Details

analyze339.0ms (7.8%)

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
37.4%	62.4%	0.1%	6
49.9%	49.9%	0.1%	7
62.4%	37.4%	0.1%	8
62.4%	37.4%	0.1%	9
71.8%	28.1%	0.1%	10
79.6%	20.3%	0.1%	11
79.6%	20.3%	0.1%	12
85%	14.8%	0.1%	13
89.3%	10.5%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample70.0ms (1.6%)

Algorithm

1×

intervals

Results

37.0ms	66×	body	1024	valid
12.0ms	142×	body	128	valid
7.0ms	30×	body	512	valid
3.0ms	18×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify9.0ms (0.2%)

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 (0.1%)

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 (cos.f64 y) (*.f64 z (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series25.0ms (0.6%)

Counts

3 → 64

Calls

3 calls:

16.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))
2.0ms	(cos.f64 y)

rewrite5.0ms (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:

3.0ms	(*.f64 z (sin.f64 y))
1.0ms	(cos.f64 y)
0.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
495×	`sub-neg_binary64`
289×	`associate-l_binary64`
258×	`unswap-sqr_binary64`
256×	`distribute-rgt-neg-in_binary64`

Counts

103 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1088
1	229	1018
2	653	1001
3	1805	999
4	3991	999
5	4797	999
6	4959	999

prune60.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Error

0.0b

Counts

83 → 9

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	24.8b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	0.2b	(fma.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 z (sin.f64 y)))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
▶	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	30.4b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	31.8b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.2b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))

Compiler

Compiled 1425 to 528 computations (62.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series23.0ms (0.5%)

Counts

2 → 40

Calls

2 calls:

15.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
7.0ms	(*.f64 (cos.f64 y) x)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 (cos.f64 y) x)
0.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

803×	`distribute-rgt-neg-in_binary64`
796×	`fma-def_binary64`
741×	`cancel-sign-sub-inv_binary64`
379×	`fma-neg_binary64`
324×	`*-commutative_binary64`

Counts

70 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	840
1	173	788
2	484	778
3	1314	771
4	3692	771
5	4945	771

prune81.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Error

0.0b

Counts

91 → 10

Alt Table

Status	Error	Program
	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) x))
	30.4b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	0.4b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	24.8b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
▶	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (log.f64 (exp.f64 (cos.f64 y))) x))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	31.8b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.4b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x)))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1467 to 559 computations (61.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (log.f64 (exp.f64 (cos.f64 y))) x))
✓	0.1b	(exp.f64 (cos.f64 y))
✓	0.1b	(*.f64 (log.f64 (exp.f64 (cos.f64 y))) x)
✓	0.3b	(log.f64 (exp.f64 (cos.f64 y)))

series30.0ms (0.7%)

Counts

4 → 76

Calls

4 calls:

18.0ms	(fma.f64 (sin.f64 y) z (*.f64 (log.f64 (exp.f64 (cos.f64 y))) x))
8.0ms	(*.f64 (log.f64 (exp.f64 (cos.f64 y))) x)
3.0ms	(exp.f64 (cos.f64 y))
2.0ms	(log.f64 (exp.f64 (cos.f64 y)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`exp-prod_binary64`
8×	`log-pow_binary64`

Counts

4 → 64

Calls

4 calls:

4.0ms	(*.f64 (log.f64 (exp.f64 (cos.f64 y))) x)
2.0ms	(log.f64 (exp.f64 (cos.f64 y)))
1.0ms	(exp.f64 (cos.f64 y))
0.0ms	(fma.f64 (sin.f64 y) z (*.f64 (log.f64 (exp.f64 (cos.f64 y))) x))

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Rules

814×	`fma-neg_binary64`
374×	`distribute-rgt-neg-in_binary64`
349×	`associate-l_binary64`
345×	`distribute-lft-neg-in_binary64`
311×	`associate-r_binary64`

Counts

140 → 132

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	130	1385
1	271	1301
2	730	1277
3	2207	1268
4	4851	1262
5	5033	1262

prune197.0ms (4.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	133	9	142

Error

0.0b

Counts

142 → 9

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) x))
	30.4b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	0.3b	(fma.f64 (sin.f64 y) z (*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3))) x))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	31.8b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	24.8b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	0.4b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x)))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 2312 to 829 computations (64.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) x))
✓	0.1b	(*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) x)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
✓	0.4b	(pow.f64 (cos.f64 y) 3)

series37.0ms (0.8%)

Counts

4 → 76

Calls

4 calls:

22.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) x))
7.0ms	(*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) x)
6.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 94

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) x)
2.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
0.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) x))

simplify106.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-neg_binary64`
354×	`*-commutative_binary64`
349×	`sub-neg_binary64`
294×	`cancel-sign-sub-inv_binary64`
231×	`unswap-sqr_binary64`

Counts

170 → 157

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	147	1663
1	298	1572
2	967	1536
3	2086	1534
4	3887	1524
5	4944	1524

prune221.0ms (5.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	157	9	166

Error

0.0b

Counts

166 → 9

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) x))
	30.4b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	0.3b	(fma.f64 (sin.f64 y) z (.f64 (cbrt.f64 (.f64 (cos.f64 y) (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x)))
	24.8b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	0.3b	(fma.f64 (sin.f64 y) z (*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3))) x))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	31.8b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 2659 to 1276 computations (52% saved)

regimes542.0ms (12.4%)

Accuracy

Total 0.1b remaining (61.6%)

Threshold costs 0.1b (61.6%)

Counts

116 → 1

Compiler

Compiled 6964 to 4366 computations (37.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample2.3s (52.9%)

Algorithm

1×

intervals

Results

1.1s	2025×	body	1024	valid
405.0ms	4512×	body	128	valid
270.0ms	987×	body	512	valid
82.0ms	468×	body	256	valid
10.0ms	8×	body	2048	valid

Compiler

Compiled 204 to 112 computations (45.1% saved)

Details

analyze339.0ms (7.8%)

sample70.0ms (1.6%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series25.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify98.0ms (2.2%)

prune60.0ms (1.4%)

localize7.0ms (0.2%)

series23.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify62.0ms (1.4%)

prune81.0ms (1.9%)

localize11.0ms (0.3%)

series30.0ms (0.7%)

rewrite9.0ms (0.2%)

simplify87.0ms (2%)

prune197.0ms (4.5%)

localize9.0ms (0.2%)

series37.0ms (0.8%)

rewrite13.0ms (0.3%)

simplify106.0ms (2.4%)

prune221.0ms (5.1%)

regimes542.0ms (12.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.3s (52.9%)

Profiling