Details

analyze349.0ms (6%)

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)

sample79.0ms (1.4%)

Algorithm

1×

intervals

Results

31.0ms	66×	body	1024	valid
13.0ms	143×	body	128	valid
8.0ms	30×	body	512	valid
3.0ms	17×	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)
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
✓	0.1b	(*.f64 z (cos.f64 y))

series26.0ms (0.4%)

Counts

3 → 64

Calls

3 calls:

17.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
7.0ms	(*.f64 z (cos.f64 y))
2.0ms	(sin.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 (cos.f64 y))
1.0ms	(sin.f64 y)
0.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

simplify108.0ms (1.9%)

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

prune68.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	9	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	9	82

Error

0.0b

Counts

82 → 9

Alt Table

Status	Error	Program
	15.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (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))))
	34.5b	(fma.f64 x (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	0.6b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	5.3b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y))) (*.f64 z (cos.f64 y)))
	25.1b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	10.1b	(fma.f64 x (log.f64 (exp.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	31.4b	(.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)))))
	34.6b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))

Compiler

Compiled 1401 to 526 computations (62.5% saved)

localize11.0ms (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)))
✓	0.2b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(cbrt.f64 (cos.f64 y))

series929.0ms (16%)

Counts

4 → 72

Calls

4 calls:

544.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
215.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
162.0ms	(cbrt.f64 (cos.f64 y))
7.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite25.0ms (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:

9.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
5.0ms	(.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))

simplify123.0ms (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

prune258.0ms (4.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	216	4	220
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	218	11	229

Error

0.0b

Counts

229 → 11

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))))
	10.1b	(fma.f64 x (log.f64 (exp.f64 (sin.f64 y))) (*.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))))
	34.5b	(fma.f64 x (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	0.6b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	5.3b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y))) (*.f64 z (cos.f64 y)))
	25.1b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	15.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 1/6) 5)) (sqrt.f64 (cbrt.f64 (cos.f64 y)))))
	15.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 y))) (cbrt.f64 (sqrt.f64 (cos.f64 y))))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))))
	34.6b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))

Compiler

Compiled 5223 to 1611 computations (69.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(pow.f64 (cos.f64 y) 2)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
	0.3b	(cbrt.f64 (cos.f64 y))

series231.0ms (4%)

Counts

3 → 40

Calls

3 calls:

221.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
7.0ms	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
3.0ms	(pow.f64 (cos.f64 y) 2)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`

Counts

3 → 61

Calls

3 calls:

7.0ms	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
2.0ms	(pow.f64 (cos.f64 y) 2)
1.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

simplify101.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

667×	`unswap-sqr_binary64`
626×	`fma-def_binary64`
343×	`fma-neg_binary64`
324×	`exp-prod_binary64`
322×	`log-prod_binary64`

Counts

101 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1345
1	282	1135
2	923	1093
3	1865	1081
4	4189	1081
5	4716	1081
6	4899	1081

prune175.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	126	11	137

Error

0.0b

Counts

137 → 11

Alt Table

Status	Error	Program
	25.1b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	10.1b	(fma.f64 x (log.f64 (exp.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2))))) (cbrt.f64 (cos.f64 y))))
	34.6b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
✓	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))))
	15.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 y))) (cbrt.f64 (sqrt.f64 (cos.f64 y))))))
	34.5b	(fma.f64 x (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	0.6b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	5.3b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y))) (*.f64 z (cos.f64 y)))
	15.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 1/6) 5)) (sqrt.f64 (cbrt.f64 (cos.f64 y)))))
▶	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (exp.f64 (log.f64 (pow.f64 (cos.f64 y) 2))))) (cbrt.f64 (cos.f64 y))))

Compiler

Compiled 2961 to 1481 computations (50% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (cos.f64 y) 2)
✓	0.3b	(cbrt.f64 (exp.f64 (log.f64 (pow.f64 (cos.f64 y) 2))))
	0.3b	(cbrt.f64 (cos.f64 y))
✓	2.4b	(log.f64 (pow.f64 (cos.f64 y) 2))

series435.0ms (7.5%)

Counts

2 → 16

Calls

2 calls:

223.0ms	(cbrt.f64 (exp.f64 (log.f64 (pow.f64 (cos.f64 y) 2))))
212.0ms	(log.f64 (pow.f64 (cos.f64 y) 2))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`log-prod_binary64`
11×	`cbrt-prod_binary64`
8×	`exp-sum_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`

Counts

2 → 42

Calls

2 calls:

3.0ms	(cbrt.f64 (exp.f64 (log.f64 (pow.f64 (cos.f64 y) 2))))
2.0ms	(log.f64 (pow.f64 (cos.f64 y) 2))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

674×	`log-prod_binary64`
567×	`cancel-sign-sub-inv_binary64`
539×	`fma-neg_binary64`
323×	`distribute-rgt-in_binary64`
298×	`unswap-sqr_binary64`

Counts

58 → 73

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	728
1	179	622
2	463	614
3	1509	611
4	4125	565
5	4801	565
6	5124	565

prune188.0ms (3.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	127	11	138

Error

0.0b

Counts

138 → 11

Alt Table

Status	Error	Program
	14.7b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (exp.f64 (neg.f64 (*.f64 y y))))) (cbrt.f64 (cos.f64 y))))
	25.1b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	10.1b	(fma.f64 x (log.f64 (exp.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2))))) (cbrt.f64 (cos.f64 y))))
	34.6b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
✓	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))))
	15.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 y))) (cbrt.f64 (sqrt.f64 (cos.f64 y))))))
	34.5b	(fma.f64 x (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	0.6b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	5.3b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y))) (*.f64 z (cos.f64 y)))
✓	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (exp.f64 (log.f64 (pow.f64 (cos.f64 y) 2))))) (cbrt.f64 (cos.f64 y))))

Compiler

Compiled 3039 to 1635 computations (46.2% saved)

regimes431.0ms (7.4%)

Accuracy

Total 0.1b remaining (51.9%)

Threshold costs 0.1b (51.9%)

Counts

95 → 1

Compiler

Compiled 6960 to 4246 computations (39% saved)

simplify2.0ms (0%)

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)

sample2.1s (36.5%)

Algorithm

1×

intervals

Results

991.0ms	2064×	body	1024	valid
373.0ms	4445×	body	128	valid
239.0ms	991×	body	512	valid
88.0ms	500×	body	256	valid

Compiler

Compiled 227 to 144 computations (36.6% saved)

Details

analyze349.0ms (6%)

sample79.0ms (1.4%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series26.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify108.0ms (1.9%)

prune68.0ms (1.2%)

localize11.0ms (0.2%)

series929.0ms (16%)

rewrite25.0ms (0.4%)

simplify123.0ms (2.1%)

prune258.0ms (4.4%)

localize16.0ms (0.3%)

series231.0ms (4%)

rewrite12.0ms (0.2%)

simplify101.0ms (1.7%)

prune175.0ms (3%)

localize14.0ms (0.2%)

series435.0ms (7.5%)

rewrite11.0ms (0.2%)

simplify76.0ms (1.3%)

prune188.0ms (3.2%)

regimes431.0ms (7.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.1s (36.5%)

Profiling