Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample4.4s (29.3%)

Results

2.3s	2038×	body	1024	valid
1.1s	4602×	body	128	valid
647.0ms	1103×	body	512	valid
272.0ms	509×	body	256	valid
9.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12
3	16	12

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 y)
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
✓	0.1b	(*.f64 z (cos.f64 y))

series53.0ms (0.4%)

Counts

3 → 64

Calls

3 calls:

38.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
12.0ms	(*.f64 z (cos.f64 y))
3.0ms	(cos.f64 y)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 39

Calls

3 calls:

6.0ms	(*.f64 z (cos.f64 y))
2.0ms	(cos.f64 y)
1.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

simplify174.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

738×	`distribute-rgt-neg-in_binary64`
593×	`fma-neg_binary64`
367×	`*-commutative_binary64`
354×	`sub-neg_binary64`
331×	`neg-mul-1_binary64`

Counts

103 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1076
1	200	1011
2	592	993
3	1661	993
4	3588	993
5	4917	993
6	5070	993

prune132.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	7	82

Error

0.0b

Counts

82 → 7

Alt Table

Status	Error	Program
	29.5b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	25.3b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
▶	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
	30.0b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	38.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	15.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))

Compiler

Compiled 1379 to 497 computations (64% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
✓	0.1b	(*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y))))
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 y)))
✓	0.6b	(expm1.f64 (cos.f64 y))

series52.0ms (0.3%)

Counts

4 → 84

Calls

4 calls:

25.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
18.0ms	(*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y))))
6.0ms	(expm1.f64 (cos.f64 y))
3.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`

Counts

4 → 52

Calls

4 calls:

4.0ms	(*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y))))
1.0ms	(expm1.f64 (cos.f64 y))
1.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
1.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

simplify124.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-neg_binary64`
369×	`associate-l_binary64`
367×	`distribute-rgt-neg-in_binary64`
343×	`distribute-lft-neg-in_binary64`
310×	`associate-r_binary64`

Counts

136 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1318
1	266	1238
2	793	1213
3	2339	1207
4	4825	1207
5	4985	1207

prune185.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Error

0.0b

Counts

120 → 7

Alt Table

Status	Error	Program
	29.5b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	25.3b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
	30.0b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	38.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	15.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))

Compiler

Compiled 1962 to 687 computations (65% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (cos.f64 y))
✓	0.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
✓	0.6b	(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))

series1.7s (11.3%)

Counts

3 → 108

Calls

3 calls:

939.0ms

(*.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

734.0ms

(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))

27.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

13.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

9.0ms

(*.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

5.0ms

(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))

simplify343.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-def_binary64`
477×	`times-frac_binary64`
443×	`associate-l_binary64`
311×	`associate-/r*_binary64`
306×	`associate-/l*_binary64`

Counts

201 → 256

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	432	7251
1	1431	6422
2	4883	6418
3	5155	6418

prune745.0ms (5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	518	5	523
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	520	10	530

Error

0.0b

Counts

530 → 10

Alt Table

Status	Error	Program
	25.3b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	3.8b	(.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	29.5b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	1.5b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))))) (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))))
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
	30.0b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	27.4b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (.f64 (sin.f64 y) x)) 2)) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	38.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 25067 to 7780 computations (69% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	0.1b	(*.f64 z (cos.f64 y))
	0.6b	(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)

series5.2s (34.6%)

Counts

1 → 36

Calls

1 calls:

5.2s	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 32

Calls

1 calls:

3.0ms

(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)

simplify134.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-def_binary64`
567×	`associate-l_binary64`
514×	`associate-r_binary64`
347×	`associate-/l*_binary64`
212×	`times-frac_binary64`

Counts

68 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1722
1	288	1563
2	935	1533
3	4420	1530
4	5051	1530

prune284.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	209	10	219

Error

0.0b

Counts

219 → 10

Alt Table

Status	Error	Program
	25.3b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	3.8b	(.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	29.5b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	1.5b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))))) (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
	30.0b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	27.4b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (.f64 (sin.f64 y) x)) 2)) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	38.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 5600 to 2587 computations (53.8% saved)

regimes1.1s (7.4%)

Accuracy

Total 0.1b remaining (50%)

Threshold costs 0.1b (50%)

Counts

89 → 1

Compiler

Compiled 7772 to 3694 computations (52.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	14	12
2	13	12

end224.0ms (1.5%)

Compiler: Compiled 325 to 125 computations (61.5% saved)

Details

analyze4.0ms (0%)

sample4.4s (29.3%)

simplify9.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series53.0ms (0.4%)

rewrite11.0ms (0.1%)

simplify174.0ms (1.2%)

prune132.0ms (0.9%)

localize22.0ms (0.1%)

series52.0ms (0.3%)

rewrite19.0ms (0.1%)

simplify124.0ms (0.8%)

prune185.0ms (1.2%)

localize19.0ms (0.1%)

series1.7s (11.3%)

rewrite48.0ms (0.3%)

simplify343.0ms (2.3%)

prune745.0ms (5%)

localize15.0ms (0.1%)

series5.2s (34.6%)

rewrite6.0ms (0%)

simplify134.0ms (0.9%)

prune284.0ms (1.9%)

regimes1.1s (7.4%)

simplify3.0ms (0%)

end224.0ms (1.5%)

Profiling