Details

analyze23.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
12.5%	12.5%	75%	2
12.5%	12.5%	75%	3
18.7%	6.2%	75%	4
21.8%	3.1%	75%	5
23.4%	1.6%	75%	6
23.4%	1.6%	75%	7
24.2%	0.8%	75%	8
24.2%	0.8%	75%	9
24.6%	0.4%	75%	10
24.6%	0.4%	75%	11
24.8%	0.2%	75%	12
24.8%	0.2%	75%	13
24.9%	0.1%	75%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample2.9s (55.7%)

Results

1.5s	2039×	body	1024	valid
764.0ms	4659×	body	128	valid
444.0ms	1048×	body	512	valid
165.0ms	504×	body	256	valid
10.0ms	6×	body	2048	valid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify30.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

736×	`rules-9-rev_binary64`
430×	`rules-20_binary64`
407×	`fma-def_binary64`
345×	`fma-neg_binary64`
207×	`rules-12_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	20	14
2	40	14
3	89	14
4	262	14
5	1051	14
6	1712	14
7	5006	14

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))
▶	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))

Compiler

Compiled 70 to 47 computations (32.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series42.0ms (0.8%)

Counts

3 → 52

Calls

3 calls:

28.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
7.0ms	(*.f64 e (cos.f64 v))
7.0ms	(*.f64 e (sin.f64 v))

rewrite87.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

917×	`fma-neg_binary64`
545×	`prod-diff_binary64`
267×	`egg-rr`
179×	`expm1-udef_binary64`
179×	`log1p-udef_binary64`

Counts

3 → 267

Calls

3 calls:

81.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
81.0ms	(*.f64 e (sin.f64 v))
81.0ms	(*.f64 e (cos.f64 v))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	231	26
2	2915	26
3	5339	26
0	0	0
1	0	0

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-neg_binary64`
625×	`rules-20_binary64`
412×	`rules-14-rev_binary64`
343×	`rules-15-rev_binary64`
292×	`rules-21_binary64`

Counts

319 → 306

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1173
1	447	1130
2	2259	1118
3	5148	1118

prune302.0ms (5.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	298	8	306
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	299	9	308

Error

0.0b

Counts

308 → 9

Alt Table

Status	Error	Program
	1.0b	(.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (/.f64 (cbrt.f64 (*.f64 e (sin.f64 v))) (fma.f64 e (cos.f64 v) 1)))
	0.2b	(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))
	27.7b	(/.f64 (fma.f64 (sqrt.f64 (sin.f64 v)) (.f64 e (sqrt.f64 (sin.f64 v))) 0) (+.f64 1 (.f64 e (cos.f64 v))))
	0.2b	(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (fma.f64 (cos.f64 v) (+.f64 e (/.f64 1 (cos.f64 v))) -1)))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)) 0) (+.f64 1 (.f64 e (cos.f64 v))))
	1.0b	(/.f64 (fma.f64 (cbrt.f64 (sin.f64 v)) (.f64 e (pow.f64 (cbrt.f64 (sin.f64 v)) 2)) 0) (+.f64 1 (.f64 e (cos.f64 v))))
	17.5b	(/.f64 (fma.f64 (cbrt.f64 e) (.f64 (sin.f64 v) (cbrt.f64 (.f64 e e))) 0) (+.f64 1 (*.f64 e (cos.f64 v))))
	1.0b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))) 3)
▶	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))

Compiler

Compiled 6832 to 3202 computations (53.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
✓	0.0b	(/.f64 1 (fma.f64 e (cos.f64 v) 1))
	0.1b	(*.f64 e (sin.f64 v))

series49.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
21.0ms	(/.f64 1 (fma.f64 e (cos.f64 v) 1))

rewrite119.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

839×	`fma-neg_binary64`
499×	`prod-diff_binary64`
184×	`egg-rr`
173×	`expm1-udef_binary64`
173×	`log1p-udef_binary64`

Counts

2 → 184

Calls

2 calls:

113.0ms	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
113.0ms	(/.f64 1 (fma.f64 e (cos.f64 v) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	224	25
2	2789	25
3	4985	25
4	5293	25
0	0	0
1	0	0

