Details

analyze549.0ms (7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
6.2%	93.7%	0.1%	6
37.5%	53.1%	9.5%	7
37.5%	51.5%	11%	8
43.7%	39.8%	16.5%	9
43.7%	38.6%	17.7%	10
46.8%	32.6%	20.6%	11
46.8%	31.9%	21.3%	12
48.4%	28.8%	22.8%	13
48.4%	28.5%	23.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample4.3s (54.7%)

Results

1.2s	2138×	body	1024	invalid
1.2s	2024×	body	1024	valid
693.0ms	4660×	body	128	valid
357.0ms	1038×	body	512	valid
353.0ms	1069×	body	512	invalid
173.0ms	527×	body	256	valid
134.0ms	518×	body	256	invalid
122.0ms	800×	body	128	invalid
8.0ms	7×	body	2048	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-neg_binary64`
610×	`div-sub_binary64`
491×	`times-frac_binary64`
410×	`associate-/l*_binary64`
352×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	16	11
2	34	11
3	73	11
4	160	11
5	361	11
6	984	11
7	3177	11
8	4701	11
9	5010	11

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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sinh.f64 y)
✓	0.0b	(/.f64 (sinh.f64 y) y)
✓	0.2b	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))

series55.0ms (0.7%)

Counts

3 → 48

Calls

3 calls:

35.0ms	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
12.0ms	(/.f64 (sinh.f64 y) y)
8.0ms	(sinh.f64 y)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

3 → 74

Calls

3 calls:

6.0ms	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
4.0ms	(/.f64 (sinh.f64 y) y)
1.0ms	(sinh.f64 y)

simplify93.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

550×	`fma-def_binary64`
445×	`associate-/l*_binary64`
383×	`times-frac_binary64`
314×	`associate-*l/_binary64`
249×	`fma-neg_binary64`

Counts

122 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	2084
1	539	1920
2	1766	1774
3	4702	1772
4	4956	1772

prune101.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	4	128

Error

0.2b

Counts

128 → 4

Alt Table

Status	Error	Program
	1.4b	(.f64 (sin.f64 x) (+.f64 1 (fma.f64 1/6 (.f64 y y) (fma.f64 1/120 (pow.f64 y 4) (*.f64 1/5040 (pow.f64 y 6))))))
▶	0.3b	(.f64 (.f64 (sin.f64 x) (sqrt.f64 (/.f64 (sinh.f64 y) y))) (sqrt.f64 (/.f64 (sinh.f64 y) y)))
	35.5b	(.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 (sin.f64 x)) (/.f64 (sinh.f64 y) y)))
	13.0b	(/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) y)

Compiler

Compiled 2135 to 835 computations (60.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sin.f64 x) (sqrt.f64 (/.f64 (sinh.f64 y) y)))
	0.0b	(/.f64 (sinh.f64 y) y)
✓	0.0b	(.f64 (.f64 (sin.f64 x) (sqrt.f64 (/.f64 (sinh.f64 y) y))) (sqrt.f64 (/.f64 (sinh.f64 y) y)))
✓	0.2b	(sqrt.f64 (/.f64 (sinh.f64 y) y))

series181.0ms (2.3%)

Counts

3 → 40

Calls

3 calls:

78.0ms	(*.f64 (sin.f64 x) (sqrt.f64 (/.f64 (sinh.f64 y) y)))
70.0ms	(.f64 (.f64 (sin.f64 x) (sqrt.f64 (/.f64 (sinh.f64 y) y))) (sqrt.f64 (/.f64 (sinh.f64 y) y)))
33.0ms	(sqrt.f64 (/.f64 (sinh.f64 y) y))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64`
37×	`add-sqr-sqrt_binary64`
32×	`associate-r_binary64`
29×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`

Counts

3 → 99

Calls

3 calls:

10.0ms	(.f64 (.f64 (sin.f64 x) (sqrt.f64 (/.f64 (sinh.f64 y) y))) (sqrt.f64 (/.f64 (sinh.f64 y) y)))
6.0ms	(*.f64 (sin.f64 x) (sqrt.f64 (/.f64 (sinh.f64 y) y)))
2.0ms	(sqrt.f64 (/.f64 (sinh.f64 y) y))

simplify151.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def_binary64`
417×	`fma-neg_binary64`
344×	`associate-/l*_binary64`
280×	`times-frac_binary64`
260×	`associate-l_binary64`

Counts

139 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	254	2999
1	637	2728
2	2134	2647
3	4820	2643
4	5069	2643

prune229.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	299	0	299
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	299	4	303

Error

0.2b

Counts

303 → 4

Alt Table

Status	Error	Program
▶	1.4b	(.f64 (sin.f64 x) (+.f64 1 (fma.f64 1/6 (.f64 y y) (fma.f64 1/120 (pow.f64 y 4) (*.f64 1/5040 (pow.f64 y 6))))))
✓	0.3b	(.f64 (.f64 (sin.f64 x) (sqrt.f64 (/.f64 (sinh.f64 y) y))) (sqrt.f64 (/.f64 (sinh.f64 y) y)))
	35.5b	(.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 (sin.f64 x)) (/.f64 (sinh.f64 y) y)))
	13.0b	(/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) y)

Compiler

Compiled 6634 to 1760 computations (73.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sin.f64 x) (+.f64 1 (fma.f64 1/6 (.f64 y y) (fma.f64 1/120 (pow.f64 y 4) (*.f64 1/5040 (pow.f64 y 6))))))
✓	0.0b	(*.f64 1/5040 (pow.f64 y 6))
✓	0.1b	(fma.f64 1/120 (pow.f64 y 4) (*.f64 1/5040 (pow.f64 y 6)))
✓	0.2b	(fma.f64 1/6 (.f64 y y) (fma.f64 1/120 (pow.f64 y 4) (.f64 1/5040 (pow.f64 y 6))))

series66.0ms (0.9%)

