Details

analyze629.0ms (14.5%)

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
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12
76.5%	23.4%	0.1%	13
81.9%	17.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.2s (51%)

Results

908.0ms	1315×	body	1024	valid
886.0ms	5886×	body	128	valid
261.0ms	663×	body	512	valid
113.0ms	391×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	22	12
3	26	12
4	26	12

prune3.0ms (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 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series13.0ms (0.3%)

Counts

2 → 40

Calls

2 calls:

12.0ms	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
2.0ms	(cos.f64 y)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 19

Calls

2 calls:

1.0ms	(cos.f64 y)
0.0ms	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
630×	`associate-l_binary64`
546×	`cancel-sign-sub-inv_binary64`
440×	`unswap-sqr_binary64`
289×	`distribute-rgt-in_binary64`

Counts

59 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	689
1	128	651
2	327	644
3	1051	640
4	4040	640
5	4979	640

prune37.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	5	51

Error

0.0b

Counts

51 → 5

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
▶	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
	0.1b	(fma.f64 z (log.f64 (exp.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
	31.5b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

Compiler

Compiled 774 to 268 computations (65.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series25.0ms (0.6%)

Counts

3 → 52

Calls

3 calls:

17.0ms	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
5.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

rewrite5.0ms (0.1%)

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:

2.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
0.0ms	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))

simplify59.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

429×	`distribute-rgt-in_binary64`
424×	`associate-l_binary64`
368×	`associate-r_binary64`
368×	`fma-neg_binary64`
226×	`exp-prod_binary64`

Counts

110 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1101
1	218	1039
2	639	1012
3	2501	1012
4	5156	1012

prune86.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	117	6	123

Error

0.0b

Counts

123 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
	37.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y))) (fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))) (fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))))
	0.2b	(fma.f64 z (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (cbrt.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
▶	0.1b	(fma.f64 z (log.f64 (exp.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
	31.5b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

Compiler

Compiled 1980 to 897 computations (54.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series18.0ms (0.4%)

Counts

3 → 52

Calls

3 calls:

14.0ms	(fma.f64 z (log.f64 (exp.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
2.0ms	(exp.f64 (cos.f64 y))
2.0ms	(log.f64 (exp.f64 (cos.f64 y)))

rewrite4.0ms (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)))
1.0ms	(exp.f64 (cos.f64 y))
0.0ms	(fma.f64 z (log.f64 (exp.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

611×	`distribute-rgt-neg-in_binary64`
490×	`fma-neg_binary64`
389×	`sub-neg_binary64`
381×	`*-commutative_binary64`
292×	`distribute-rgt-in_binary64`

Counts

92 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	968
1	195	911
2	498	896
3	1619	889
4	3976	889
5	4972	889

prune84.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	108	6	114

Error

0.0b

Counts

114 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
	37.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y))) (fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))) (fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))))
▶	0.2b	(fma.f64 z (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (cbrt.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (log.f64 (exp.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
	31.5b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

Compiler

Compiled 1733 to 619 computations (64.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (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))
✓	0.4b	(cbrt.f64 (cos.f64 y))

series399.0ms (9.2%)

Counts

4 → 40

Calls

4 calls:

218.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
176.0ms	(cbrt.f64 (cos.f64 y))
3.0ms	(pow.f64 (cos.f64 y) 2)
2.0ms	(*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (cbrt.f64 (cos.f64 y)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`cbrt-prod_binary64`
30×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
11×	`associate-l_binary64`

Counts

4 → 94

Calls

4 calls:

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

simplify119.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

996×	`fma-neg_binary64`
279×	`associate-+l+_binary64`
276×	`log-prod_binary64`
275×	`exp-prod_binary64`
225×	`*-commutative_binary64`

Counts

134 → 156

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1473
1	291	1436
2	858	1391
3	1998	1027
4	3708	999
5	4642	999
6	4900	999
7	4923	999

prune166.0ms (3.8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	155	7	162

Error

0.0b

Counts

162 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
	37.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y))) (fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))) (fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))))
✓	0.2b	(fma.f64 z (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (cbrt.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	0.2b	(fma.f64 z (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (log.f64 (exp.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
	31.5b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

Compiler

Compiled 3273 to 1401 computations (57.2% saved)

regimes174.0ms (4%)

Accuracy

Total 0.0b remaining (52.6%)

Threshold costs 0.0b (52.6%)

Counts

39 → 1

Compiler

Compiled 2432 to 1522 computations (37.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

end112.0ms (2.6%)

Compiler: Compiled 165 to 100 computations (39.4% saved)

Details

analyze629.0ms (14.5%)

sample2.2s (51%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series13.0ms (0.3%)

rewrite2.0ms (0%)

simplify58.0ms (1.3%)

prune37.0ms (0.9%)

localize9.0ms (0.2%)

series25.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify59.0ms (1.4%)

prune86.0ms (2%)

localize10.0ms (0.2%)

series18.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify68.0ms (1.6%)

prune84.0ms (1.9%)

localize11.0ms (0.3%)

series399.0ms (9.2%)

rewrite13.0ms (0.3%)

simplify119.0ms (2.8%)

prune166.0ms (3.8%)

regimes174.0ms (4%)

simplify2.0ms (0%)

end112.0ms (2.6%)

Profiling