Details

analyze3.5s (25.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample415.0ms (3%)

Algorithm

1×

intervals

Results

296.0ms	71×	body	2048	valid
70.0ms	92×	body	1024	valid
22.0ms	51×	body	512	valid
8.0ms	24×	body	256	valid
3.0ms	17×	body	128	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`div-sub_binary64`
430×	`fma-def_binary64`
335×	`times-frac_binary64`
160×	`sub-neg_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	67	14
5	115	14
6	212	14
7	416	14
8	699	14
9	1176	14
10	1555	14
11	1621	14
12	1652	14
13	1679	14
14	1689	14
15	1693	14
16	1693	14
17	1592	14

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

29.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	29.9b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 20 to 12 computations (40% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.8b	(-.f64 x (tan.f64 x))
0.8b	(-.f64 x (sin.f64 x))

rewrite138.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

28.9b

Rules

59×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

3 → 114

Calls

3 calls:

16.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (sin.f64 x))
6.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 2078 to 405 computations (80.5% saved)

series124.0ms (0.9%)

Error

Counts

3 → 27

Calls

3 calls:

38.0ms	(-.f64 x (tan.f64 x))
37.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
14.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 905 to 583 computations (35.6% saved)

simplify193.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
329×	`fma-neg_binary64`
250×	`associate-/l/_binary64`
226×	`cancel-sign-sub-inv_binary64`
200×	`distribute-rgt-in_binary64`

Counts

141 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	2798
1	582	2518
2	1943	2398
3	4623	2398
4	4890	2398

prune48.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Error

Counts

70 → 3

Alt Table

Status	Error	Program
	30.4b	(.f64 (.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x))))
▶	30.0b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
	33.4b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 792 to 327 computations (58.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (cos.f64 x))
0.1b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
1.5b	(+.f64 (/.f64 1 (cos.f64 x)) -1)

rewrite131.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

48×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
41×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 138

Calls

4 calls:

22.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
10.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
5.0ms	(/.f64 (sin.f64 x) x)
5.0ms	(/.f64 1 (cos.f64 x))

Compiler

Compiled 2665 to 1472 computations (44.8% saved)

series60.0ms (0.4%)

Error

Counts

4 → 13

Calls

4 calls:

18.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
12.0ms	(/.f64 (sin.f64 x) x)
11.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
11.0ms	(/.f64 1 (cos.f64 x))

Compiler

Compiled 465 to 349 computations (24.9% saved)

simplify202.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
458×	`associate-l_binary64`
410×	`associate-*l/_binary64`
374×	`associate-r_binary64`
338×	`associate-/l*_binary64`

Counts

151 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	2073
1	458	1896
2	1194	1877
3	3971	1877
4	4789	1877
5	5246	1877

prune33.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	89	3	92

Error

Counts

92 → 3

Alt Table

Status	Error	Program
▶	30.4b	(.f64 (.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x))))
✓	30.0b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
	33.4b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 1397 to 687 computations (50.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 x (tan.f64 x))
0.8b	(-.f64 x (sin.f64 x))
0.8b	(-.f64 x (sin.f64 x))
0.8b	(-.f64 x (sin.f64 x))

rewrite60.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

44×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
36×	`prod-diff_binary64`
36×	`add-cube-cbrt_binary64`
12×	`cancel-sign-sub-inv_binary64`

Counts

4 → 120

Calls

4 calls:

5.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 3969 to 606 computations (84.7% saved)

series50.0ms (0.4%)

Error

Counts

4 → 29

Calls

4 calls:

12.0ms	(-.f64 x (tan.f64 x))
10.0ms	(-.f64 x (sin.f64 x))
10.0ms	(-.f64 x (sin.f64 x))
9.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 1587 to 745 computations (53.1% saved)

simplify132.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

484×	`fma-def_binary64`
446×	`fma-neg_binary64`
368×	`distribute-rgt-in_binary64`
280×	`cancel-sign-sub-inv_binary64`
262×	`distribute-lft-in_binary64`

Counts

149 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	1824
1	303	1496
2	906	1312
3	2199	1312
4	4400	1312
5	4948	1312
6	4757	1312

prune18.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Error

Counts

77 → 3

Alt Table

Status	Error	Program
✓	30.4b	(.f64 (.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x))))
✓	30.0b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
▶	33.4b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 1036 to 311 computations (70% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 27/112000 (pow.f64 x 6))
0.1b	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
0.2b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
20.2b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

rewrite80.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`
9×	`prod-diff_binary64`

Counts

4 → 79

Calls

4 calls:

5.0ms	(*.f64 27/112000 (pow.f64 x 6))
3.0ms	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
0.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
0.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))

Compiler

Compiled 2376 to 1799 computations (24.3% saved)

series53.0ms (0.4%)

Error

Counts

4 → 23

Calls

4 calls:

15.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
12.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
9.0ms	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
7.0ms	(*.f64 27/112000 (pow.f64 x 6))

Compiler

Compiled 700 to 565 computations (19.3% saved)

simplify126.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

439×	`fma-neg_binary64`
370×	`fma-def_binary64`
341×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`
292×	`exp-prod_binary64`

Counts

102 → 62

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	1881
1	259	1730
2	796	1531
3	2807	1518
4	4371	1509
5	4995	1509
6	4752	1509

prune31.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	62	3	65

Error

Counts

65 → 3

Alt Table

Status	Error	Program
	30.4b	(.f64 (.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x))))
	30.0b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
	33.4b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 907 to 655 computations (27.8% saved)

regimes164.0ms (1.2%)

Accuracy

Total 0.2b remaining (88.5%)

Threshold costs 0.2b (88.5%)

Compiler

Compiled 2184 to 1256 computations (42.5% saved)

bsearch74.0ms (0.5%)

Steps

Iters	Range		Point
11	2.5872051487947843e-17	1460.760245555016	2.6377554044873825
10	-193821556.7072915	-0.039402681489257504	-4.889551851038275

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
13×	`*-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	160
1	70	160
2	81	160
3	97	160
4	114	160
5	124	160
6	129	160
7	130	160
8	129	160

end2.0ms (0%)

Compiler: Compiled 105 to 66 computations (37.1% saved)

sample8.1s (58.2%)

Algorithm

1×

intervals

Results

5.1s	2029×	body	2048	valid
1.7s	2962×	body	1024	valid
438.0ms	1498×	body	512	valid
156.0ms	771×	body	256	valid
140.0ms	104×	body	4096	valid
78.0ms	636×	body	128	valid

Compiler

Compiled 172 to 108 computations (37.2% saved)

Details

analyze3.5s (25.3%)

sample415.0ms (3%)

simplify103.0ms (0.7%)

prune2.0ms (0%)

localize13.0ms (0.1%)

rewrite138.0ms (1%)

series124.0ms (0.9%)

simplify193.0ms (1.4%)

prune48.0ms (0.3%)

localize18.0ms (0.1%)

rewrite131.0ms (0.9%)

series60.0ms (0.4%)

simplify202.0ms (1.5%)

prune33.0ms (0.2%)

localize12.0ms (0.1%)

rewrite60.0ms (0.4%)

series50.0ms (0.4%)

simplify132.0ms (0.9%)

prune18.0ms (0.1%)

localize10.0ms (0.1%)

rewrite80.0ms (0.6%)

series53.0ms (0.4%)

simplify126.0ms (0.9%)

prune31.0ms (0.2%)

regimes164.0ms (1.2%)

bsearch74.0ms (0.5%)

simplify9.0ms (0.1%)

end2.0ms (0%)

sample8.1s (58.2%)

Profiling