Counts

4 → 48

Calls

4 calls:

49.0ms	(.f64 (sin.f64 x) (+.f64 1 (fma.f64 1/6 (.f64 y y) (fma.f64 1/120 (pow.f64 y 4) (*.f64 1/5040 (pow.f64 y 6))))))
9.0ms	(fma.f64 1/6 (.f64 y y) (fma.f64 1/120 (pow.f64 y 4) (.f64 1/5040 (pow.f64 y 6))))
4.0ms	(fma.f64 1/120 (pow.f64 y 4) (*.f64 1/5040 (pow.f64 y 6)))
3.0ms	(*.f64 1/5040 (pow.f64 y 6))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-exp-log_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 72

Calls

4 calls:

13.0ms	(*.f64 1/5040 (pow.f64 y 6))
6.0ms	(.f64 (sin.f64 x) (+.f64 1 (fma.f64 1/6 (.f64 y y) (fma.f64 1/120 (pow.f64 y 4) (*.f64 1/5040 (pow.f64 y 6))))))
0.0ms	(fma.f64 1/6 (.f64 y y) (fma.f64 1/120 (pow.f64 y 4) (.f64 1/5040 (pow.f64 y 6))))
0.0ms	(fma.f64 1/120 (pow.f64 y 4) (*.f64 1/5040 (pow.f64 y 6)))

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

717×	`associate-+r+_binary64`
413×	`associate--r+_binary64`
352×	`associate--l+_binary64`
238×	`cancel-sign-sub-inv_binary64`
180×	`fma-def_binary64`

Counts

120 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2918
1	520	2676
2	1978	2621
3	5055	2621

prune183.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	126	4	130

Error

0.2b

Counts

130 → 4

Alt Table

Status	Error	Program
▶	1.4b	(.f64 (sin.f64 x) (+.f64 1 (fma.f64 1/6 (.f64 y y) (fma.f64 1/120 (pow.f64 y 4) (.f64 (.f64 1/5040 (pow.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) 6)) (pow.f64 (cbrt.f64 y) 6))))))
✓	0.3b	(.f64 (.f64 (sin.f64 x) (sqrt.f64 (/.f64 (sinh.f64 y) y))) (sqrt.f64 (/.f64 (sinh.f64 y) y)))
	35.5b	(.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 (sin.f64 x)) (/.f64 (sinh.f64 y) y)))
	13.0b	(/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) y)

Compiler

Compiled 3958 to 2723 computations (31.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) 6)
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(pow.f64 (cbrt.f64 y) 6)
✓	0.6b	(cbrt.f64 y)

series234.0ms (3%)

Counts

4 → 48

Calls

4 calls:

84.0ms	(pow.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) 6)
64.0ms	(pow.f64 (cbrt.f64 y) 6)
46.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
41.0ms	(cbrt.f64 y)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow1_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

4 → 104

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
4.0ms	(pow.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) 6)
2.0ms	(pow.f64 (cbrt.f64 y) 6)
1.0ms	(cbrt.f64 y)

simplify96.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

733×	`log-prod_binary64`
716×	`exp-prod_binary64`
485×	`unswap-sqr_binary64`
481×	`sqr-pow_binary64`
363×	`cube-prod_binary64`

Counts

152 → 144

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	1016
1	193	854
2	573	782
3	1356	731
4	3402	728
5	4364	728
6	5004	728

prune258.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	180	4	184

Error

0.2b

Counts

184 → 4

Alt Table

Status	Error	Program
	1.4b	(.f64 (sin.f64 x) (+.f64 1 (fma.f64 1/6 (.f64 y y) (fma.f64 1/120 (pow.f64 y 4) (.f64 (.f64 1/5040 (pow.f64 (*.f64 (cbrt.f64 y) (log1p.f64 (expm1.f64 (cbrt.f64 y)))) 6)) (pow.f64 (cbrt.f64 y) 6))))))
	13.0b	(/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) y)
✓	0.3b	(.f64 (.f64 (sin.f64 x) (sqrt.f64 (/.f64 (sinh.f64 y) y))) (sqrt.f64 (/.f64 (sinh.f64 y) y)))
	35.5b	(.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 (sin.f64 x)) (/.f64 (sinh.f64 y) y)))

Compiler

Compiled 5938 to 3422 computations (42.4% saved)

regimes989.0ms (12.7%)

Accuracy

Total 0.0b remaining (47.4%)

Threshold costs 0.0b (47.4%)

Counts

150 → 1

Compiler

Compiled 15410 to 10967 computations (28.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	17	26
2	16	26

end84.0ms (1.1%)

Compiler: Compiled 108 to 70 computations (35.2% saved)

Details

analyze549.0ms (7%)

sample4.3s (54.7%)

simplify54.0ms (0.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series55.0ms (0.7%)

rewrite13.0ms (0.2%)

simplify93.0ms (1.2%)

prune101.0ms (1.3%)

localize8.0ms (0.1%)

series181.0ms (2.3%)

rewrite25.0ms (0.3%)

simplify151.0ms (1.9%)

prune229.0ms (2.9%)

localize13.0ms (0.2%)

series66.0ms (0.9%)

rewrite23.0ms (0.3%)

simplify83.0ms (1.1%)

prune183.0ms (2.3%)

localize19.0ms (0.2%)

series234.0ms (3%)

rewrite16.0ms (0.2%)

simplify96.0ms (1.2%)

prune258.0ms (3.3%)

regimes989.0ms (12.7%)

simplify2.0ms (0%)

end84.0ms (1.1%)

Profiling