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)

sample4.6s (62.4%)

Results

2.4s	2040×	body	1024	valid
1.1s	4603×	body	128	valid
722.0ms	1097×	body	512	valid
251.0ms	512×	body	256	valid
9.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify43.0ms (0.6%)

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

prune6.0ms (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)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series56.0ms (0.8%)

Counts

3 → 64

Calls

3 calls:

36.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
16.0ms	(*.f64 z (sin.f64 y))
3.0ms	(cos.f64 y)

rewrite11.0ms (0.2%)

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

simplify190.0ms (2.6%)

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

prune120.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Error

0.0b

Counts

83 → 8

Alt Table

Status	Error	Program
	0.3b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	1.3b	(.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)))))
	37.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	31.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	29.4b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.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))))
	27.6b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
▶	0.2b	(fma.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 1401 to 508 computations (63.7% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 z (sin.f64 y)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.4b	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
✓	0.4b	(pow.f64 (cos.f64 y) 3)

series46.0ms (0.6%)

Counts

3 → 52

Calls

3 calls:

30.0ms	(fma.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 z (sin.f64 y)))
12.0ms	(pow.f64 (cos.f64 y) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

3 → 58

Calls

3 calls:

4.0ms	(pow.f64 (cos.f64 y) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
1.0ms	(fma.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 z (sin.f64 y)))

simplify138.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

769×	`cancel-sign-sub-inv_binary64`
455×	`fma-neg_binary64`
447×	`associate-l_binary64`
398×	`associate-r_binary64`
328×	`log-prod_binary64`

Counts

110 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	1100
1	214	1040
2	632	1014
3	2403	1012
4	4824	1012
5	5016	1012

prune230.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	133	9	142

Error

0.0b

Counts

142 → 9

Alt Table

Status	Error	Program
	15.6b	(fma.f64 x (cbrt.f64 (exp.f64 (.f64 (log.f64 (cos.f64 y)) 3))) (.f64 z (sin.f64 y)))
	27.6b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
▶	0.3b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	1.3b	(.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)))))
	37.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	31.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	29.4b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.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))))
✓	0.2b	(fma.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 2421 to 1095 computations (54.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
✓	0.1b	(exp.f64 (cos.f64 y))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.4b	(log.f64 (exp.f64 (cos.f64 y)))

series24.0ms (0.3%)

Counts

3 → 52

Calls

3 calls:

19.0ms	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
3.0ms	(exp.f64 (cos.f64 y))
2.0ms	(log.f64 (exp.f64 (cos.f64 y)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`exp-prod_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`

Counts

3 → 40

Calls

3 calls:

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

simplify152.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

723×	`distribute-rgt-neg-in_binary64`
508×	`fma-neg_binary64`
420×	`*-commutative_binary64`
342×	`sub-neg_binary64`
319×	`neg-mul-1_binary64`

Counts

92 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	967
1	191	912
2	491	898
3	1533	889
4	3489	889
5	4707	889
6	5019	889

prune204.0ms (2.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	123	10	133

Error

0.0b

Counts

133 → 10

Alt Table

Status	Error	Program
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
▶	0.4b	(fma.f64 x (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3))) (*.f64 z (sin.f64 y)))
	15.6b	(fma.f64 x (cbrt.f64 (exp.f64 (.f64 (log.f64 (cos.f64 y)) 3))) (.f64 z (sin.f64 y)))
	27.6b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.3b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	1.3b	(.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)))))
	37.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	31.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	29.4b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
✓	0.2b	(fma.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 2186 to 747 computations (65.8% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.3b	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3))
✓	0.4b	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3)))
✓	0.9b	(pow.f64 (exp.f64 (cos.f64 y)) 3)

series27.0ms (0.4%)

Counts

3 → 28

Calls

3 calls:

17.0ms	(pow.f64 (exp.f64 (cos.f64 y)) 3)
6.0ms	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3))
3.0ms	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
15×	`log-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

13.0ms	(pow.f64 (exp.f64 (cos.f64 y)) 3)
4.0ms	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3)))
3.0ms	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3))

simplify175.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-neg_binary64`
545×	`associate-l_binary64`
485×	`associate-r_binary64`
379×	`log-prod_binary64`
219×	`exp-prod_binary64`

Counts

106 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1183
1	249	1087
2	718	1005
3	2935	1001
4	4667	1001
5	4933	1001

prune289.0ms (3.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	157	9	166

Error

0.0b

Counts

166 → 9

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.4b	(fma.f64 x (log1p.f64 (expm1.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3))))) (*.f64 z (sin.f64 y)))
	1.3b	(.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)))))
	0.4b	(fma.f64 x (expm1.f64 (log1p.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3))))) (*.f64 z (sin.f64 y)))
	31.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	29.4b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.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))))
	27.6b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.2b	(fma.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 3080 to 1468 computations (52.3% saved)

regimes706.0ms (9.6%)

Accuracy

Total 0.1b remaining (53%)

Threshold costs 0.1b (53%)

Counts

84 → 1

Compiler

Compiled 5836 to 3674 computations (37% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`exp-1-e_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	17	18
2	16	18

end238.0ms (3.2%)

Compiler: Compiled 190 to 114 computations (40% saved)

Details

analyze4.0ms (0%)

sample4.6s (62.4%)

simplify43.0ms (0.6%)

prune6.0ms (0.1%)

localize15.0ms (0.2%)

series56.0ms (0.8%)

rewrite11.0ms (0.2%)

simplify190.0ms (2.6%)

prune120.0ms (1.6%)

localize19.0ms (0.3%)

series46.0ms (0.6%)

rewrite11.0ms (0.2%)

simplify138.0ms (1.9%)

prune230.0ms (3.1%)

localize10.0ms (0.1%)

series24.0ms (0.3%)

rewrite6.0ms (0.1%)

simplify152.0ms (2.1%)

prune204.0ms (2.8%)

localize23.0ms (0.3%)

series27.0ms (0.4%)

rewrite26.0ms (0.3%)

simplify175.0ms (2.4%)

prune289.0ms (3.9%)

regimes706.0ms (9.6%)

simplify4.0ms (0.1%)

end238.0ms (3.2%)

Profiling