Details

analyze814.0ms (9.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample151.0ms (1.8%)

Algorithm

1×

intervals

Results

71.0ms	65×	body	2048	valid
49.0ms	101×	body	1024	valid
12.0ms	43×	body	512	valid
4.0ms	21×	body	256	valid
3.0ms	3×	body	4096	valid
2.0ms	23×	body	128	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

145×	`fma-def_binary64`
111×	`fma-neg_binary64`
28×	`cancel-sign-sub-inv_binary64`
27×	`div-sub_binary64`
21×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	17	6
2	23	6
3	33	6
4	55	6
5	71	6
6	100	6
7	153	6
8	219	6
9	264	6
10	299	6
11	306	6
12	268	6

prune5.0ms (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
▶	0.3b	(tan.f64 (/.f64 x 2))
	31.5b	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 38 to 29 computations (23.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(tan.f64 (/.f64 x 2))

series8.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

7.0ms

(tan.f64 (/.f64 x 2))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

1.0ms

(tan.f64 (/.f64 x 2))

simplify265.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

763×	`sqr-pow_binary64`
711×	`cube-prod_binary64`
661×	`fabs-mul_binary64`
632×	`unswap-sqr_binary64`
608×	`pow-sqr_binary64`

Counts

22 → 19

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	278
1	71	265
2	142	265
3	294	265
4	501	265
5	960	265
6	1341	265
7	1880	265
8	2038	265
9	2280	265
10	2573	265
11	2967	265
12	3350	265
13	3903	265
14	4010	265
15	4157	265
16	4366	265
17	4486	265
18	4613	265
19	4982	265
20	4843	265

prune26.0ms (0.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	13	6	19
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	14	7	21

Error

0.1b

Counts

21 → 7

Alt Table

Status	Error	Program
	30.2b	(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
	31.5b	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
	0.8b	(.f64 (.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) (cbrt.f64 (tan.f64 (/.f64 x 2)))) (cbrt.f64 (tan.f64 (/.f64 x 2))))
	34.2b	(exp.f64 (log.f64 (tan.f64 (/.f64 x 2))))
	31.1b	(log.f64 (exp.f64 (tan.f64 (/.f64 x 2))))
▶	0.4b	(log1p.f64 (expm1.f64 (tan.f64 (/.f64 x 2))))
	9.0b	(expm1.f64 (log1p.f64 (tan.f64 (/.f64 x 2))))

Compiler

Compiled 318 to 258 computations (18.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(expm1.f64 (tan.f64 (/.f64 x 2)))
✓	0.3b	(log1p.f64 (expm1.f64 (tan.f64 (/.f64 x 2))))
	0.3b	(tan.f64 (/.f64 x 2))

series19.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(expm1.f64 (tan.f64 (/.f64 x 2)))
9.0ms	(log1p.f64 (expm1.f64 (tan.f64 (/.f64 x 2))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (tan.f64 (/.f64 x 2)))
0.0ms	(log1p.f64 (expm1.f64 (tan.f64 (/.f64 x 2))))

simplify128.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

794×	`associate-/l/_binary64`
577×	`distribute-lft-out_binary64`
520×	`fma-def_binary64`
378×	`*-commutative_binary64`
373×	`associate-/r/_binary64`

Counts

46 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	587
1	123	557
2	253	554
3	585	546
4	1376	546
5	1979	546
6	2334	546
7	2919	546
8	4961	546
9	4933	546

prune56.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Error

0.1b

Counts

72 → 10

Alt Table

Status	Error	Program
	30.2b	(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
	33.0b	(log1p.f64 (log.f64 (exp.f64 (expm1.f64 (tan.f64 (/.f64 x 2))))))
	31.2b	(log1p.f64 (-.f64 (exp.f64 (tan.f64 (/.f64 x 2))) 1))
	2.3b	(log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (tan.f64 (/.f64 x 2))))))
	20.5b	(cbrt.f64 (pow.f64 (tan.f64 (/.f64 x 2)) 3))
	31.2b	(log.f64 (+.f64 1 (expm1.f64 (tan.f64 (/.f64 x 2)))))
	31.5b	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
▶	0.8b	(.f64 (.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) (cbrt.f64 (tan.f64 (/.f64 x 2)))) (cbrt.f64 (tan.f64 (/.f64 x 2))))
	34.2b	(exp.f64 (log.f64 (tan.f64 (/.f64 x 2))))
	9.0b	(expm1.f64 (log1p.f64 (tan.f64 (/.f64 x 2))))

