Details

analyze1.1s (17.1%)

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
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample2.9s (43.9%)

Results

1.4s	2302×	body	1024	valid
654.0ms	4131×	body	128	valid
594.0ms	1276×	body	512	valid
156.0ms	544×	body	256	valid
30.0ms	198×	body	128	invalid
3.0ms	3×	body	2048	valid
1.0ms	2×	body	1024	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

105×	`fma-def_binary64`
66×	`fma-neg_binary64`
27×	`cancel-sign-sub-inv_binary64`
19×	`sub-neg_binary64`
11×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

prune3.0ms (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
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	0.3b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))

Compiler

Compiled 73 to 53 computations (27.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 B)
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
✓	0.2b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 x (tan.f64 B))

series88.0ms (1.3%)

Counts

4 → 56

Calls

4 calls:

39.0ms	(/.f64 x (tan.f64 B))
39.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
8.0ms	(/.f64 1 (sin.f64 B))
2.0ms	(sin.f64 B)

rewrite59.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
240×	`add-sqr-sqrt_binary64`
232×	`*-un-lft-identity_binary64`
223×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

4 → 304

Calls

4 calls:

15.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
2.0ms	(/.f64 x (tan.f64 B))
2.0ms	(/.f64 1 (sin.f64 B))
1.0ms	(sin.f64 B)

simplify240.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/l*_binary64`
453×	`times-frac_binary64`
297×	`fma-neg_binary64`
215×	`cancel-sign-sub-inv_binary64`
182×	`associate-/l/_binary64`

Counts

360 → 365

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	327	13369
1	790	8583
2	1892	6789
3	4533	6789
4	4786	6789

prune463.0ms (7.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	353	12	365
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	355	12	367

Error

0.0b

Counts

367 → 12

Alt Table

Status	Error	Program
	24.1b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	13.3b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (tan.f64 B) (cbrt.f64 x))))
	38.3b	(/.f64 (-.f64 1 x) B)
	13.3b	(-.f64 (/.f64 1 (cbrt.f64 (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	9.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	31.7b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B))))
	0.7b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	0.8b	(+.f64 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (pow.f64 (cbrt.f64 (tan.f64 B)) 3)))

Compiler

Compiled 12593 to 4029 computations (68% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
✓	0.2b	(/.f64 x (sin.f64 B))
	0.2b	(/.f64 1 (sin.f64 B))
✓	0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

series63.0ms (1%)

Counts

3 → 52

Calls

3 calls:

26.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
21.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
16.0ms	(/.f64 x (sin.f64 B))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
13×	`fma-neg_binary64`

Counts

3 → 105

Calls

3 calls:

13.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
5.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
2.0ms	(/.f64 x (sin.f64 B))

simplify139.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-def_binary64`
414×	`fma-neg_binary64`
372×	`associate-/l*_binary64`
342×	`times-frac_binary64`
338×	`associate-*l/_binary64`

Counts

157 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	2974
1	476	2749
2	1426	2544
3	4328	2511
4	4945	2511
5	4995	2511
6	4920	2511

prune212.0ms (3.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	218	4	222
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	222	12	234

Error

Counts

234 → 12

Alt Table

Status	Error	Program
	24.1b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.3b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
▶	0.3b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	31.7b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
	13.3b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (tan.f64 B) (cbrt.f64 x))))
	13.3b	(-.f64 (/.f64 1 (cbrt.f64 (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	9.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	32.3b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
	9.5b	(/.f64 (-.f64 (.f64 1 (sin.f64 B)) (.f64 (sin.f64 B) (.f64 x (cos.f64 B)))) (.f64 (sin.f64 B) (sin.f64 B)))

Compiler

Compiled 5008 to 1881 computations (62.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 B)
✓	0.1b	(*.f64 x (cos.f64 B))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))

series26.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

19.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
7.0ms	(*.f64 x (cos.f64 B))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

2 → 52

Calls

2 calls:

