrt.f64 (PI.f64)))))
	0.5b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
✓	0.2b	(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))
▶	0.3b	(/.f64 (*.f64 1/2 (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))) (+.f64 b a))

Compiler

Compiled 2628 to 1100 computations (58.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))
	0.3b	(/.f64 (PI.f64) a)
✓	0.3b	(/.f64 (PI.f64) b)
✓	0.6b	(/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))

series53.0ms (0.8%)

Counts

3 → 48

Calls

3 calls:

31.0ms	(/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))
20.0ms	(/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))
2.0ms	(/.f64 (PI.f64) b)

rewrite130.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

770×	`times-frac_binary64`
656×	`add-sqr-sqrt_binary64`
552×	`*-un-lft-identity_binary64`
222×	`add-cube-cbrt_binary64`
191×	`distribute-lft-out--_binary64`

Counts

3 → 420

Calls

3 calls:

22.0ms	(/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))
16.0ms	(/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))
2.0ms	(/.f64 (PI.f64) b)

simplify385.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-def_binary64`
492×	`times-frac_binary64`
456×	`associate-/r/_binary64`
323×	`associate-/l/_binary64`
318×	`distribute-rgt-in_binary64`

Counts

468 → 469

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	333	14913
1	724	14109
2	2216	13710
3	4496	13710
4	5084	13710

prune1.0s (14.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	500	0	500
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	500	6	506

Error

Counts

506 → 6

Alt Table

Status	Error	Program
	0.3b	(/.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64)) (.f64 a b))
	0.5b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
	0.5b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 (.f64 a b) (sqrt.f64 (PI.f64)))))
	0.5b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
✓	0.2b	(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))
✓	0.3b	(/.f64 (*.f64 1/2 (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))) (+.f64 b a))

Compiler

Compiled 16857 to 4685 computations (72.2% saved)

regimes431.0ms (6.3%)

Accuracy

Total 0.3b remaining (93%)

Threshold costs 0.3b (93%)

Counts

131 → 1

Compiler

Compiled 9313 to 5880 computations (36.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	18	28
2	22	28
3	24	28
4	25	28
5	25	28

end94.0ms (1.4%)

Compiler: Compiled 149 to 100 computations (32.9% saved)

Details

analyze1.4s (20.5%)

sample2.0s (29.9%)

simplify37.0ms (0.5%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

series55.0ms (0.8%)

rewrite35.0ms (0.5%)

simplify320.0ms (4.7%)

prune237.0ms (3.5%)

localize12.0ms (0.2%)

series19.0ms (0.3%)

rewrite10.0ms (0.1%)

simplify75.0ms (1.1%)

prune217.0ms (3.2%)

localize7.0ms (0.1%)

series31.0ms (0.5%)

rewrite20.0ms (0.3%)

simplify64.0ms (0.9%)

prune113.0ms (1.7%)

localize17.0ms (0.2%)

series53.0ms (0.8%)

rewrite130.0ms (1.9%)

simplify385.0ms (5.6%)

prune1.0s (14.7%)

regimes431.0ms (6.3%)

simplify3.0ms (0%)

end94.0ms (1.4%)

Profiling