Details

analyze303.0ms (8.5%)

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
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample82.0ms (2.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 49 to 37 computations (24.5% saved)

simplify36.0ms (1%)

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

prune4.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
	15.9b	(.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

▶

0.4b

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

15.9b

(*.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 (0.3%)

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 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
✓	0.3b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
✓	0.3b	(/.f64 (PI.f64) a)

series55.0ms (1.5%)

Counts

4 → 72

Calls

4 calls:

23.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
19.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
11.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
2.0ms	(/.f64 (PI.f64) a)

rewrite36.0ms (1%)

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:

15.0ms	(*.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))

simplify206.0ms (5.8%)

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	5398
1	676	4819
2	2133	4749
3	4629	4748
4	4989	4748
5	4998	4748
6	4972	4748

prune243.0ms (6.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	9	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	230	9	239

Error

Counts

239 → 9

Alt Table

Status	Error	Program
	32.6b	(.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 b a))) (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 b a))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	1.0b	(.f64 (/.f64 1/2 (+.f64 b a)) (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)))) (.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (/.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (cbrt.f64 (-.f64 b a)))))
▶	0.3b	(/.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 b a)) (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)))
	15.8b	(.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 (.f64 b b) (*.f64 a a))))
	34.6b	(.f64 (/.f64 (PI.f64) (.f64 b b)) (-.f64 (/.f64 1/2 a) (/.f64 1/2 b)))
	0.4b	(.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))))
	25.9b	(.f64 1/2 (/.f64 (PI.f64) (.f64 a (*.f64 a b))))

Compiler

Compiled 7048 to 2695 computations (61.8% saved)

localize10.0ms (0.3%)

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))
	0.3b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
	0.3b	(/.f64 (PI.f64) a)

series19.0ms (0.5%)

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 (0.3%)

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))

simplify74.0ms (2.1%)

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

prune161.0ms (4.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	181	8	189

Error

Counts

189 → 8

Alt Table

Status	Error	Program
	32.6b	(.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 b a))) (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 b a))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
▶	0.3b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
	0.4b	(.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))))
✓	0.3b	(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))
	0.7b	(/.f64 1/2 (/.f64 (+.f64 b a) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	34.6b	(.f64 (/.f64 (PI.f64) (.f64 b b)) (-.f64 (/.f64 1/2 a) (/.f64 1/2 b)))
	25.9b	(.f64 1/2 (/.f64 (PI.f64) (.f64 a (*.f64 a b))))

Compiler

Compiled 4973 to 2019 computations (59.4% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (/.f64 (PI.f64) (.f64 a b)))
✓	0.2b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
✓	0.4b	(/.f64 (PI.f64) (*.f64 a b))

series41.0ms (1.2%)

Counts

3 → 24

Calls

3 calls:

18.0ms	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
12.0ms	(.f64 1/2 (/.f64 (PI.f64) (.f64 a b)))
11.0ms	(/.f64 (PI.f64) (*.f64 a b))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`times-frac_binary64`

Counts

3 → 84

Calls

3 calls:

10.0ms	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
5.0ms	(.f64 1/2 (/.f64 (PI.f64) (.f64 a b)))
3.0ms	(/.f64 (PI.f64) (*.f64 a b))

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

860×	`associate-/r*_binary64`
606×	`associate-/l/_binary64`
435×	`associate-/r/_binary64`
248×	`fma-def_binary64`
140×	`cancel-sign-sub-inv_binary64`

Counts

108 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2343
1	474	2001
2	1614	1934
3	4969	1934

prune103.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	126	7	133

Error

Counts

133 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
▶	0.4b	(.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))))
	0.6b	(/.f64 1/2 (/.f64 (+.f64 b a) (/.f64 (PI.f64) (*.f64 a b))))
	32.6b	(.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 b a))) (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 b a))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	0.6b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
✓	0.3b	(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))
	34.6b	(.f64 (/.f64 (PI.f64) (.f64 b b)) (-.f64 (/.f64 1/2 a) (/.f64 1/2 b)))

Compiler

Compiled 2481 to 1038 computations (58.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (PI.f64) b)
	0.3b	(/.f64 (PI.f64) a)
✓	0.3b	(.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))))
✓	0.4b	(/.f64 (sqrt.f64 1/2) (+.f64 a b))

series47.0ms (1.3%)

Counts

3 → 48

Calls

3 calls:

31.0ms	(.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))))
12.0ms	(/.f64 (sqrt.f64 1/2) (+.f64 a b))
4.0ms	(/.f64 (PI.f64) b)

rewrite48.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-exp-log_binary64`
55×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
48×	`add-cbrt-cube_binary64`
41×	`add-sqr-sqrt_binary64`

Counts

3 → 146

Calls

3 calls:

26.0ms	(.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))))
5.0ms	(/.f64 (sqrt.f64 1/2) (+.f64 a b))
2.0ms	(/.f64 (PI.f64) b)

simplify151.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

430×	`associate-/l/_binary64`
300×	`fma-def_binary64`
297×	`fma-neg_binary64`
289×	`associate-/r/_binary64`
219×	`distribute-rgt-in_binary64`

Counts

194 → 226

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	286	5789
1	632	4654
2	2089	4444
3	4768	4432
4	5021	4432

prune229.0ms (6.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	257	7	264

Error

Counts

264 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
✓	0.4b	(.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))))
	0.6b	(/.f64 1/2 (/.f64 (+.f64 b a) (/.f64 (PI.f64) (*.f64 a b))))
	32.6b	(.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 b a))) (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 b a))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	0.6b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
✓	0.3b	(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))
	34.6b	(.f64 (/.f64 (PI.f64) (.f64 b b)) (-.f64 (/.f64 1/2 a) (/.f64 1/2 b)))

Compiler

Compiled 8139 to 3880 computations (52.3% saved)

regimes630.0ms (17.7%)

Accuracy

Total 0.2b remaining (90.7%)

Threshold costs 0.2b (90.7%)

Counts

167 → 1

Compiler

Compiled 11614 to 7416 computations (36.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	13	17
2	13	17

end0.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample964.0ms (27%)

Algorithm

1×

intervals

Results

617.0ms	8000×	body	128	valid
27.0ms	354×	body	128	invalid

Compiler

Compiled 168 to 117 computations (30.4% saved)

Details

analyze303.0ms (8.5%)

sample82.0ms (2.3%)

simplify36.0ms (1%)

prune4.0ms (0.1%)

localize11.0ms (0.3%)

series55.0ms (1.5%)

rewrite36.0ms (1%)

simplify206.0ms (5.8%)

prune243.0ms (6.8%)

localize10.0ms (0.3%)

series19.0ms (0.5%)

rewrite10.0ms (0.3%)

simplify74.0ms (2.1%)

prune161.0ms (4.5%)

localize6.0ms (0.2%)

series41.0ms (1.2%)

rewrite22.0ms (0.6%)

simplify61.0ms (1.7%)

prune103.0ms (2.9%)

localize12.0ms (0.3%)

series47.0ms (1.3%)

rewrite48.0ms (1.4%)

simplify151.0ms (4.2%)

prune229.0ms (6.4%)

regimes630.0ms (17.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample964.0ms (27%)

Profiling