Details

analyze1.3s (20.2%)

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
12.5%	87.5%	0%	5
18.7%	81.2%	0%	6
21.9%	78.1%	0%	7
23.4%	76.5%	0%	8
23.4%	76.5%	0%	9
23.4%	76.5%	0%	10
23.6%	76.3%	0%	11
23.7%	76.2%	0%	12
23.7%	76.2%	0%	13
23.7%	76.2%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample3.2s (51%)

Results

1.5s	2027×	body	2048	valid
587.0ms	1162×	body	1024	valid
508.0ms	1629×	body	512	valid
290.0ms	2605×	body	128	valid
151.0ms	733×	body	256	valid
77.0ms	100×	body	4096	valid

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

426×	`fma-def_binary64`
293×	`fma-neg_binary64`
85×	`div-sub_binary64`
74×	`associate-/l*_binary64`
63×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.1b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.5b	(-.f64 1 (cos.f64 x))
✓	10.2b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series7.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

4.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms	(-.f64 1 (cos.f64 x))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
7×	`add-cbrt-cube_binary64`

Counts

2 → 63

Calls

2 calls:

7.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

simplify141.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-neg_binary64`
411×	`associate-l_binary64`
405×	`times-frac_binary64`
353×	`associate-r_binary64`
344×	`fma-def_binary64`

Counts

79 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1152
1	283	1017
2	853	961
3	3327	961
4	4699	961
5	4954	961
6	4828	961

prune91.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	81	10	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Error

0.0b

Counts

92 → 10

Alt Table

Status	Error	Program
	46.5b	(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
	29.5b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
▶	10.6b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	30.1b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (.f64 x x) (+.f64 (.f64 1 1) (+.f64 (.f64 (cos.f64 x) (cos.f64 x)) (*.f64 1 (cos.f64 x))))))
	32.9b	(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
	30.1b	(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
	30.1b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	29.5b	(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))
	30.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (.f64 x x))) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (.f64 x x)))) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
	30.1b	(/.f64 (exp.f64 (log.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))

Compiler

Compiled 1816 to 929 computations (48.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓	0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	0.5b	(+.f64 1 (cos.f64 x))
✓	10.0b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series42.0ms (0.7%)

Counts

4 → 40

Calls

4 calls:

19.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
18.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
25×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
17×	`add-sqr-sqrt_binary64`

Counts

4 → 122

Calls

4 calls:

10.0ms	(+.f64 1 (cos.f64 x))
9.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
7.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))

simplify98.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-*l/_binary64`
540×	`associate-/r/_binary64`
423×	`fma-def_binary64`
335×	`fma-neg_binary64`
214×	`cancel-sign-sub-inv_binary64`

Counts

162 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	2904
1	504	2230
2	1767	2192
3	4643	2192
4	4935	2192

prune176.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	201	5	206
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	209	7	216

Error

Counts

216 → 7

Alt Table

Status	Error	Program
	0.4b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
▶	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	30.1b	(/.f64 1 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))))
	11.1b	(/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (*.f64 x x) (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x))))))
	30.1b	(/.f64 (exp.f64 (log.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
	10.3b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))

Compiler

Compiled 4392 to 1971 computations (55.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
✓	0.1b	(/.f64 (sin.f64 x) x)
✓	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

series34.0ms (0.6%)

Counts

3 → 28

Calls

3 calls:

16.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
15.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
3.0ms	(/.f64 (sin.f64 x) x)

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 93

Calls

3 calls:

8.0ms	(/.f64 (sin.f64 x) x)
7.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
7.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

simplify112.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary64`
593×	`associate-/l/_binary64`
549×	`associate-*l/_binary64`
440×	`associate-l_binary64`
391×	`associate-/r*_binary64`

Counts

121 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	2266
1	433	2003
2	1333	1993
3	4088	1989
4	4749	1989
5	5173	1989

prune183.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	148	6	154

Error

Counts

154 → 6

Alt Table

Status	Error	Program
	0.1b	(/.f64 (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2))) (.f64 x (cos.f64 (/.f64 x 2))))
▶	0.1b	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
	0.4b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
	11.1b	(/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (*.f64 x x) (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x))))))
	30.1b	(/.f64 (exp.f64 (log.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
	10.3b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))

Compiler

Compiled 2798 to 1410 computations (49.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
✓	0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
✓	0.2b	(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))

series38.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

13.0ms	(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
12.0ms	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
12.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 90

Calls

3 calls:

13.0ms	(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
5.0ms	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

simplify114.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
564×	`associate-/l/_binary64`
528×	`associate-*l/_binary64`
426×	`associate-l_binary64`
419×	`associate-*r/_binary64`

Counts

126 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2493
1	409	2220
2	1393	2212
3	4135	2208
4	4653	2208
5	4952	2208

prune117.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Error

Counts

138 → 6

Alt Table

Status	Error	Program
	0.1b	(/.f64 (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2))) (.f64 x (cos.f64 (/.f64 x 2))))
✓	0.1b	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
	11.1b	(/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (*.f64 x x) (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x))))))
	30.1b	(/.f64 (exp.f64 (log.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
	10.3b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
	0.4b	(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

Compiler

Compiled 2436 to 1461 computations (40% saved)

regimes334.0ms (5.4%)

Accuracy

Total 0.1b remaining (86.6%)

Threshold costs 0.1b (86.6%)

Counts

165 → 1

Compiler

Compiled 5232 to 3493 computations (33.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	10	17
2	10	17

end96.0ms (1.6%)

Compiler: Compiled 115 to 77 computations (33% saved)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

Details

analyze1.3s (20.2%)

sample3.2s (51%)

simplify48.0ms (0.8%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series7.0ms (0.1%)

rewrite15.0ms (0.2%)

simplify141.0ms (2.3%)

prune91.0ms (1.5%)

localize9.0ms (0.1%)

series42.0ms (0.7%)

rewrite37.0ms (0.6%)

simplify98.0ms (1.6%)

prune176.0ms (2.8%)

localize8.0ms (0.1%)

series34.0ms (0.6%)

rewrite27.0ms (0.4%)

simplify112.0ms (1.8%)

prune183.0ms (2.9%)

localize9.0ms (0.1%)

series38.0ms (0.6%)

rewrite39.0ms (0.6%)

simplify114.0ms (1.8%)

prune117.0ms (1.9%)

regimes334.0ms (5.4%)

simplify2.0ms (0%)

end96.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12