Details

analyze336.0ms (6.7%)

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
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)

sample86.0ms (1.7%)

Algorithm

1×

intervals

Results

40.0ms	76×	body	1024	valid
11.0ms	132×	body	128	valid
7.0ms	31×	body	512	valid
3.0ms	16×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify6.0ms (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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 66 to 39 computations (40.9% saved)

localize7.0ms (0.1%)

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 x (cos.f64 y))
✓	0.1b	(*.f64 z (sin.f64 y))

series31.0ms (0.6%)

Counts

3 → 84

Calls

3 calls:

13.0ms	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
11.0ms	(*.f64 z (sin.f64 y))
7.0ms	(*.f64 x (cos.f64 y))

rewrite12.0ms (0.2%)

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:

4.0ms	(*.f64 x (cos.f64 y))
3.0ms	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
3.0ms	(*.f64 z (sin.f64 y))

simplify114.0ms (2.3%)

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 → 105

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

prune88.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	11	105
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	12	107

Error

0.0b

Counts

107 → 12

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (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)))) (cbrt.f64 (sin.f64 y))))
	40.3b	(/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (-.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
	32.0b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	27.7b	(+.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)))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (cbrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	29.0b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.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)))))
	18.2b	(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 y) z) 3)))
	15.9b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.4b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	29.9b	(/.f64 (.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)) (-.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))) (-.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z)))

Compiler

Compiled 2129 to 723 computations (66% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series14.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

14.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

517×	`distribute-rgt-neg-in_binary64`
435×	`distribute-lft-neg-in_binary64`
388×	`associate-l_binary64`
356×	`distribute-rgt-in_binary64`
340×	`fma-def_binary64`

Counts

46 → 29

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	572
1	76	547
2	205	545
3	603	542
4	2172	542
5	5100	542

prune70.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	67	11	78

Error

0.0b

Counts

78 → 11

Alt Table

Status	Error	Program
	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	27.7b	(+.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)))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 y) z)) (cbrt.f64 (.f64 (sin.f64 y) z))) (cbrt.f64 (*.f64 (sin.f64 y) z))))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (cbrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	32.0b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sin.f64 y) (sqrt.f64 z))))
	29.9b	(/.f64 (.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)) (-.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))) (-.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z)))
	18.2b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	40.3b	(/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (-.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
	29.0b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 (.f64 (sin.f64 y) z)) (sqrt.f64 (*.f64 (sin.f64 y) z))))
	15.9b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	0.4b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))

Compiler

Compiled 1369 to 505 computations (63.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(.f64 (.f64 x (*.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))

series511.0ms (10.3%)

Counts

3 → 48

Calls

3 calls:

262.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
241.0ms	(cbrt.f64 (cos.f64 y))
8.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

40.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (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))

simplify98.0ms (2%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-def_binary64`
610×	`unswap-sqr_binary64`
426×	`fma-neg_binary64`
366×	`*-commutative_binary64`
361×	`log-prod_binary64`

Counts

129 → 133

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	129	1459
1	299	1232
2	1037	1167
3	1977	1123
4	4368	1105
5	4887	1105
6	4986	1105

prune246.0ms (4.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	218	11	229

Error

0.0b

Counts

229 → 11

Alt Table

Status	Error	Program
	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
▶	0.2b	(+.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 y) z)) (cbrt.f64 (.f64 (sin.f64 y) z))) (cbrt.f64 (*.f64 (sin.f64 y) z))))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (cbrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.3b	(+.f64 (.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	29.0b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 (.f64 (sin.f64 y) z)) (sqrt.f64 (*.f64 (sin.f64 y) z))))
	0.4b	(+.f64 (.f64 (.f64 x (cbrt.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	16.0b	(+.f64 (.f64 (.f64 x (log.f64 (exp.f64 (pow.f64 (cos.f64 y) 2/3)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	15.9b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	32.0b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sin.f64 y) (sqrt.f64 z))))
	18.2b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))

Compiler

Compiled 5447 to 1557 computations (71.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(.f64 (.f64 x (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))

series11.0ms (0.2%)

Counts

2 → 28

Calls

2 calls:

7.0ms	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
4.0ms	(pow.f64 (cos.f64 y) 2)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
11×	`prod-exp_binary64`
6×	`associate-r_binary64`
6×	`add-cbrt-cube_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 47

Calls

2 calls:

7.0ms	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify104.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-neg_binary64`
576×	`unswap-sqr_binary64`
435×	`sqr-pow_binary64`
433×	`fma-def_binary64`
336×	`*-commutative_binary64`

Counts

75 → 76

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	110	1034
1	253	880
2	787	833
3	1566	815
4	3415	635
5	3980	617
6	4678	617
7	4942	617
8	4901	617

prune168.0ms (3.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	137	11	148

Error

0.0b

Counts

148 → 11

Alt Table

Status	Error	Program
	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
✓	0.2b	(+.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 y) z)) (cbrt.f64 (.f64 (sin.f64 y) z))) (cbrt.f64 (*.f64 (sin.f64 y) z))))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (cbrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.3b	(+.f64 (.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	29.0b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 (.f64 (sin.f64 y) z)) (sqrt.f64 (*.f64 (sin.f64 y) z))))
	0.4b	(+.f64 (.f64 (.f64 x (cbrt.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	16.0b	(+.f64 (.f64 (.f64 x (log.f64 (exp.f64 (pow.f64 (cos.f64 y) 2/3)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	15.9b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	32.0b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sin.f64 y) (sqrt.f64 z))))
	18.2b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))

Compiler

Compiled 3195 to 1504 computations (52.9% saved)

regimes458.0ms (9.2%)

Accuracy

Total 0.1b remaining (58.7%)

Threshold costs 0.1b (58.7%)

Counts

101 → 1

Compiler

Compiled 6956 to 4238 computations (39.1% saved)

simplify2.0ms (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)

sample2.4s (48.8%)

Algorithm

1×

intervals

Results

1.2s	2051×	body	1024	valid
397.0ms	4381×	body	128	valid
263.0ms	1016×	body	512	valid
97.0ms	546×	body	256	valid
8.0ms	6×	body	2048	valid

Compiler

Compiled 258 to 144 computations (44.2% saved)

Details

analyze336.0ms (6.7%)

sample86.0ms (1.7%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series31.0ms (0.6%)

rewrite12.0ms (0.2%)

simplify114.0ms (2.3%)

prune88.0ms (1.8%)

localize8.0ms (0.2%)

series14.0ms (0.3%)

rewrite1.0ms (0%)

simplify84.0ms (1.7%)

prune70.0ms (1.4%)

localize11.0ms (0.2%)

series511.0ms (10.3%)

rewrite50.0ms (1%)

simplify98.0ms (2%)

prune246.0ms (4.9%)

localize13.0ms (0.3%)

series11.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify104.0ms (2.1%)

prune168.0ms (3.4%)

regimes458.0ms (9.2%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (48.8%)

Profiling