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

796×	`rules-20_binary64`
743×	`fma-neg_binary64`
521×	`rules-15-rev_binary64`
396×	`rules-21_binary64`
151×	`fma-def_binary64`

Counts

232 → 229

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	157	1578
1	546	1516
2	2823	1516
3	5679	1516

prune356.0ms (6.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	339	0	339
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	339	9	348

Error

0.0b

Counts

348 → 9

Alt Table

Status	Error	Program
	1.0b	(.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (/.f64 (cbrt.f64 (*.f64 e (sin.f64 v))) (fma.f64 e (cos.f64 v) 1)))
	0.2b	(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))
	27.7b	(/.f64 (fma.f64 (sqrt.f64 (sin.f64 v)) (.f64 e (sqrt.f64 (sin.f64 v))) 0) (+.f64 1 (.f64 e (cos.f64 v))))
▶	0.2b	(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (fma.f64 (cos.f64 v) (+.f64 e (/.f64 1 (cos.f64 v))) -1)))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)) 0) (+.f64 1 (.f64 e (cos.f64 v))))
	1.0b	(/.f64 (fma.f64 (cbrt.f64 (sin.f64 v)) (.f64 e (pow.f64 (cbrt.f64 (sin.f64 v)) 2)) 0) (+.f64 1 (.f64 e (cos.f64 v))))
	17.5b	(/.f64 (fma.f64 (cbrt.f64 e) (.f64 (sin.f64 v) (cbrt.f64 (.f64 e e))) 0) (+.f64 1 (*.f64 e (cos.f64 v))))
	1.0b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))) 3)
✓	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))

Compiler

Compiled 8856 to 4611 computations (47.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (fma.f64 (cos.f64 v) (+.f64 e (/.f64 1 (cos.f64 v))) -1)))
✓	0.1b	(/.f64 1 (cos.f64 v))
	0.1b	(*.f64 e (sin.f64 v))
✓	33.3b	(fma.f64 (cos.f64 v) (+.f64 e (/.f64 1 (cos.f64 v))) -1)

series62.0ms (1.2%)

Counts

3 → 52

Calls

3 calls:

36.0ms	(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (fma.f64 (cos.f64 v) (+.f64 e (/.f64 1 (cos.f64 v))) -1)))
20.0ms	(fma.f64 (cos.f64 v) (+.f64 e (/.f64 1 (cos.f64 v))) -1)
6.0ms	(/.f64 1 (cos.f64 v))

rewrite80.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

702×	`prod-diff_binary64`
132×	`add-sqr-sqrt_binary64`
124×	`log1p-expm1-u_binary64`
124×	`expm1-log1p-u_binary64`
121×	`add-cbrt-cube_binary64`

Counts

3 → 94

Calls

3 calls:

78.0ms	(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (fma.f64 (cos.f64 v) (+.f64 e (/.f64 1 (cos.f64 v))) -1)))
78.0ms	(/.f64 1 (cos.f64 v))
78.0ms	(fma.f64 (cos.f64 v) (+.f64 e (/.f64 1 (cos.f64 v))) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	304	35
2	3774	35
3	5168	35
0	0	0
1	0	0

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

739×	`rules-13_binary64`
597×	`fma-neg_binary64`
586×	`rules-20_binary64`
416×	`rules-14-rev_binary64`
318×	`rules-15-rev_binary64`

Counts

146 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1143
1	439	1100
2	2137	1090
3	6493	1090

prune261.0ms (4.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	243	10	253

Error

Counts

253 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (/.f64 (cbrt.f64 (*.f64 e (sin.f64 v))) (fma.f64 e (cos.f64 v) 1)))
▶	0.2b	(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))
	27.7b	(/.f64 (fma.f64 (sqrt.f64 (sin.f64 v)) (.f64 e (sqrt.f64 (sin.f64 v))) 0) (+.f64 1 (.f64 e (cos.f64 v))))
✓	0.2b	(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (fma.f64 (cos.f64 v) (+.f64 e (/.f64 1 (cos.f64 v))) -1)))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)) 0) (+.f64 1 (.f64 e (cos.f64 v))))
	1.0b	(/.f64 (fma.f64 (cbrt.f64 (sin.f64 v)) (.f64 e (pow.f64 (cbrt.f64 (sin.f64 v)) 2)) 0) (+.f64 1 (.f64 e (cos.f64 v))))
	17.5b	(/.f64 (fma.f64 (cbrt.f64 e) (.f64 (sin.f64 v) (cbrt.f64 (.f64 e e))) 0) (+.f64 1 (*.f64 e (cos.f64 v))))
	0.6b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (fma.f64 (cos.f64 v) (+.f64 e (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cos.f64 v)) 2) -1) (pow.f64 (cbrt.f64 (cos.f64 v)) -1))) -1)))
	1.0b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))) 3)
✓	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))

