Details

analyze2.0s (15.7%)

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%	100%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample9.2s (73.3%)

Results

5.6s	2085×	body	2048	valid
2.3s	3134×	body	1024	valid
608.0ms	1485×	body	512	valid
218.0ms	766×	body	256	valid
167.0ms	108×	body	4096	valid
136.0ms	678×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify89.0ms (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 → 1

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

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

35.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	35.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 x)
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	2.4b	(-.f64 x (sin.f64 x))
✓	2.4b	(-.f64 x (tan.f64 x))

series23.0ms (0.2%)

Counts

4 → 34

Calls

4 calls:

10.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (tan.f64 x))
5.0ms	(sin.f64 x)
2.0ms	(-.f64 x (sin.f64 x))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

7.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
3.0ms	(-.f64 x (sin.f64 x))
1.0ms	(sin.f64 x)

simplify143.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

497×	`fma-neg_binary64`
313×	`cancel-sign-sub-inv_binary64`
252×	`associate-/l/_binary64`
221×	`associate-/r/_binary64`
204×	`distribute-rgt-in_binary64`

Counts

157 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	3109
1	618	2685
2	2075	2567
3	4500	2563
4	4985	2563
5	4872	2563

prune88.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	165	4	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	4	170

Error

0.0b

Counts

170 → 4

Alt Table

Status	Error	Program
	35.3b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
▶	28.3b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	35.8b	(/.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
	35.1b	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 x (neg.f64 (tan.f64 x))))

Compiler

Compiled 3446 to 1021 computations (70.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	0.1b	(.f64 9/40 (.f64 x x))
✓	13.5b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

series10.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
3.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
3.0ms	(.f64 9/40 (.f64 x x))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 52

Calls

3 calls:

5.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
4.0ms	(.f64 9/40 (.f64 x x))
0.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

407×	`fma-neg_binary64`
399×	`associate-+r+_binary64`
379×	`associate-+l+_binary64`
320×	`fma-def_binary64`
300×	`times-frac_binary64`

Counts

88 → 81

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1147
1	199	1072
2	668	980
3	2038	980
4	4543	969
5	4942	969

prune54.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	81	4	85

Error

0.0b

Counts

85 → 4

Alt Table

Status	Error	Program
	35.3b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
✓	28.3b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	35.8b	(/.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
▶	35.1b	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 x (neg.f64 (tan.f64 x))))

Compiler

Compiled 1605 to 1167 computations (27.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 x)
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 x (neg.f64 (tan.f64 x))))
	2.4b	(-.f64 x (sin.f64 x))
✓	2.4b	(+.f64 x (neg.f64 (tan.f64 x)))

series17.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 x (neg.f64 (tan.f64 x))))
6.0ms	(+.f64 x (neg.f64 (tan.f64 x)))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`distribute-lft-out_binary64`

Counts

2 → 75

Calls

2 calls:

8.0ms	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 x (neg.f64 (tan.f64 x))))
4.0ms	(+.f64 x (neg.f64 (tan.f64 x)))

simplify99.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

465×	`fma-def_binary64`
375×	`distribute-rgt-in_binary64`
369×	`times-frac_binary64`
316×	`fma-neg_binary64`
295×	`distribute-lft-in_binary64`

Counts

99 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	2042
1	459	1962
2	1385	1934
3	4860	1934
4	4999	1934

prune97.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	180	4	184

Error

0.0b

Counts

184 → 4

Alt Table

Status	Error	Program
▶	35.3b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
✓	28.3b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	35.8b	(/.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
✓	35.1b	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 x (neg.f64 (tan.f64 x))))

Compiler

Compiled 3567 to 997 computations (72% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sin.f64 x) x)
✓	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
✓	0.1b	(/.f64 1 (cos.f64 x))
✓	2.8b	(+.f64 (/.f64 1 (cos.f64 x)) -1)

series30.0ms (0.2%)

Counts

4 → 32

Calls

4 calls:

13.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
7.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
6.0ms	(/.f64 1 (cos.f64 x))
3.0ms	(/.f64 (sin.f64 x) x)

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

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:

13.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
9.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
3.0ms	(/.f64 (sin.f64 x) x)
3.0ms	(/.f64 1 (cos.f64 x))

simplify103.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

443×	`fma-def_binary64`
410×	`associate-*l/_binary64`
341×	`associate-/l*_binary64`
334×	`distribute-rgt-in_binary64`
312×	`associate-*r/_binary64`

Counts

170 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	2417
1	573	2236
2	1485	2213
3	4391	2213
4	4980	2213

prune142.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	215	4	219

Error

0.0b

Counts

219 → 4

Alt Table

Status	Error	Program
✓	35.3b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
✓	28.3b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	35.8b	(/.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
✓	35.1b	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 x (neg.f64 (tan.f64 x))))

Compiler

Compiled 4456 to 2430 computations (45.5% saved)

regimes84.0ms (0.7%)

Accuracy

Total 0.0b remaining (15.7%)

Threshold costs 0.0b (15.7%)

Counts

27 → 3

Compiler

Compiled 758 to 508 computations (33% saved)

bsearch55.0ms (0.4%)

Steps

Iters	Range		Point
9	0.0013573560290461768	193865.61278390023	0.029073431474603176
9	-0.4710171046121895	-1.599903182968793e-7	-0.02981343514249264

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
6×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	60
1	35	60
2	46	60
3	52	60
4	55	60
5	55	60

end143.0ms (1.1%)

Compiler: Compiled 137 to 85 computations (38% saved)

Details

analyze2.0s (15.7%)

sample9.2s (73.3%)

simplify89.0ms (0.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series23.0ms (0.2%)

rewrite23.0ms (0.2%)

simplify143.0ms (1.1%)

prune88.0ms (0.7%)

localize7.0ms (0.1%)

series10.0ms (0.1%)

rewrite12.0ms (0.1%)

simplify73.0ms (0.6%)

prune54.0ms (0.4%)

localize9.0ms (0.1%)

series17.0ms (0.1%)

rewrite17.0ms (0.1%)

simplify99.0ms (0.8%)

prune97.0ms (0.8%)

localize14.0ms (0.1%)

series30.0ms (0.2%)

rewrite35.0ms (0.3%)

simplify103.0ms (0.8%)

prune142.0ms (1.1%)

regimes84.0ms (0.7%)

bsearch55.0ms (0.4%)

simplify6.0ms (0%)

end143.0ms (1.1%)

Profiling