Details

analyze441.0ms (7.1%)

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
25%	74.9%	0.1%	6
49.9%	49.9%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
71.8%	28.1%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
85%	14.8%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample218.0ms (3.5%)

Algorithm

1×

intervals

Results

165.0ms	66×	body	1024	valid
14.0ms	139×	body	128	valid
10.0ms	41×	body	512	valid
2.0ms	10×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify8.0ms (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)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series28.0ms (0.5%)

Counts

3 → 64

Calls

3 calls:

16.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
11.0ms	(*.f64 z (cos.f64 y))
2.0ms	(sin.f64 y)

rewrite6.0ms (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:

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

simplify109.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-neg_binary64`
413×	`sub-neg_binary64`
295×	`associate-l_binary64`
259×	`unswap-sqr_binary64`
258×	`associate-r_binary64`

Counts

103 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	1076
1	225	1013
2	651	994
3	1798	994
4	3982	994
5	4885	994
6	5000	994
7	4925	994

prune56.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Error

0.0b

Counts

82 → 8

Alt Table

Status	Error	Program
	31.5b	(fma.f64 x (exp.f64 (log.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	18.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	41.6b	(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)))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 z (cos.f64 y))) (cbrt.f64 (.f64 z (cos.f64 y)))) (cbrt.f64 (*.f64 z (cos.f64 y)))))
	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	33.3b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
▶	0.1b	(fma.f64 x (log1p.f64 (expm1.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	30.6b	(.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)))))

Compiler

Compiled 1385 to 500 computations (63.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (log1p.f64 (expm1.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.1b	(*.f64 z (cos.f64 y))
✓	0.1b	(expm1.f64 (sin.f64 y))
✓	0.2b	(log1p.f64 (expm1.f64 (sin.f64 y)))

series27.0ms (0.4%)

Counts

3 → 60

Calls

3 calls:

22.0ms	(fma.f64 x (log1p.f64 (expm1.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
3.0ms	(expm1.f64 (sin.f64 y))
2.0ms	(log1p.f64 (expm1.f64 (sin.f64 y)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log1p-expm1-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

0.0ms	(expm1.f64 (sin.f64 y))
0.0ms	(log1p.f64 (expm1.f64 (sin.f64 y)))
0.0ms	(fma.f64 x (log1p.f64 (expm1.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

664×	`cancel-sign-sub-inv_binary64`
590×	`distribute-rgt-neg-in_binary64`
495×	`sub-neg_binary64`
431×	`distribute-lft-neg-in_binary64`
380×	`fma-neg_binary64`

Counts

92 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	907
1	179	854
2	469	836
3	1312	834
4	3040	834
5	4491	834
6	4935	834

prune83.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	110	8	118

Error

0.0b

Counts

118 → 8

Alt Table

Status	Error	Program
	31.5b	(fma.f64 x (exp.f64 (log.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	18.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	41.6b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) x (*.f64 (cos.f64 y) z)) 3))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 z (cos.f64 y))) (cbrt.f64 (.f64 z (cos.f64 y)))) (cbrt.f64 (*.f64 z (cos.f64 y)))))
▶	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	33.3b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 x (log1p.f64 (expm1.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	30.6b	(.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)))))

Compiler

Compiled 1859 to 624 computations (66.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
✓	0.2b	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(cbrt.f64 (cos.f64 y))

series1.1s (17.6%)

Counts

4 → 72

Calls

4 calls:

625.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
267.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
184.0ms	(cbrt.f64 (cos.f64 y))
9.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 102

Calls

4 calls:

10.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
6.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
5.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
1.0ms	(cbrt.f64 (cos.f64 y))

simplify127.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-neg_binary64`
609×	`unswap-sqr_binary64`
446×	`*-commutative_binary64`
370×	`cancel-sign-sub-inv_binary64`
351×	`log-prod_binary64`

Counts

174 → 172

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	2118
1	352	1762
2	1218	1642
3	2345	1606
4	4484	1588
5	4900	1588
6	4962	1588

prune214.0ms (3.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	217	3	220
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	218	10	228

Error

0.0b

Counts

228 → 10

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
	31.5b	(fma.f64 x (exp.f64 (log.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.5b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (cbrt.f64 (cbrt.f64 (cos.f64 y))))))
	1.0b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))))
	41.6b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) x (*.f64 (cos.f64 y) z)) 3))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 z (cos.f64 y))) (cbrt.f64 (.f64 z (cos.f64 y)))) (cbrt.f64 (*.f64 z (cos.f64 y)))))
✓	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	33.3b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 x (log1p.f64 (expm1.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	30.6b	(.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)))))

Compiler

Compiled 5156 to 1570 computations (69.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
✓	0.2b	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))

series636.0ms (10.3%)

Counts

3 → 52

Calls

3 calls:

624.0ms	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
9.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
3.0ms	(pow.f64 (cos.f64 y) 2)

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`unpow-prod-down_binary64`
18×	`associate-r_binary64`
16×	`prod-exp_binary64`

Counts

3 → 85

Calls

3 calls:

9.0ms	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
7.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary64`
568×	`unswap-sqr_binary64`
398×	`*-commutative_binary64`
354×	`cancel-sign-sub-inv_binary64`
289×	`log-prod_binary64`

Counts

137 → 141

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	164	1962
1	368	1687
2	1211	1550
3	2361	1550
4	4311	1548
5	4956	1548

prune186.0ms (3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	166	9	175

Error

0.0b

Counts

175 → 9

Alt Table

Status	Error	Program
	1.0b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2)))) (cbrt.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))))) (cbrt.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))))) (cbrt.f64 (cos.f64 y))))
	41.6b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) x (*.f64 (cos.f64 y) z)) 3))
	31.5b	(fma.f64 x (exp.f64 (log.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 z (cos.f64 y))) (cbrt.f64 (.f64 z (cos.f64 y)))) (cbrt.f64 (*.f64 z (cos.f64 y)))))
✓	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	33.3b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 x (log1p.f64 (expm1.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (exp.f64 (log.f64 (pow.f64 (cos.f64 y) 2))) 1/3)) (cbrt.f64 (cos.f64 y))))
	30.6b	(.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)))))

Compiler

Compiled 3789 to 1891 computations (50.1% saved)

regimes355.0ms (5.7%)

Accuracy

Total 0.1b remaining (48.8%)

Threshold costs 0.1b (48.8%)

Counts

88 → 1

Compiler

Compiled 6084 to 3690 computations (39.3% saved)

simplify2.0ms (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

end0.0ms (0%)

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

sample2.3s (37.6%)

Algorithm

1×

intervals

Results

1.1s	1980×	body	1024	valid
417.0ms	4461×	body	128	valid
260.0ms	1037×	body	512	valid
93.0ms	513×	body	256	valid
10.0ms	9×	body	2048	valid

Compiler

Compiled 206 to 125 computations (39.3% saved)

Details

analyze441.0ms (7.1%)

sample218.0ms (3.5%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series28.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify109.0ms (1.8%)

prune56.0ms (0.9%)

localize11.0ms (0.2%)

series27.0ms (0.4%)

rewrite2.0ms (0%)

simplify84.0ms (1.4%)

prune83.0ms (1.3%)

localize12.0ms (0.2%)

series1.1s (17.6%)

rewrite26.0ms (0.4%)

simplify127.0ms (2.1%)

prune214.0ms (3.5%)

localize13.0ms (0.2%)

series636.0ms (10.3%)

rewrite22.0ms (0.4%)

simplify100.0ms (1.6%)

prune186.0ms (3%)

regimes355.0ms (5.7%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (37.6%)

Profiling