Details

analyze1.8s (15.3%)

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)

sample8.5s (72.2%)

Results

5.1s	2030×	body	2048	valid
2.2s	3151×	body	1024	valid
657.0ms	1572×	body	512	valid
217.0ms	718×	body	256	valid
151.0ms	104×	body	4096	valid
115.0ms	681×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	7	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

29.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.4b	(-.f64 x (tan.f64 x))
✓	1.5b	(-.f64 x (sin.f64 x))

series17.0ms (0.1%)

Counts

3 → 30

Calls

3 calls:

9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms	(-.f64 x (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))

rewrite75.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

865×	`expm1-log1p-u_binary64`
618×	`prod-diff_binary64`
142×	`egg-rr`
81×	`add-sqr-sqrt_binary64`
78×	`log1p-expm1-u_binary64`

Counts

3 → 142

Calls

3 calls:

68.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
68.0ms	(-.f64 x (tan.f64 x))
68.0ms	(-.f64 x (sin.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	26
1	172	26
2	2395	26
3	5109	26
0	0	0
1	0	0

simplify92.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

272×	`fma-def_binary64`
250×	`rules-4_binary64`
246×	`rules-15-rev_binary64`
226×	`rules-13_binary64`
210×	`rules-20_binary64`

Counts

172 → 172

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	92	658
1	246	658
2	969	650
3	4921	628
4	4947	622
5	4997	622
6	4963	622

prune95.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	169	4	173

Error

0.0b

Counts

173 → 4

Alt Table

Status	Error	Program
	29.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) 2)
✓	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
▶	29.7b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
	33.8b	(-.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 3461 to 1131 computations (67.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
✓	0.1b	(*.f64 (cos.f64 x) x)
✓	0.2b	(/.f64 (sin.f64 x) x)
✓	0.2b	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))

series24.0ms (0.2%)

Counts

4 → 18

Calls

4 calls:

8.0ms	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))
7.0ms	(/.f64 (sin.f64 x) x)
6.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
3.0ms	(*.f64 (cos.f64 x) x)

rewrite84.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

518×	`log-prod_binary64`
222×	`log-div_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`
165×	`log-pow_binary64`

Counts

4 → 144

Calls

4 calls:

81.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
81.0ms	(*.f64 (cos.f64 x) x)
81.0ms	(/.f64 (sin.f64 x) x)
81.0ms	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	240	35
2	3233	35
3	5274	35
0	0	0
1	0	0

simplify37.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

785×	`rules-13_binary64`
642×	`rules-20_binary64`
542×	`fma-neg_binary64`
322×	`rules-21_binary64`
232×	`rules-14-rev_binary64`

Counts

162 → 169

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	58	210
1	163	198
2	590	198
3	2363	198
4	5485	198

prune104.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	169	4	173

Error

0.0b

Counts

173 → 4

Alt Table

Status	Error	Program
▶	29.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) 2)
✓	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	29.7b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
	33.8b	(-.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 3324 to 1370 computations (58.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) 2)
	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	1.4b	(-.f64 x (tan.f64 x))
	1.5b	(-.f64 x (sin.f64 x))

series25.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

25.0ms

(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) 2)

rewrite68.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

758×	`fma-neg_binary64`
643×	`prod-diff_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`
98×	`add-sqr-sqrt_binary64`

Counts

1 → 80

Calls

1 calls:

65.0ms

(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	225	14
2	2857	14
3	5008	14
0	0	0
1	0	0

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`rules-7-rev_binary64`
32×	`rules-21_binary64`
31×	`rules-14-rev_binary64`
24×	`rules-6_binary64`
15×	`rules-1_binary64`

Counts

92 → 94

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	456
1	145	456
2	580	456

prune139.0ms (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	266	0	266
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	266	4	270

Error

0.0b

Counts

270 → 4

Alt Table

Status	Error	Program
✓	29.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) 2)
✓	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	29.7b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
▶	33.8b	(-.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 6611 to 2236 computations (66.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	0.1b	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
✓	0.3b	(*.f64 27/112000 (pow.f64 x 6))
✓	18.9b	(-.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))

series14.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
4.0ms	(-.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))
3.0ms	(*.f64 27/112000 (pow.f64 x 6))
3.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

rewrite93.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

590×	`prod-diff_binary64`
163×	`egg-rr`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`
146×	`add-sqr-sqrt_binary64`

Counts

4 → 163

Calls

4 calls:

89.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
89.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
89.0ms	(*.f64 27/112000 (pow.f64 x 6))
89.0ms	(-.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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	53
1	363	53
2	3831	53
3	4674	53
0	0	0
1	0	0

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

802×	`rules-20_binary64`
541×	`rules-15_binary64`
460×	`rules-15-rev_binary64`
368×	`rules-21_binary64`
327×	`rules-4_binary64`

Counts

199 → 181

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	424
1	53	424
2	161	424
3	534	424
4	2596	424
5	4633	424
6	5326	424

prune165.0ms (1.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	180	5	185

Error

Counts

185 → 5

Alt Table

Status	Error	Program
✓	29.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) 2)
✓	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	29.7b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
✓	33.8b	(-.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))
	34.3b	(log1p.f64 (expm1.f64 (-.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 5236 to 3994 computations (23.7% saved)

regimes141.0ms (1.2%)

Accuracy

Total 0.2b remaining (92.8%)

Threshold costs 0.2b (92.8%)

Counts

53 → 3

Compiler

Compiled 1580 to 1146 computations (27.5% saved)

bsearch49.0ms (0.4%)

Steps

Iters	Range		Point
10	9.190145687768286e-5	113294488792.16826	4.99533306627316
8	-99.69361360461316	-0.026239293976662876	-0.09740715512336516

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	70
1	35	70
2	34	70

end102.0ms (0.9%)

Compiler: Compiled 172 to 118 computations (31.4% saved)

Details

analyze1.8s (15.3%)

sample8.5s (72.2%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series17.0ms (0.1%)

rewrite75.0ms (0.6%)

simplify92.0ms (0.8%)

prune95.0ms (0.8%)

localize12.0ms (0.1%)

series24.0ms (0.2%)

rewrite84.0ms (0.7%)

simplify37.0ms (0.3%)

prune104.0ms (0.9%)

localize10.0ms (0.1%)

series25.0ms (0.2%)

rewrite68.0ms (0.6%)

simplify15.0ms (0.1%)

prune139.0ms (1.2%)

localize14.0ms (0.1%)

series14.0ms (0.1%)

rewrite93.0ms (0.8%)

simplify66.0ms (0.6%)

prune165.0ms (1.4%)

regimes141.0ms (1.2%)

bsearch49.0ms (0.4%)

simplify7.0ms (0.1%)

end102.0ms (0.9%)

Profiling