Details

analyze706.0ms (9.9%)

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)

sample127.0ms (1.8%)

Algorithm

1×

intervals

Results

72.0ms	78×	body	1024	valid
19.0ms	135×	body	128	valid
13.0ms	29×	body	512	valid
4.0ms	14×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify19.0ms (0.3%)

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

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 44 to 25 computations (43.2% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

7.0ms	(*.f64 x (cos.f64 y))
6.0ms	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
6.0ms	(*.f64 z (sin.f64 y))

series282.0ms (4%)

Counts

3 → 84

Calls

3 calls:

150.0ms	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
76.0ms	(*.f64 x (cos.f64 y))
56.0ms	(*.f64 z (sin.f64 y))

simplify293.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-neg_binary64`
552×	`fma-def_binary64`
410×	`sub-neg_binary64`
279×	`*-commutative_binary64`
268×	`distribute-rgt-neg-in_binary64`

Counts

138 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1414
1	340	1380
2	1080	1357
3	2388	1357
4	4538	1357
5	4653	1357
6	4935	1357
7	4908	1357

prune90.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	198	13	211
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	199	13	212

Error

0.0b

Counts

212 → 13

Alt Table

Status	Error	Program
	22.2b	(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	36.1b	(+.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	16.0b	(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 y) z) 3)))
	28.4b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	17.4b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	32.6b	(fma.f64 y z (fma.f64 (.f64 x (.f64 y y)) -1/2 x))
	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
▶	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	33.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	34.0b	(+.f64 (log1p.f64 (expm1.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	32.3b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 2073 to 735 computations (64.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
	0.6b	(cbrt.f64 z)
	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 z)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

series469.0ms (6.6%)

Counts

2 → 24

Calls

2 calls:

241.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
228.0ms	(cbrt.f64 z)

simplify94.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune114.0ms (1.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	272	2	274
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	274	13	287

Error

0.0b

Counts

287 → 13

Alt Table

Status	Error	Program
▶	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	0.9b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 5) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 z) (sin.f64 y))))
	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	36.1b	(+.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	17.4b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	32.6b	(fma.f64 y z (fma.f64 (.f64 x (.f64 y y)) -1/2 x))
	0.8b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	33.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	28.4b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	34.0b	(+.f64 (log1p.f64 (expm1.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	32.3b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 2647 to 816 computations (69.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
	0.6b	(cbrt.f64 (sin.f64 y))
	0.6b	(cbrt.f64 (sin.f64 y))
✓	0.6b	(cbrt.f64 (sin.f64 y))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

6.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
1.0ms	(cbrt.f64 (sin.f64 y))

series447.0ms (6.3%)

Counts

2 → 24

Calls

2 calls:

230.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
216.0ms	(cbrt.f64 (sin.f64 y))

simplify106.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-neg_binary64`
712×	`log-prod_binary64`
510×	`fma-def_binary64`
495×	`unswap-sqr_binary64`
303×	`*-commutative_binary64`

Counts

79 → 147

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	878
1	217	796
2	568	756
3	1360	732
4	3222	612
5	4168	612
6	4671	612
7	4903	612

prune164.0ms (2.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	274	2	276
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	275	14	289

Error

0.0b

Counts

289 → 14

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	0.9b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 5) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 z) (sin.f64 y))))
▶	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	36.1b	(+.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	17.4b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	32.6b	(fma.f64 y z (fma.f64 (.f64 x (.f64 y y)) -1/2 x))
	8.3b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (log.f64 (exp.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))))) (cbrt.f64 (sin.f64 y))))
✓	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	33.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	28.4b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.7b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (sin.f64 y))))))
	34.0b	(+.f64 (log1p.f64 (expm1.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	32.3b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 3668 to 1266 computations (65.5% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
	8.5b	(cbrt.f64 (*.f64 z (sin.f64 y)))
	8.5b	(cbrt.f64 (*.f64 z (sin.f64 y)))
✓	8.5b	(cbrt.f64 (*.f64 z (sin.f64 y)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`pow1/3_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 44

Calls

2 calls:

4.0ms	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
2.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))

series1.3s (18.3%)

Counts

2 → 48

Calls

2 calls:

720.0ms	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
581.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))

simplify105.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

915×	`fma-neg_binary64`
530×	`associate-l_binary64`
439×	`associate-r_binary64`
359×	`distribute-rgt-neg-in_binary64`
343×	`distribute-lft-neg-in_binary64`

Counts

92 → 170

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1896
1	311	1643
2	826	1316
3	2819	1050
4	4857	1050
5	5066	1050

prune183.0ms (2.6%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	353	0	353
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	353	14	367

Error

0.0b

Counts

367 → 14

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	0.9b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 5) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	36.1b	(+.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	17.4b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	32.6b	(fma.f64 y z (fma.f64 (.f64 x (.f64 y y)) -1/2 x))
	8.3b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (log.f64 (exp.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))))) (cbrt.f64 (sin.f64 y))))
✓	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	33.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	28.4b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.7b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (sin.f64 y))))))
	34.0b	(+.f64 (log1p.f64 (expm1.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	32.3b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 4255 to 1268 computations (70.2% saved)

regimes300.0ms (4.2%)

Accuracy

Total 0.1b remaining (61.1%)

Threshold costs 0.1b (61.1%)

Compiler

Compiled 4990 to 3152 computations (36.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	17	14
2	16	14

end0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample2.2s (30.9%)

Algorithm

1×

intervals

Results

998.0ms	1989×	body	1024	valid
407.0ms	4499×	body	128	valid
257.0ms	1009×	body	512	valid
92.0ms	502×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 310 to 176 computations (43.2% saved)

Details

analyze706.0ms (9.9%)

sample127.0ms (1.8%)

simplify19.0ms (0.3%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

rewrite23.0ms (0.3%)

series282.0ms (4%)

simplify293.0ms (4.1%)

prune90.0ms (1.3%)

localize13.0ms (0.2%)

rewrite7.0ms (0.1%)

series469.0ms (6.6%)

simplify94.0ms (1.3%)

prune114.0ms (1.6%)

localize12.0ms (0.2%)

rewrite9.0ms (0.1%)

series447.0ms (6.3%)

simplify106.0ms (1.5%)

prune164.0ms (2.3%)

localize22.0ms (0.3%)

rewrite8.0ms (0.1%)

series1.3s (18.3%)

simplify105.0ms (1.5%)

prune183.0ms (2.6%)

regimes300.0ms (4.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (30.9%)

Profiling