Details

analyze23.0ms (0.5%)

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	2037×	body	1024	valid
764.0ms	4687×	body	128	valid
437.0ms	1004×	body	512	valid
158.0ms	525×	body	256	valid
5.0ms	3×	body	2048	valid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	17	15
2	23	15
3	26	15
4	27	15

Stop Event

1×

saturated

Counts

1 → 2

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
	0.1b	(*.f64 (sin.f64 v) (/.f64 e (fma.f64 e (cos.f64 v) 1)))
▶	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))

Compiler

Compiled 73 to 47 computations (35.6% saved)

localize10.0ms (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))
✓	0.1b	(*.f64 e (cos.f64 v))

series40.0ms (0.8%)

Counts

3 → 52

Calls

3 calls:

27.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
6.0ms	(*.f64 e (cos.f64 v))
6.0ms	(*.f64 e (sin.f64 v))

rewrite49.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

370×	`prod-diff_binary64`
254×	`fma-def_binary64`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`
166×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	208	27
2	2817	27

Stop Event

1×	node limit

Counts

3 → 81

Calls

3 calls:

48.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
48.0ms	(*.f64 e (sin.f64 v))
48.0ms	(*.f64 e (cos.f64 v))

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

691×	`times-frac_binary64`
485×	`fma-def_binary64`
464×	`associate-/l*_binary64`
292×	`cancel-sign-sub-inv_binary64`
132×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1173
1	403	1130
2	1559	1082

Stop Event

1×	node limit

Counts

133 → 120

prune111.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Error

0.0b

Counts

122 → 6

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (pow.f64 (.f64 e (cos.f64 v)) 2))) (-.f64 1 (.f64 e (cos.f64 v))))
	0.2b	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	30.6b	(/.f64 (cbrt.f64 (.f64 (pow.f64 e 3) (pow.f64 (sin.f64 v) 3))) (+.f64 1 (.f64 e (cos.f64 v))))
	0.5b	(pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))) -1)
	23.7b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 e (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))) 2)
	1.1b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 e (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))) 3)

Compiler

Compiled 2626 to 1436 computations (45.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (pow.f64 (.f64 e (cos.f64 v)) 2))) (-.f64 1 (.f64 e (cos.f64 v))))
	0.1b	(*.f64 e (sin.f64 v))
	0.1b	(*.f64 e (cos.f64 v))
✓	0.1b	(pow.f64 (*.f64 e (cos.f64 v)) 2)

series82.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

71.0ms	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (pow.f64 (.f64 e (cos.f64 v)) 2))) (-.f64 1 (.f64 e (cos.f64 v))))
11.0ms	(pow.f64 (*.f64 e (cos.f64 v)) 2)

rewrite61.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

841×	`prod-diff_binary64`
150×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`
145×	`expm1-log1p-u_binary64`
143×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	309	26
2	4185	26

Stop Event

1×	node limit

Counts

2 → 73

Calls

2 calls:

60.0ms	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (pow.f64 (.f64 e (cos.f64 v)) 2))) (-.f64 1 (.f64 e (cos.f64 v))))
60.0ms	(pow.f64 (*.f64 e (cos.f64 v)) 2)

simplify42.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

932×	`times-frac_binary64`
704×	`fma-def_binary64`
225×	`unswap-sqr_binary64`
131×	`associate-r_binary64`
129×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	1856
1	526	1818
2	2217	1755

Stop Event

1×	node limit

Counts

121 → 105

prune192.0ms (3.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	185	6	191

Error

0.0b

Counts

191 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (pow.f64 (.f64 e (cos.f64 v)) 2))) (-.f64 1 (.f64 e (cos.f64 v))))
	30.6b	(/.f64 (cbrt.f64 (.f64 (pow.f64 e 3) (pow.f64 (sin.f64 v) 3))) (+.f64 1 (.f64 e (cos.f64 v))))
▶	0.2b	(/.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v)))
	0.5b	(pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))) -1)
	23.7b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 e (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))) 2)
	1.1b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 e (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))) 3)

Compiler

Compiled 5807 to 3096 computations (46.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v))
	0.1b	(*.f64 e (cos.f64 v))
	0.1b	(pow.f64 (*.f64 e (cos.f64 v)) 2)
✓	0.2b	(/.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v)))

series103.0ms (2%)

Counts

2 → 48

Calls

2 calls:

70.0ms	(/.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v)))
33.0ms	(/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v))

rewrite86.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

934×	`prod-diff_binary64`
155×	`add-sqr-sqrt_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`
148×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	317	34
2	4500	34

Stop Event

1×	node limit

Counts

2 → 135

Calls

2 calls:

82.0ms	(/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v))
82.0ms	(/.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v)))

simplify46.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

926×	`times-frac_binary64`
851×	`fma-def_binary64`
197×	`unswap-sqr_binary64`
153×	`associate-+r+_binary64`
148×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	2062
1	572	2033
2	2380	1974

Stop Event

1×	node limit

Counts

183 → 173

prune331.0ms (6.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	259	5	264
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	261	9	270

