Details

analyze2.1s (26%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.9s (35.6%)

Results

1.5s	2015×	body	1024	valid
745.0ms	4631×	body	128	valid
436.0ms	1067×	body	512	valid
161.0ms	538×	body	256	valid
6.0ms	5×	body	2048	valid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify7.0ms (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

prune4.0ms (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 2 expressions with local error:

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

series23.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
7.0ms	(*.f64 z (cos.f64 y))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 z (cos.f64 y))
0.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

simplify109.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

660×	`distribute-rgt-neg-in_binary64`
557×	`distribute-lft-neg-in_binary64`
467×	`fma-neg_binary64`
332×	`*-commutative_binary64`
297×	`neg-mul-1_binary64`

Counts

90 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	960
1	173	908
2	526	895
3	1471	895
4	3145	895
5	4780	895
6	4991	895
7	4926	895

prune46.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	6	65

Error

0.1b

Counts

65 → 6

Alt Table

Status	Error	Program
	34.0b	(.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)))))
	28.2b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) z) 3)))
	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
▶	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	15.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))

Compiler

Compiled 1074 to 363 computations (66.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series32.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

17.0ms	(*.f64 (sin.f64 y) x)
14.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 (sin.f64 y) x)
0.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))

simplify77.0ms (1%)

Algorithm

1×	egg-herbie

Rules

410×	`fma-neg_binary64`
405×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`
293×	`distribute-rgt-in_binary64`
279×	`distribute-lft-in_binary64`

Counts

70 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	852
1	184	793
2	507	781
3	1282	780
4	2630	780
5	4874	780
6	4926	780

prune52.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	65	7	72

Error

0.0b

Counts

72 → 7

Alt Table

Status	Error	Program
	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	29.6b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (.f64 (sin.f64 y) x)) (sqrt.f64 (*.f64 (sin.f64 y) x))))
	28.2b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) z) 3)))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	31.1b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	15.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
▶	0.7b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x)))

Compiler

Compiled 1123 to 391 computations (65.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (sin.f64 y)) x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x))
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
✓	0.7b	(cbrt.f64 (sin.f64 y))

series917.0ms (11.3%)

Counts

4 → 72

Calls

4 calls:

435.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) x)
245.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
227.0ms	(cbrt.f64 (sin.f64 y))
9.0ms	(.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x))
6.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) x)
5.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
1.0ms	(cbrt.f64 (sin.f64 y))

simplify119.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

469×	`fma-neg_binary64`
416×	`*-commutative_binary64`
400×	`cancel-sign-sub-inv_binary64`
279×	`fma-def_binary64`
209×	`associate-+l+_binary64`

Counts

175 → 163

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	174	1900
1	420	1693
2	1301	1631
3	2528	1613
4	4679	1487
5	4848	1487
6	4864	1487

prune185.0ms (2.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	208	3	211
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	208	10	218

Error

0.0b

Counts

218 → 10

Alt Table

Status	Error	Program
	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	29.6b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (.f64 (sin.f64 y) x)) (sqrt.f64 (*.f64 (sin.f64 y) x))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
▶	0.8b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (.f64 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (sin.f64 y)))) x)))
	0.9b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y)))) (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y))))) (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y))))) (*.f64 (cbrt.f64 (sin.f64 y)) x)))
	3.0b	(fma.f64 (cos.f64 y) z (.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (.f64 (cbrt.f64 (sin.f64 y)) x)))
	28.2b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) z) 3)))
	31.1b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	15.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
✓	0.7b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x)))

Compiler

Compiled 5182 to 1512 computations (70.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y))))
	0.5b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
✓	0.6b	(cbrt.f64 (cbrt.f64 (sin.f64 y)))
	0.7b	(cbrt.f64 (sin.f64 y))

series439.0ms (5.4%)

Counts

2 → 24

Calls

2 calls:

261.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y))))
177.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 y)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`

Counts

2 → 72

Calls

2 calls:

8.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y))))
1.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 y)))

simplify139.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-neg_binary64`
581×	`cancel-sign-sub-inv_binary64`
484×	`fma-def_binary64`
379×	`sqr-pow_binary64`
303×	`sub-neg_binary64`

Counts

96 → 106

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	112	1628
1	230	1628
2	551	1504
3	1299	1465
4	2724	1217
5	3979	1217
6	4540	1217
7	4858	1217
8	4842	1217

prune341.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	339	2	341
Fresh	2	6	8
Picked	1	0	1
Done	1	0	1
Total	343	8	351

Error

0.0b

Counts

351 → 8

Alt Table

Status	Error	Program
	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	29.6b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (.f64 (sin.f64 y) x)) (sqrt.f64 (*.f64 (sin.f64 y) x))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	3.5b	(fma.f64 (cos.f64 y) z (.f64 (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (sin.f64 y)))) x)))
	3.0b	(fma.f64 (cos.f64 y) z (.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (.f64 (cbrt.f64 (sin.f64 y)) x)))
	28.2b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) z) 3)))
	15.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	0.8b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) 6)) (cbrt.f64 (cbrt.f64 (sin.f64 y)))) x)))

Compiler

Compiled 11842 to 2781 computations (76.5% saved)

regimes390.0ms (4.8%)

Accuracy

Total 0.1b remaining (53%)

Threshold costs 0.1b (53%)

Counts

97 → 1

Compiler

Compiled 7380 to 4150 computations (43.8% 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

end137.0ms (1.7%)

Compiler: Compiled 197 to 105 computations (46.7% saved)

Details

analyze2.1s (26%)

sample2.9s (35.6%)

simplify7.0ms (0.1%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series23.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify109.0ms (1.3%)

prune46.0ms (0.6%)

localize7.0ms (0.1%)

series32.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify77.0ms (1%)

prune52.0ms (0.6%)

localize11.0ms (0.1%)

series917.0ms (11.3%)

rewrite25.0ms (0.3%)

simplify119.0ms (1.5%)

prune185.0ms (2.3%)

localize16.0ms (0.2%)

series439.0ms (5.4%)

rewrite15.0ms (0.2%)

simplify139.0ms (1.7%)

prune341.0ms (4.2%)

regimes390.0ms (4.8%)

simplify2.0ms (0%)

end137.0ms (1.7%)

Profiling