6.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
3.0ms	(*.f64 x (cos.f64 B))

simplify87.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

600×	`div-sub_binary64`
557×	`fma-def_binary64`
511×	`fma-neg_binary64`
391×	`associate-l_binary64`
329×	`associate-r_binary64`

Counts

92 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1498
1	372	1396
2	1170	1379
3	3882	1377
4	4657	1377
5	5719	1377

prune95.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	97	10	107

Error

Counts

107 → 10

Alt Table

Status	Error	Program
	24.1b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
▶	0.3b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	9.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	14.3b	(.f64 (sqrt.f64 (-.f64 1 (.f64 x (cos.f64 B)))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x (cos.f64 B)))) (sin.f64 B)))
	0.3b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (log1p.f64 (expm1.f64 (sin.f64 B))))
	13.3b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	13.3b	(-.f64 (/.f64 1 (cbrt.f64 (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	32.3b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
	9.5b	(/.f64 (-.f64 (.f64 1 (sin.f64 B)) (.f64 (sin.f64 B) (.f64 x (cos.f64 B)))) (.f64 (sin.f64 B) (sin.f64 B)))

Compiler

Compiled 2003 to 1006 computations (49.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
	0.2b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 (cos.f64 B) (sin.f64 B))
✓	0.2b	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))

series54.0ms (0.8%)

Counts

3 → 52

Calls

3 calls:

26.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
21.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
7.0ms	(/.f64 (cos.f64 B) (sin.f64 B))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
13×	`fma-neg_binary64`

Counts

3 → 105

Calls

3 calls:

7.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
5.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
3.0ms	(/.f64 (cos.f64 B) (sin.f64 B))

simplify124.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-def_binary64`
430×	`times-frac_binary64`
324×	`fma-neg_binary64`
322×	`associate-*r/_binary64`
318×	`associate-*l/_binary64`

Counts

157 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	192	3051
1	468	2821
2	1527	2620
3	4356	2587
4	4697	2587
5	4880	2587

prune167.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	214	10	224

Error

Counts

224 → 10

Alt Table

Status	Error	Program
	24.1b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
✓	0.3b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	9.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	14.3b	(.f64 (sqrt.f64 (-.f64 1 (.f64 x (cos.f64 B)))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x (cos.f64 B)))) (sin.f64 B)))
	0.3b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (log1p.f64 (expm1.f64 (sin.f64 B))))
	13.3b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	13.3b	(-.f64 (/.f64 1 (cbrt.f64 (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	32.3b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
	9.5b	(/.f64 (-.f64 (.f64 1 (sin.f64 B)) (.f64 (sin.f64 B) (.f64 x (cos.f64 B)))) (.f64 (sin.f64 B) (sin.f64 B)))

Compiler

Compiled 4536 to 1686 computations (62.8% saved)

regimes485.0ms (7.4%)

Accuracy

Total 0.1b remaining (91.5%)

Threshold costs 0.1b (91.5%)

Counts

154 → 1

Compiler

Compiled 7588 to 5190 computations (31.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	19	17
2	23	17
3	26	17
4	27	17
5	24	17

end147.0ms (2.2%)

Compiler: Compiled 234 to 146 computations (37.6% saved)

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

Details

analyze1.1s (17.1%)

sample2.9s (43.9%)

simplify13.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series88.0ms (1.3%)

rewrite59.0ms (0.9%)

simplify240.0ms (3.6%)

prune463.0ms (7.1%)

localize8.0ms (0.1%)

series63.0ms (1%)

rewrite27.0ms (0.4%)

simplify139.0ms (2.1%)

prune212.0ms (3.2%)

localize7.0ms (0.1%)

series26.0ms (0.4%)

rewrite11.0ms (0.2%)

simplify87.0ms (1.3%)

prune95.0ms (1.5%)

localize8.0ms (0.1%)

series54.0ms (0.8%)

rewrite21.0ms (0.3%)

simplify124.0ms (1.9%)

prune167.0ms (2.5%)

regimes485.0ms (7.4%)

simplify3.0ms (0%)

end147.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14