Error

Counts

270 → 9

Alt Table

Status	Error	Program
	0.5b	(pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))) -1)
	5.5b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v))))) 2) (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (.f64 e (cos.f64 v)) 2)) (sin.f64 v)) 2))) (cbrt.f64 (.f64 (sin.f64 v) (/.f64 e (+.f64 1 (.f64 e (cos.f64 v)))))))
✓	0.1b	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (pow.f64 (.f64 e (cos.f64 v)) 2))) (-.f64 1 (.f64 e (cos.f64 v))))
	30.6b	(/.f64 (cbrt.f64 (.f64 (pow.f64 e 3) (pow.f64 (sin.f64 v) 3))) (+.f64 1 (.f64 e (cos.f64 v))))
	0.6b	(pow.f64 (.f64 (+.f64 1 (.f64 e (cos.f64 v))) (/.f64 (/.f64 1 (sin.f64 v)) e)) -1)
✓	0.2b	(/.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v)))
	10.1b	(/.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) 3) (pow.f64 (sin.f64 v) 3))))
	10.1b	(/.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v)) 3)))
▶	0.4b	(.f64 (sqrt.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v))))) (.f64 (sqrt.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v))))) (/.f64 (sin.f64 v) (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)))))

Compiler

Compiled 10262 to 5338 computations (48% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 e (cos.f64 v))
	0.1b	(pow.f64 (*.f64 e (cos.f64 v)) 2)
✓	0.3b	(.f64 (sqrt.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v))))) (.f64 (sqrt.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v))))) (/.f64 (sin.f64 v) (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)))))
✓	0.3b	(.f64 (sqrt.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v))))) (/.f64 (sin.f64 v) (-.f64 1 (pow.f64 (.f64 e (cos.f64 v)) 2))))

series167.0ms (3.3%)

Counts

2 → 44

Calls

2 calls:

95.0ms

(*.f64 (sqrt.f64 (*.f64 e (-.f64 1 (*.f64 e (cos.f64 v))))) (/.f64 (sin.f64 v) (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2))))

72.0ms

(*.f64 (sqrt.f64 (*.f64 e (-.f64 1 (*.f64 e (cos.f64 v))))) (*.f64 (sqrt.f64 (*.f64 e (-.f64 1 (*.f64 e (cos.f64 v))))) (/.f64 (sin.f64 v) (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)))))

rewrite61.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

832×	`prod-diff_binary64`
167×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
159×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	64
1	349	64
2	4519	64

Stop Event

1×	node limit

Counts

2 → 45

Calls

2 calls:

60.0ms

(*.f64 (sqrt.f64 (*.f64 e (-.f64 1 (*.f64 e (cos.f64 v))))) (*.f64 (sqrt.f64 (*.f64 e (-.f64 1 (*.f64 e (cos.f64 v))))) (/.f64 (sin.f64 v) (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)))))

60.0ms

(*.f64 (sqrt.f64 (*.f64 e (-.f64 1 (*.f64 e (cos.f64 v))))) (/.f64 (sin.f64 v) (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2))))

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

260×	`associate-+r+_binary64`
254×	`fma-def_binary64`
219×	`sub-neg_binary64`
208×	`fma-neg_binary64`
192×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	327	3689
1	1031	3604
2	4360	3604

Stop Event

1×	node limit

Counts

89 → 103

prune286.0ms (5.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	224	8	232

Error

Counts

232 → 8

Alt Table

Status	Error	Program
	1.1b	(pow.f64 (cbrt.f64 (.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (/.f64 (sin.f64 v) (-.f64 1 (pow.f64 (.f64 e (cos.f64 v)) 2))))) 3)
	30.6b	(/.f64 (cbrt.f64 (.f64 (pow.f64 e 3) (pow.f64 (sin.f64 v) 3))) (+.f64 1 (.f64 e (cos.f64 v))))
✓	0.1b	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (pow.f64 (.f64 e (cos.f64 v)) 2))) (-.f64 1 (.f64 e (cos.f64 v))))
	0.6b	(pow.f64 (.f64 (+.f64 1 (.f64 e (cos.f64 v))) (/.f64 (/.f64 1 (sin.f64 v)) e)) -1)
✓	0.2b	(/.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v)))
	10.1b	(/.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) 3) (pow.f64 (sin.f64 v) 3))))
	10.1b	(/.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v)))) (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)) (sin.f64 v)) 3)))
✓	0.4b	(.f64 (sqrt.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v))))) (.f64 (sqrt.f64 (.f64 e (-.f64 1 (.f64 e (cos.f64 v))))) (/.f64 (sin.f64 v) (-.f64 1 (pow.f64 (*.f64 e (cos.f64 v)) 2)))))

Compiler

Compiled 10399 to 6006 computations (42.2% saved)

regimes291.0ms (5.6%)

Accuracy

Total 0.1b remaining (84.6%)

Threshold costs 0.1b (84.6%)

Counts

99 → 1

Compiler

Compiled 5612 to 3824 computations (31.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	26	31
2	40	31
3	48	31
4	53	31
5	54	31

Stop Event

1×

saturated

end144.0ms (2.8%)

Compiler: Compiled 233 to 156 computations (33% saved)

Details

analyze23.0ms (0.5%)

sample2.9s (55.7%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series40.0ms (0.8%)

rewrite49.0ms (1%)

simplify31.0ms (0.6%)

prune111.0ms (2.2%)

localize12.0ms (0.2%)

series82.0ms (1.6%)

rewrite61.0ms (1.2%)

simplify42.0ms (0.8%)

prune192.0ms (3.7%)

localize12.0ms (0.2%)

series103.0ms (2%)

rewrite86.0ms (1.7%)

simplify46.0ms (0.9%)

prune331.0ms (6.4%)

localize14.0ms (0.3%)

series167.0ms (3.3%)

rewrite61.0ms (1.2%)

simplify71.0ms (1.4%)

prune286.0ms (5.6%)

regimes291.0ms (5.6%)

simplify3.0ms (0%)

end144.0ms (2.8%)

Profiling