Details

analyze22.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
12.5%	12.5%	75%	2
12.5%	12.5%	75%	3
18.7%	6.2%	75%	4
21.8%	3.1%	75%	5
23.4%	1.6%	75%	6
23.4%	1.6%	75%	7
24.2%	0.8%	75%	8
24.2%	0.8%	75%	9
24.6%	0.4%	75%	10
24.6%	0.4%	75%	11
24.8%	0.2%	75%	12
24.8%	0.2%	75%	13
24.9%	0.1%	75%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample83.0ms (1.9%)

Algorithm

1×

intervals

Results

26.0ms	50×	body	1024	valid
13.0ms	149×	body	128	valid
11.0ms	44×	body	512	valid
6.0ms	256×	pre	128	true
2.0ms	13×	body	256	valid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	17	15
2	23	15
3	26	15
4	27	15
5	26	15

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 47 to 28 computations (40.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 v)
✓	0.0b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(*.f64 e (sin.f64 v))

series41.0ms (0.9%)

Counts

3 → 32

Calls

3 calls:

32.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
7.0ms	(*.f64 e (sin.f64 v))
2.0ms	(cos.f64 v)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 52

Calls

3 calls:

4.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
3.0ms	(*.f64 e (sin.f64 v))
1.0ms	(cos.f64 v)

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-/r*_binary64`
503×	`fma-def_binary64`
289×	`cancel-sign-sub-inv_binary64`
287×	`associate-/r/_binary64`
260×	`associate-/l/_binary64`

Counts

84 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	1787
1	522	1642
2	2032	1598
3	5006	1598

prune96.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	7	97

Error

0.0b

Counts

97 → 7

Alt Table

Status	Error	Program
	22.6b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
▶	0.1b	(.f64 (sin.f64 v) (+.f64 e (.f64 (cos.f64 v) (-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (.f64 e e)))))
	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	36.6b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e e) e) (.f64 (*.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (cbrt.f64 (.f64 e (sin.f64 v)))) (cbrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 2301 to 1195 computations (48.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (.f64 e e))
✓	0.1b	(*.f64 (cos.f64 v) (pow.f64 e 3))
✓	0.1b	(.f64 (cos.f64 v) (-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (*.f64 e e)))
✓	0.1b	(.f64 (sin.f64 v) (+.f64 e (.f64 (cos.f64 v) (-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (.f64 e e)))))

series101.0ms (2.3%)

Counts

4 → 76

Calls

4 calls:

44.0ms	(.f64 (sin.f64 v) (+.f64 e (.f64 (cos.f64 v) (-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (.f64 e e)))))
26.0ms	(.f64 (cos.f64 v) (-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (*.f64 e e)))
16.0ms	(-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (.f64 e e))
14.0ms	(*.f64 (cos.f64 v) (pow.f64 e 3))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
13×	`add-exp-log_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

4 → 101

Calls

4 calls:

6.0ms	(.f64 (cos.f64 v) (-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (*.f64 e e)))
5.0ms	(-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (.f64 e e))
5.0ms	(*.f64 (cos.f64 v) (pow.f64 e 3))
5.0ms	(.f64 (sin.f64 v) (+.f64 e (.f64 (cos.f64 v) (-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (.f64 e e)))))

simplify102.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

745×	`cancel-sign-sub-inv_binary64`
417×	`fma-neg_binary64`
393×	`unswap-sqr_binary64`
346×	`associate-r_binary64`
321×	`associate-l_binary64`

Counts

177 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4265
1	761	3902
2	2905	3868
3	5196	3868

prune206.0ms (4.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	206	8	214

Error

0.0b

Counts

214 → 8

Alt Table

Status	Error	Program
	22.6b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(.f64 (sin.f64 v) (+.f64 e (.f64 (cos.f64 v) (-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (.f64 e e)))))
▶	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	36.6b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e e) e) (.f64 (*.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (cbrt.f64 (.f64 e (sin.f64 v)))) (cbrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	1.0b	(.f64 (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (.f64 (fma.f64 (cos.f64 v) (-.f64 (.f64 (pow.f64 e 3) (cos.f64 v)) (*.f64 e e)) e) (cbrt.f64 (sin.f64 v))))

