Details

analyze398.0ms (7.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample3.1s (58.9%)

Results

1.5s	2039×	body	2048	valid
483.0ms	1179×	body	1024	valid
463.0ms	1553×	body	512	valid
293.0ms	2613×	body	128	valid
152.0ms	779×	body	256	valid
91.0ms	93×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify23.0ms (0.4%)

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

27.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.7b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.6b	(-.f64 1 (cos.f64 x))
✓	12.6b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series6.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

4.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms	(-.f64 1 (cos.f64 x))

rewrite12.0ms (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:

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

simplify114.0ms (2.2%)

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

prune84.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	82	9	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Error

0.0b

Counts

92 → 9

Alt Table

Status	Error	Program
	27.7b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) (*.f64 x x))
	27.7b	(/.f64 (-.f64 (.f64 1 1) (.f64 (cos.f64 x) (cos.f64 x))) (*.f64 x (fma.f64 x (cos.f64 x) x)))
	43.6b	(*.f64 (/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) x) (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))
	35.9b	(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 1/24 (.f64 x x) (.f64 1/40320 (pow.f64 x 6))))
	37.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 1 (cos.f64 x)) (.f64 x x)) (/.f64 (-.f64 1 (cos.f64 x)) (.f64 x x))) (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
	27.7b	(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
	27.8b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	27.7b	(/.f64 (+.f64 1 (.f64 (neg.f64 1) (cos.f64 x))) (.f64 x x))
▶	13.2b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

Compiler

Compiled 1774 to 897 computations (49.4% saved)

localize9.0ms (0.2%)

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))
✓	0.4b	(+.f64 1 (cos.f64 x))
✓	12.7b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series39.0ms (0.7%)

Counts

4 → 40

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
16.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))

rewrite30.0ms (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:

8.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
6.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms	(+.f64 1 (cos.f64 x))

simplify96.0ms (1.8%)

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

prune260.0ms (5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	200	6	206
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	209	6	215

Error

Counts

215 → 6

Alt Table

Status	Error	Program
	13.2b	(/.f64 (expm1.f64 (log1p.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))) (.f64 x x))
	0.1b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
▶	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	13.2b	(/.f64 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (pow.f64 (cos.f64 x) 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 (cos.f64 x) (cos.f64 x)) (.f64 1 (cos.f64 x))))) (*.f64 x x))
	0.1b	(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))
	12.9b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))

Compiler

Compiled 4398 to 1977 computations (55% saved)

localize8.0ms (0.2%)

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)))

series29.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

13.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
13.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
3.0ms	(/.f64 (sin.f64 x) x)

rewrite19.0ms (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:

6.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
6.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
2.0ms	(/.f64 (sin.f64 x) x)

simplify111.0ms (2.1%)

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

prune139.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	148	5	153

Error

Counts

153 → 5

Alt Table

Status	Error	Program
	13.2b	(/.f64 (expm1.f64 (log1p.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))) (.f64 x x))
	0.1b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
▶	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 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	12.9b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))

Compiler

Compiled 2748 to 1378 computations (49.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	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 (sin.f64 x) x)
✓	0.1b	(*.f64 x (cos.f64 (/.f64 x 2)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2)))

series23.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

10.0ms	(/.f64 (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2))) (.f64 x (cos.f64 (/.f64 x 2))))
7.0ms	(*.f64 x (cos.f64 (/.f64 x 2)))
5.0ms	(*.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2)))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`associate-l_binary64`
13×	`*-un-lft-identity_binary64`

Counts

3 → 82

Calls

3 calls:

11.0ms	(/.f64 (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2))) (.f64 x (cos.f64 (/.f64 x 2))))
6.0ms	(*.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2)))
3.0ms	(*.f64 x (cos.f64 (/.f64 x 2)))

simplify85.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
389×	`*-commutative_binary64`
327×	`associate-/r/_binary64`
324×	`cancel-sign-sub-inv_binary64`
295×	`times-frac_binary64`

Counts

118 → 159

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	2591
1	460	2102
2	1806	2092
3	3286	2088
4	4949	2088

prune176.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	200	5	205

Error

Counts

205 → 5

Alt Table

Status	Error	Program
	13.2b	(/.f64 (expm1.f64 (log1p.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))) (.f64 x x))
	0.1b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
✓	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 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	12.9b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))

Compiler

Compiled 4662 to 2708 computations (41.9% saved)

regimes357.0ms (6.8%)

Accuracy

Total 0.1b remaining (84.6%)

Threshold costs 0.1b (84.6%)

Counts

182 → 1

Compiler

Compiled 6543 to 4207 computations (35.7% 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

end84.0ms (1.6%)

Compiler: Compiled 98 to 67 computations (31.6% 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

analyze398.0ms (7.6%)

sample3.1s (58.9%)

simplify23.0ms (0.4%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series6.0ms (0.1%)

rewrite12.0ms (0.2%)

simplify114.0ms (2.2%)

prune84.0ms (1.6%)

localize9.0ms (0.2%)

series39.0ms (0.7%)

rewrite30.0ms (0.6%)

simplify96.0ms (1.8%)

prune260.0ms (5%)

localize8.0ms (0.2%)

series29.0ms (0.5%)

rewrite19.0ms (0.4%)

simplify111.0ms (2.1%)

prune139.0ms (2.7%)

localize11.0ms (0.2%)

series23.0ms (0.4%)

rewrite25.0ms (0.5%)

simplify85.0ms (1.6%)

prune176.0ms (3.4%)

regimes357.0ms (6.8%)

simplify2.0ms (0%)

end84.0ms (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