Compiler

Compiled 921 to 769 computations (16.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f64 (tan.f64 (/.f64 x 2)))
	0.3b	(tan.f64 (/.f64 x 2))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) (cbrt.f64 (tan.f64 (/.f64 x 2)))) (cbrt.f64 (tan.f64 (/.f64 x 2))))
✓	0.5b	(*.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) (cbrt.f64 (tan.f64 (/.f64 x 2))))

series696.0ms (8.4%)

Counts

3 → 36

Calls

3 calls:

440.0ms

(*.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) (cbrt.f64 (tan.f64 (/.f64 x 2))))

248.0ms

(cbrt.f64 (tan.f64 (/.f64 x 2)))

7.0ms

(*.f64 (*.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) (cbrt.f64 (tan.f64 (/.f64 x 2)))) (cbrt.f64 (tan.f64 (/.f64 x 2))))

rewrite58.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
17×	`cbrt-div_binary64`
17×	`tan-quot_binary64`

Counts

3 → 104

Calls

3 calls:

12.0ms

(*.f64 (*.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) (cbrt.f64 (tan.f64 (/.f64 x 2)))) (cbrt.f64 (tan.f64 (/.f64 x 2))))

6.0ms

(*.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) (cbrt.f64 (tan.f64 (/.f64 x 2))))

4.0ms

(cbrt.f64 (tan.f64 (/.f64 x 2)))

simplify182.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

900×	`fma-def_binary64`
388×	`sqr-pow_binary64`
242×	`unswap-sqr_binary64`
241×	`associate-+l+_binary64`
233×	`*-commutative_binary64`

Counts

140 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	153	2636
1	311	2528
2	756	2183
3	1403	2069
4	2601	1768
5	4296	1768
6	4861	1768
7	4936	1768

prune267.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	264	5	269
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	269	10	279

Error

0.0b

Counts

279 → 10

Alt Table

Status	Error	Program
▶	0.8b	(pow.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) 3)
	30.2b	(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
	1.6b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (tan.f64 (/.f64 x 2)))) 8) (cbrt.f64 (cbrt.f64 (tan.f64 (/.f64 x 2)))))
	16.4b	(.f64 (pow.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (pow.f64 (cos.f64 (*.f64 1/2 x)) 2)) 1/3) (cbrt.f64 (tan.f64 (/.f64 x 2))))
	31.2b	(log1p.f64 (-.f64 (exp.f64 (tan.f64 (/.f64 x 2))) 1))
	0.9b	(/.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 x 2))) (cbrt.f64 (sin.f64 (/.f64 x 2)))) (cbrt.f64 (sin.f64 (/.f64 x 2)))) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 x 2))) (cbrt.f64 (cos.f64 (/.f64 x 2)))) (cbrt.f64 (cos.f64 (/.f64 x 2)))))
	31.5b	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
	34.2b	(exp.f64 (log.f64 (tan.f64 (/.f64 x 2))))
	1.1b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (tan.f64 (/.f64 x 2)))) 4) (cbrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) 2))) (cbrt.f64 (tan.f64 (/.f64 x 2))))
	9.0b	(expm1.f64 (log1p.f64 (tan.f64 (/.f64 x 2))))

Compiler

Compiled 6447 to 5348 computations (17% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f64 (tan.f64 (/.f64 x 2)))
	0.3b	(tan.f64 (/.f64 x 2))
✓	0.7b	(pow.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) 3)

series298.0ms (3.6%)

Counts

1 → 12

Calls

1 calls:

282.0ms

(pow.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) 3)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 33

Calls

1 calls:

9.0ms

(pow.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) 3)

simplify122.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-l_binary64`
428×	`associate-r_binary64`
420×	`log-prod_binary64`
415×	`exp-prod_binary64`
300×	`cube-prod_binary64`

