Details

analyze25.0ms (0.4%)

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)

sample3.0s (47.1%)

Results

1.6s	2036×	body	1024	valid
791.0ms	4679×	body	128	valid
479.0ms	1040×	body	512	valid
157.0ms	492×	body	256	valid
15.0ms	9×	body	2048	valid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify7.0ms (0.1%)

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%)

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)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series39.0ms (0.6%)

Counts

2 → 28

Calls

2 calls:

30.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
9.0ms	(*.f64 e (sin.f64 v))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

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

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

590×	`associate-/r*_binary64`
466×	`fma-def_binary64`
433×	`fma-neg_binary64`
287×	`associate-/r/_binary64`
260×	`associate-/l/_binary64`

Counts

71 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	1682
1	475	1537
2	1911	1497
3	4795	1497
4	5052	1497

prune82.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Error

0.0b

Counts

80 → 6

Alt Table

Status	Error	Program
	22.7b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
▶	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	1.0b	(/.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))
	34.1b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e (sin.f64 v)) (.f64 e (sin.f64 v))) (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	0.4b	(-.f64 (+.f64 (.f64 e (sin.f64 v)) (.f64 (pow.f64 (cos.f64 v) 2) (.f64 (pow.f64 e 3) (sin.f64 v)))) (+.f64 (.f64 (cos.f64 v) (.f64 (pow.f64 e 2) (sin.f64 v))) (.f64 (pow.f64 (cos.f64 v) 3) (*.f64 (pow.f64 e 4) (sin.f64 v)))))
	1.0b	(/.f64 (.f64 (.f64 e (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 2047 to 1064 computations (48% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)))

series50.0ms (0.8%)

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 (0.2%)

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))

simplify126.0ms (2%)

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

prune192.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	175	6	181
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	179	8	187

Error

0.0b

Counts

187 → 8

Alt Table

Status	Error	Program
	1.0b	(/.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 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
	28.8b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))) (/.f64 e (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
	0.4b	(-.f64 (+.f64 (.f64 e (sin.f64 v)) (.f64 (pow.f64 (cos.f64 v) 2) (.f64 (pow.f64 e 3) (sin.f64 v)))) (+.f64 (.f64 (cos.f64 v) (.f64 (pow.f64 e 2) (sin.f64 v))) (.f64 (pow.f64 (cos.f64 v) 3) (*.f64 (pow.f64 e 4) (sin.f64 v)))))
▶	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 e (/.f64 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))) (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))) (/.f64 (cbrt.f64 e) (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
	1.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))) (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))) (/.f64 e (cbrt.f64 (/.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))))

Compiler

Compiled 4557 to 2234 computations (51% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series188.0ms (2.9%)

Counts

4 → 72

Calls

4 calls:

71.0ms	(/.f64 e (/.f64 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)) (sin.f64 v)))
43.0ms	(/.f64 1 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))
41.0ms	(/.f64 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))
32.0ms	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 e (/.f64 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))))

rewrite93.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

353×	`times-frac_binary64`
257×	`add-sqr-sqrt_binary64`
192×	`*-un-lft-identity_binary64`
184×	`add-cube-cbrt_binary64`
109×	`sqrt-prod_binary64`

Counts

4 → 341

Calls

4 calls:

31.0ms	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 e (/.f64 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))))
6.0ms	(/.f64 e (/.f64 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)) (sin.f64 v)))
3.0ms	(/.f64 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))
3.0ms	(/.f64 1 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))

simplify219.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-r_binary64`
411×	`associate-l_binary64`
348×	`associate-*l/_binary64`
346×	`associate-/l*_binary64`
302×	`associate-/r/_binary64`

Counts

413 → 509

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	558	13946
1	1580	12543
2	5189	12543

prune650.0ms (10.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	508	1	509
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	509	8	517

Error

0.0b

Counts

517 → 8

Alt Table

Status	Error	Program
	1.0b	(/.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 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
	28.8b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))) (/.f64 e (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
	0.6b	(fma.f64 e (sin.f64 v) (.f64 (sin.f64 v) (-.f64 (.f64 (pow.f64 (cos.f64 v) 2) (pow.f64 e 3)) (.f64 (cos.f64 v) (.f64 e e)))))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))) (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))) (/.f64 (cbrt.f64 e) (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
	1.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))) (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))) (/.f64 e (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 e (/.f64 (sqrt.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))))

Compiler

Compiled 18162 to 10235 computations (43.6% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series92.0ms (1.4%)

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))))
36.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e)))
12.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))

rewrite25.0ms (0.4%)

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))

simplify187.0ms (2.9%)

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 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	303	4863
1	789	4300
2	3050	4253
3	4840	4253
4	4952	4253
5	4997	4253
6	4946	4253

prune208.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	211	4	215
Fresh	5	1	6
Picked	0	1	1
Done	0	1	1
Total	216	7	223

Error

Counts

223 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (/.f64 (sqrt.f64 (sqrt.f64 e)) (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 e))))
	0.4b	(/.f64 (sqrt.f64 e) (*.f64 (sqrt.f64 (/.f64 1 e)) (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	1.0b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
	0.1b	(*.f64 (sin.f64 v) (/.f64 e (fma.f64 e (cos.f64 v) 1)))
	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e)))))
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 e (/.f64 (sqrt.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))))

Compiler

Compiled 5591 to 2391 computations (57.2% saved)

regimes963.0ms (15%)

Accuracy

Total 0.1b remaining (79.5%)

Threshold costs 0.1b (79.5%)

Counts

239 → 1

Compiler

Compiled 15827 to 10055 computations (36.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	15
1	16	15
2	13	15

end111.0ms (1.7%)

Compiler: Compiled 148 to 96 computations (35.1% saved)

Details

analyze25.0ms (0.4%)

sample3.0s (47.1%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series39.0ms (0.6%)

rewrite10.0ms (0.1%)

simplify72.0ms (1.1%)

prune82.0ms (1.3%)

localize8.0ms (0.1%)

series50.0ms (0.8%)

rewrite15.0ms (0.2%)

simplify126.0ms (2%)

prune192.0ms (3%)

localize11.0ms (0.2%)

series188.0ms (2.9%)

rewrite93.0ms (1.5%)

simplify219.0ms (3.4%)

prune650.0ms (10.1%)

localize12.0ms (0.2%)

series92.0ms (1.4%)

rewrite25.0ms (0.4%)

simplify187.0ms (2.9%)

prune208.0ms (3.2%)

regimes963.0ms (15%)

simplify2.0ms (0%)

end111.0ms (1.7%)

Profiling