Compiler

Compiled 6146 to 2922 computations (52.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 v)
✓	0.1b	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))
✓	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))

series49.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
18.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 101

Calls

2 calls:

4.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
2.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

simplify119.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

565×	`associate-/r/_binary64`
530×	`fma-def_binary64`
425×	`associate-/l/_binary64`
345×	`fma-neg_binary64`
299×	`cancel-sign-sub-inv_binary64`

Counts

149 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	4112
1	711	3934
2	2536	3870
3	5000	3870
4	5207	3870

prune166.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	194	4	198
Fresh	5	1	6
Picked	0	1	1
Done	0	1	1
Total	199	7	206

Error

Counts

206 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
▶	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
	0.9b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
✓	0.1b	(.f64 (sin.f64 v) (+.f64 e (.f64 (cos.f64 v) (-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (.f64 e e)))))
	1.0b	(.f64 (.f64 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (sqrt.f64 e)) (/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v)))))
	1.1b	(/.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (sin.f64 v) (cbrt.f64 e))))
	36.6b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e e) e) (.f64 (*.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 4615 to 2258 computations (51.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 v)
✓	0.2b	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e)))
✓	0.3b	(*.f64 (sin.f64 v) (sqrt.f64 e))
✓	0.3b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))

series93.0ms (2.1%)

Counts

3 → 44

Calls

3 calls:

43.0ms	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
37.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e)))
13.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`
28×	`sqrt-prod_binary64`

Counts

3 → 121

Calls

3 calls:

7.0ms	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
4.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e)))
4.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))

simplify179.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
434×	`cancel-sign-sub-inv_binary64`
229×	`fma-neg_binary64`
214×	`associate-r_binary64`
148×	`unswap-sqr_binary64`

Counts

165 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	303	4872
1	789	4300
2	3050	4253
3	4840	4253
4	4952	4253
5	4997	4253
6	4946	4253

prune174.0ms (3.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	210	7	217

Error

Counts

217 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
✓	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
	0.9b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
✓	0.1b	(.f64 (sin.f64 v) (+.f64 e (.f64 (cos.f64 v) (-.f64 (.f64 (cos.f64 v) (pow.f64 e 3)) (.f64 e e)))))
	1.0b	(.f64 (.f64 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (sqrt.f64 e)) (/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v)))))
	36.6b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e e) e) (.f64 (*.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	1.0b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))) (sqrt.f64 e)))

Compiler

Compiled 5346 to 2320 computations (56.6% saved)

regimes442.0ms (10%)

Accuracy

Total 0.6b remaining (95.3%)

Threshold costs 0.6b (95.3%)

Counts

153 → 1

Compiler

Compiled 7769 to 4979 computations (35.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	20	23
2	27	23
3	31	23
4	33	23
5	33	23

end1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample2.4s (53.4%)

Algorithm

1×

intervals

Results

1.0s	1979×	body	1024	valid
396.0ms	4502×	body	128	valid
259.0ms	1020×	body	512	valid
157.0ms	8000×	pre	128	true
87.0ms	495×	body	256	valid
5.0ms	4×	body	2048	valid

Compiler

Compiled 167 to 105 computations (37.1% saved)

Details

analyze22.0ms (0.5%)

sample83.0ms (1.9%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series41.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify55.0ms (1.2%)

prune96.0ms (2.2%)

localize11.0ms (0.2%)

series101.0ms (2.3%)

rewrite25.0ms (0.6%)

simplify102.0ms (2.3%)

prune206.0ms (4.7%)

localize8.0ms (0.2%)

series49.0ms (1.1%)

rewrite15.0ms (0.3%)

simplify119.0ms (2.7%)

prune166.0ms (3.8%)

localize9.0ms (0.2%)

series93.0ms (2.1%)

rewrite24.0ms (0.6%)

simplify179.0ms (4.1%)

prune174.0ms (3.9%)

regimes442.0ms (10%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.4s (53.4%)

Profiling