Counts

45 → 48

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	742
1	185	681
2	503	605
3	2117	545
4	4215	545
5	4568	545
6	5106	545

prune74.0ms (0.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	92	12	104

Error

0.0b

Counts

104 → 12

Alt Table

Status	Error	Program
✓	0.8b	(pow.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) 3)
	30.2b	(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
	0.9b	(pow.f64 (/.f64 (cbrt.f64 (sin.f64 (/.f64 x 2))) (cbrt.f64 (cos.f64 (/.f64 x 2)))) 3)
	0.9b	(/.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 x 2))) (cbrt.f64 (sin.f64 (/.f64 x 2)))) (cbrt.f64 (sin.f64 (/.f64 x 2)))) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 x 2))) (cbrt.f64 (cos.f64 (/.f64 x 2)))) (cbrt.f64 (cos.f64 (/.f64 x 2)))))
	31.2b	(log1p.f64 (-.f64 (exp.f64 (tan.f64 (/.f64 x 2))) 1))
	0.9b	(pow.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))))) 3)
	29.0b	(pow.f64 (log.f64 (exp.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))))) 3)
	31.5b	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
	16.4b	(.f64 (pow.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (pow.f64 (cos.f64 (*.f64 1/2 x)) 2)) 1/3) (cbrt.f64 (tan.f64 (/.f64 x 2))))
	34.2b	(exp.f64 (log.f64 (tan.f64 (/.f64 x 2))))
	1.1b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (tan.f64 (/.f64 x 2)))) 4) (cbrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (/.f64 x 2))) 2))) (cbrt.f64 (tan.f64 (/.f64 x 2))))
	9.0b	(expm1.f64 (log1p.f64 (tan.f64 (/.f64 x 2))))

Compiler

Compiled 1510 to 1271 computations (15.8% saved)

regimes297.0ms (3.6%)

Accuracy

Total 0.2b remaining (82.5%)

Threshold costs 0.2b (82.5%)

Counts

139 → 1

Compiler

Compiled 4974 to 4226 computations (15% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	8	14
2	8	14

end1.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample4.8s (57.4%)

Algorithm

1×

intervals

Results

2.1s	1947×	body	2048	valid
1.5s	3051×	body	1024	valid
395.0ms	1488×	body	512	valid
141.0ms	770×	body	256	valid
109.0ms	97×	body	4096	valid
73.0ms	646×	body	128	valid
3.0ms	1×	body	8192	valid

Compiler

Compiled 184 to 156 computations (15.2% saved)

Iter	Nodes	Cost
0	7	6
1	17	6
2	23	6
3	33	6
4	55	6
5	71	6
6	100	6
7	153	6
8	219	6
9	264	6
10	299	6
11	306	6
12	268	6

Iter	Nodes	Cost
0	7	6
1	17	6
2	23	6
3	33	6
4	55	6
5	71	6
6	100	6
7	153	6
8	219	6
9	264	6
10	299	6
11	306	6
12	268	6

Details

analyze814.0ms (9.8%)

sample151.0ms (1.8%)

simplify21.0ms (0.2%)

prune5.0ms (0.1%)

localize4.0ms (0.1%)

series8.0ms (0.1%)

rewrite2.0ms (0%)

simplify265.0ms (3.2%)

prune26.0ms (0.3%)

localize8.0ms (0.1%)

series19.0ms (0.2%)

rewrite1.0ms (0%)

simplify128.0ms (1.5%)

prune56.0ms (0.7%)

localize8.0ms (0.1%)

series696.0ms (8.4%)

rewrite58.0ms (0.7%)

simplify182.0ms (2.2%)

prune267.0ms (3.2%)

localize7.0ms (0.1%)

series298.0ms (3.6%)

rewrite21.0ms (0.3%)

simplify122.0ms (1.5%)

prune74.0ms (0.9%)

regimes297.0ms (3.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample4.8s (57.4%)

Profiling

Iter	Nodes	Cost
0	7	6
1	17	6
2	23	6
3	33	6
4	55	6
5	71	6
6	100	6
7	153	6
8	219	6
9	264	6
10	299	6
11	306	6
12	268	6