Details

analyze730.0ms (7.5%)

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
37.4%	62.4%	0.1%	6
49.9%	49.9%	0.1%	7
62.4%	37.4%	0.1%	8
62.4%	37.4%	0.1%	9
71.8%	28.1%	0.1%	10
79.6%	20.3%	0.1%	11
79.6%	20.3%	0.1%	12
85%	14.8%	0.1%	13
89.3%	10.5%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample130.0ms (1.3%)

Algorithm

1×

intervals

Results

75.0ms	74×	body	1024	valid
21.0ms	139×	body	128	valid
13.0ms	29×	body	512	valid
4.0ms	14×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
36×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

prune3.0ms (0%)

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize19.0ms (0.2%)

Local error

Found 3 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))
✓	0.1b	(*.f64 x (cos.f64 y))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

6.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
6.0ms	(*.f64 z (sin.f64 y))
6.0ms	(*.f64 x (cos.f64 y))

series179.0ms (1.9%)

Counts

3 → 84

Calls

3 calls:

90.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
46.0ms	(*.f64 x (cos.f64 y))
43.0ms	(*.f64 z (sin.f64 y))

simplify164.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary64`
513×	`fma-def_binary64`
401×	`sub-neg_binary64`
272×	`distribute-rgt-neg-in_binary64`
257×	`*-commutative_binary64`

Counts

140 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	1548
1	342	1505
2	1070	1476
3	2342	1476
4	4338	1476
5	4932	1476

prune175.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	180	13	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	13	194

Error

0.0b

Counts

194 → 13

Alt Table

Status	Error	Program
	33.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.3b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.6b	(-.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))))
	26.4b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (cbrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))) (cbrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))))
▶	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	24.5b	(-.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)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	16.7b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	33.4b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	29.9b	(-.f64 (log1p.f64 (expm1.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	39.3b	(cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z)) 3))

Compiler

Compiled 2180 to 755 computations (65.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
	0.5b	(cbrt.f64 z)
	0.5b	(cbrt.f64 z)
✓	0.5b	(cbrt.f64 z)

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

8.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

series909.0ms (9.4%)

Counts

2 → 24

Calls

2 calls:

460.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
448.0ms	(cbrt.f64 z)

simplify106.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune220.0ms (2.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	272	2	274
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	274	13	287

Error

0.0b

Counts

287 → 13

Alt Table

Status	Error	Program
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	33.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.3b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
▶	0.6b	(-.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))))
	26.4b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	0.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 5) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 z) (sin.f64 y))))
	16.7b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	33.4b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	29.9b	(-.f64 (log1p.f64 (expm1.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	39.3b	(cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z)) 3))

Compiler

Compiled 2649 to 822 computations (69% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

13.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
2.0ms	(cbrt.f64 (sin.f64 y))

series1.0s (10.5%)

Counts

2 → 24

Calls

2 calls:

575.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
446.0ms	(cbrt.f64 (sin.f64 y))

simplify156.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-neg_binary64`
712×	`log-prod_binary64`
510×	`fma-def_binary64`
495×	`unswap-sqr_binary64`
303×	`*-commutative_binary64`

Counts

79 → 147

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	878
1	217	796
2	568	756
3	1360	732
4	3222	612
5	4168	612
6	4671	612
7	4903	612

prune284.0ms (2.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	275	1	276
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	276	13	289

Error

0.0b

Counts

289 → 13

Alt Table

Status	Error	Program
	33.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.3b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	0.6b	(-.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))))
	26.4b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	9.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (log.f64 (exp.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))))) (cbrt.f64 (sin.f64 y))))
▶	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	0.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 5) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 z) (sin.f64 y))))
	16.7b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	33.4b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	29.9b	(-.f64 (log1p.f64 (expm1.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	39.3b	(cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z)) 3))

Compiler

Compiled 3606 to 1244 computations (65.5% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
	8.5b	(cbrt.f64 (*.f64 z (sin.f64 y)))
	8.5b	(cbrt.f64 (*.f64 z (sin.f64 y)))
✓	8.5b	(cbrt.f64 (*.f64 z (sin.f64 y)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`pow1/3_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 44

Calls

2 calls:

9.0ms	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
4.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))

series2.1s (21.5%)

Counts

2 → 48

Calls

2 calls:

1.2s	(cbrt.f64 (*.f64 z (sin.f64 y)))
854.0ms	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))

simplify112.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

915×	`fma-neg_binary64`
530×	`associate-l_binary64`
439×	`associate-r_binary64`
359×	`distribute-rgt-neg-in_binary64`
343×	`distribute-lft-neg-in_binary64`

Counts

92 → 170

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1896
1	311	1643
2	826	1316
3	2819	1050
4	4857	1050
5	5066	1050

prune132.0ms (1.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	353	0	353
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	353	13	366

Error

0.0b

Counts

366 → 13

Alt Table

Status	Error	Program
	33.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.3b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	0.6b	(-.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))))
	26.4b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	9.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (log.f64 (exp.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))))) (cbrt.f64 (sin.f64 y))))
✓	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	0.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 5) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 z) (sin.f64 y))))
	16.7b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	33.4b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	29.9b	(-.f64 (log1p.f64 (expm1.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	39.3b	(cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z)) 3))

Compiler

Compiled 4224 to 1257 computations (70.2% saved)

regimes337.0ms (3.5%)

Accuracy

Total 0.1b remaining (61.4%)

Threshold costs 0.1b (61.4%)

Compiler

Compiled 5882 to 3592 computations (38.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`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	18	14
2	26	14
3	31	14
4	33	14
5	33	14

end1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample2.8s (28.4%)

Algorithm

1×

intervals

Results

1.2s	1949×	body	1024	valid
534.0ms	4550×	body	128	valid
377.0ms	1003×	body	512	valid
121.0ms	497×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 279 to 165 computations (40.9% saved)

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

Details

analyze730.0ms (7.5%)

sample130.0ms (1.3%)

simplify37.0ms (0.4%)

prune3.0ms (0%)

localize19.0ms (0.2%)

rewrite21.0ms (0.2%)

series179.0ms (1.9%)

simplify164.0ms (1.7%)

prune175.0ms (1.8%)

localize22.0ms (0.2%)

rewrite14.0ms (0.1%)

series909.0ms (9.4%)

simplify106.0ms (1.1%)

prune220.0ms (2.3%)

localize21.0ms (0.2%)

rewrite20.0ms (0.2%)

series1.0s (10.5%)

simplify156.0ms (1.6%)

prune284.0ms (2.9%)

localize26.0ms (0.3%)

rewrite17.0ms (0.2%)

series2.1s (21.5%)

simplify112.0ms (1.2%)

prune132.0ms (1.4%)

regimes337.0ms (3.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.8s (28.4%)

Profiling

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14