Details

analyze469.0ms (8.1%)

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
37.4%	62.4%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
65.5%	34.3%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
81.9%	17.9%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.3s (40.5%)

Results

1.0s	1342×	body	1024	valid
874.0ms	5920×	body	128	valid
293.0ms	663×	body	512	valid
90.0ms	328×	body	256	valid
6.0ms	3×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify20.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

230×	`fma-def_binary64`
171×	`fma-neg_binary64`
66×	`cancel-sign-sub-inv_binary64`
44×	`associate--r+_binary64`
44×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series22.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

16.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
4×	`fma-neg_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
3.0ms	(*.f64 z (sin.f64 y))

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-neg_binary64`
410×	`fma-def_binary64`
366×	`associate-l_binary64`
322×	`associate-r_binary64`
269×	`distribute-rgt-neg-in_binary64`

Counts

104 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1326
1	276	1263
2	879	1219
3	3114	1209
4	4789	1209
5	5015	1209

prune78.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	6	90

Error

0.0b

Counts

90 → 6

Alt Table

Status	Error	Program
	22.4b	(fma.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (+.f64 x (cos.f64 y))) (neg.f64 (*.f64 z (sin.f64 y))))
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	31.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.3b	(-.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))))
▶	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	19.3b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))

Compiler

Compiled 1531 to 462 computations (69.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 z) (sin.f64 y))
✓	0.3b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series255.0ms (4.4%)

Counts

4 → 72

Calls

4 calls:

160.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
37.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
35.0ms	(cbrt.f64 z)
23.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite22.0ms (0.4%)

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:

7.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
3.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify122.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-def_binary64`
720×	`fma-neg_binary64`
501×	`cancel-sign-sub-inv_binary64`
496×	`*-commutative_binary64`
395×	`unswap-sqr_binary64`

Counts

175 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1734
1	311	1507
2	1181	1430
3	2385	1407
4	4566	1395
5	4973	1395
6	4943	1395

prune176.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	196	6	202

Error

0.0b

Counts

202 → 6

Alt Table

Status	Error	Program
	22.4b	(fma.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (+.f64 x (cos.f64 y))) (neg.f64 (*.f64 z (sin.f64 y))))
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	31.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
▶	0.3b	(-.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))))
	28.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (sin.f64 y))))
	19.3b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))

Compiler

Compiled 4254 to 1143 computations (73.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
✓	0.3b	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
✓	0.6b	(cbrt.f64 (sin.f64 y))

series986.0ms (17%)

Counts

4 → 72

Calls

4 calls:

579.0ms	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
221.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
178.0ms	(cbrt.f64 (sin.f64 y))
7.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))

rewrite26.0ms (0.5%)

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:

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

simplify126.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

601×	`unswap-sqr_binary64`
518×	`fma-neg_binary64`
478×	`*-commutative_binary64`
394×	`cancel-sign-sub-inv_binary64`
368×	`log-prod_binary64`

Counts

174 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	173	2226
1	429	1857
2	1367	1728
3	2548	1694
4	4453	1676
5	4953	1676
6	5033	1676

prune228.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	225	2	227
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	227	6	233

Error

Counts

233 → 6

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y))))))
	22.4b	(fma.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (+.f64 x (cos.f64 y))) (neg.f64 (*.f64 z (sin.f64 y))))
	1.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (pow.f64 (*.f64 (sin.f64 y) (sin.f64 y)) 1/3)) (cbrt.f64 (sin.f64 y))))
	31.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	19.3b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))

Compiler

Compiled 5496 to 1683 computations (69.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
✓	0.3b	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y)))))
	0.5b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
	0.6b	(cbrt.f64 (sin.f64 y))

series10.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y)))))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-cbrt-cube_binary64`
6×	`cbrt-unprod_binary64`
6×	`prod-exp_binary64`

Counts

1 → 23

Calls

1 calls:

7.0ms

(*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y)))))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

835×	`fma-def_binary64`
367×	`fma-neg_binary64`
334×	`unswap-sqr_binary64`
301×	`*-commutative_binary64`
300×	`unsub-neg_binary64`

Counts

47 → 40

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	74	881
1	194	421
2	607	411
3	1056	407
4	1918	393
5	3246	393
6	4534	393
7	4961	393

prune201.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	223	5	228

Error

Counts

228 → 5

Alt Table

Status	Error	Program
	22.4b	(fma.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (+.f64 x (cos.f64 y))) (neg.f64 (*.f64 z (sin.f64 y))))
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	31.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	19.3b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	1.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y))))))

Compiler

Compiled 5731 to 1640 computations (71.4% saved)

regimes379.0ms (6.5%)

Accuracy

Total 0.0b remaining (41.2%)

Threshold costs 0.0b (41.2%)

Counts

89 → 1

Compiler

Compiled 6712 to 4286 computations (36.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	16	14
2	26	14
3	32	14
4	36	14
5	37	14
6	37	14

end85.0ms (1.5%)

Compiler: Compiled 117 to 73 computations (37.6% saved)

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14

Details

analyze469.0ms (8.1%)

sample2.3s (40.5%)

simplify20.0ms (0.4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series22.0ms (0.4%)

rewrite9.0ms (0.2%)

simplify84.0ms (1.5%)

prune78.0ms (1.4%)

localize10.0ms (0.2%)

series255.0ms (4.4%)

rewrite22.0ms (0.4%)

simplify122.0ms (2.1%)

prune176.0ms (3%)

localize11.0ms (0.2%)

series986.0ms (17%)

rewrite26.0ms (0.5%)

simplify126.0ms (2.2%)

prune228.0ms (3.9%)

localize17.0ms (0.3%)

series10.0ms (0.2%)

rewrite9.0ms (0.2%)

simplify80.0ms (1.4%)

prune201.0ms (3.5%)

regimes379.0ms (6.5%)

simplify3.0ms (0.1%)

end85.0ms (1.5%)

Profiling

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14