Compiler

Compiled 6264 to 3357 computations (46.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (cos.f64 v) (/.f64 1 e))
✓	0.2b	(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))

series30.0ms (0.6%)

Counts

2 → 41

Calls

2 calls:

24.0ms	(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))
6.0ms	(+.f64 (cos.f64 v) (/.f64 1 e))

rewrite59.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

912×	`expm1-log1p-u_binary64`
468×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
86×	`log1p-expm1-u_binary64`
84×	`add-cbrt-cube_binary64`

Counts

2 → 78

Calls

2 calls:

57.0ms	(+.f64 (cos.f64 v) (/.f64 1 e))
57.0ms	(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	207	23
2	2631	23
3	5190	23
0	0	0
1	0	0

simplify42.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

538×	`fma-def_binary64`
466×	`fma-neg_binary64`
410×	`rules-13_binary64`
396×	`rules-20_binary64`
386×	`rules-14-rev_binary64`

Counts

119 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	999
1	351	983
2	1681	971
3	5443	971

prune116.0ms (2.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	112	10	122

Error

Counts

122 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (/.f64 (cbrt.f64 (*.f64 e (sin.f64 v))) (fma.f64 e (cos.f64 v) 1)))
✓	0.2b	(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))
	27.7b	(*.f64 (sqrt.f64 (sin.f64 v)) (/.f64 (sqrt.f64 (sin.f64 v)) (+.f64 (cos.f64 v) (/.f64 1 e))))
✓	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)) 0) (+.f64 1 (.f64 e (cos.f64 v))))
	1.0b	(/.f64 (fma.f64 (cbrt.f64 (sin.f64 v)) (.f64 e (pow.f64 (cbrt.f64 (sin.f64 v)) 2)) 0) (+.f64 1 (.f64 e (cos.f64 v))))
	17.5b	(/.f64 (fma.f64 (cbrt.f64 e) (.f64 (sin.f64 v) (cbrt.f64 (.f64 e e))) 0) (+.f64 1 (*.f64 e (cos.f64 v))))
	0.6b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (fma.f64 (cos.f64 v) (+.f64 e (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cos.f64 v)) 2) -1) (pow.f64 (cbrt.f64 (cos.f64 v)) -1))) -1)))
	1.0b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))) 3)
✓	0.2b	(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (fma.f64 (cos.f64 v) (+.f64 e (/.f64 1 (cos.f64 v))) -1)))

Compiler

Compiled 2290 to 1388 computations (39.4% saved)

regimes342.0ms (6.5%)

Accuracy

Total 0.1b remaining (85.5%)

Threshold costs 0.1b (85.5%)

Counts

114 → 1

Compiler

Compiled 6056 to 4241 computations (30% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	12	18
2	11	18

end142.0ms (2.7%)

Compiler: Compiled 210 to 143 computations (31.9% saved)

Details

analyze23.0ms (0.4%)

sample2.9s (55.7%)

simplify30.0ms (0.6%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series42.0ms (0.8%)

rewrite87.0ms (1.7%)

simplify50.0ms (1%)

prune302.0ms (5.7%)

localize8.0ms (0.2%)

series49.0ms (0.9%)

rewrite119.0ms (2.2%)

simplify60.0ms (1.1%)

prune356.0ms (6.7%)

localize12.0ms (0.2%)

series62.0ms (1.2%)

rewrite80.0ms (1.5%)

simplify49.0ms (0.9%)

prune261.0ms (4.9%)

localize7.0ms (0.1%)

series30.0ms (0.6%)

rewrite59.0ms (1.1%)

simplify42.0ms (0.8%)

prune116.0ms (2.2%)

regimes342.0ms (6.5%)

simplify1.0ms (0%)

end142.0ms (2.7%)

Profiling