Details

analyze436.0ms (6.8%)

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)

sample3.0s (47.4%)

Results

1.6s	2034×	body	1024	valid
829.0ms	4668×	body	128	valid
423.0ms	1009×	body	512	valid
160.0ms	535×	body	256	valid
15.0ms	10×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify17.0ms (0.3%)

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

prune2.0ms (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)

localize8.0ms (0.1%)

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))

series31.0ms (0.5%)

Counts

3 → 84

Calls

3 calls:

16.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
8.0ms	(*.f64 x (cos.f64 y))
7.0ms	(*.f64 z (sin.f64 y))

rewrite12.0ms (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:

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

simplify93.0ms (1.5%)

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 → 110

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

prune110.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	99	11	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	11	111

Error

0.0b

Counts

111 → 11

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (cos.f64 y) (neg.f64 (*.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)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	30.8b	(.f64 (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	15.1b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.5b	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	31.7b	(-.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)))
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (cbrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	30.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	31.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 2080 to 697 computations (66.5% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series17.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

17.0ms

(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Rules

867×	`fma-neg_binary64`
806×	`cancel-sign-sub-inv_binary64`
392×	`associate-l_binary64`
384×	`fma-def_binary64`
326×	`associate-r_binary64`

Counts

46 → 28

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	656
1	90	627
2	214	627
3	626	623
4	2397	623
5	4589	623
6	5113	623

prune65.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	65	11	76

Error

0.0b

Counts

76 → 11

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (neg.f64 (*.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)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	30.8b	(.f64 (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	15.1b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	0.5b	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	31.7b	(-.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)))
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (cbrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	30.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	31.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1329 to 519 computations (60.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
✓	0.2b	(.f64 (.f64 x (*.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))

series1.1s (17.6%)

Counts

4 → 72

Calls

4 calls:

637.0ms	(.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
243.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
240.0ms	(cbrt.f64 (cos.f64 y))
8.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite27.0ms (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:

8.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
8.0ms	(.f64 x (.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))

simplify126.0ms (2%)

Algorithm

1×	egg-herbie

Rules

630×	`fma-neg_binary64`
609×	`unswap-sqr_binary64`
447×	`*-commutative_binary64`
410×	`cancel-sign-sub-inv_binary64`
351×	`log-prod_binary64`

Counts

174 → 172

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	152	2118
1	356	1762
2	1217	1642
3	2354	1606
4	4417	1588
5	4882	1588
6	4947	1588

prune243.0ms (3.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	221	10	231

Error

0.0b

Counts

231 → 10

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (neg.f64 (*.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)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	30.8b	(.f64 (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	15.1b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (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)))
▶	0.4b	(-.f64 (.f64 (.f64 x (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	15.2b	(-.f64 (.f64 (.f64 x (pow.f64 (cos.f64 y) 2/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	30.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	31.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 5355 to 1582 computations (70.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x (expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y)))
✓	0.2b	(expm1.f64 (log1p.f64 (*.f64 (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))

series251.0ms (3.9%)

Counts

2 → 36

Calls

2 calls:

241.0ms	(expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))
10.0ms	(.f64 (.f64 x (expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64`
5×	`add-cbrt-cube_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 34

Calls

2 calls:

5.0ms	(.f64 (.f64 x (expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y)))
0.0ms	(expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))

simplify102.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

907×	`fma-neg_binary64`
650×	`unswap-sqr_binary64`
467×	`fma-def_binary64`
387×	`cancel-sign-sub-inv_binary64`
274×	`*-commutative_binary64`

Counts

70 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	92	1139
1	221	715
2	681	645
3	1253	637
4	2621	635
5	4101	635
6	4858	635
7	4934	635

prune222.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	206	10	216

Error

0.0b

Counts

216 → 10

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (neg.f64 (*.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)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	0.4b	(-.f64 (.f64 (.f64 x (expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2))))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	30.8b	(.f64 (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	15.1b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (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)))
	15.2b	(-.f64 (.f64 (.f64 x (pow.f64 (cos.f64 y) 2/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	30.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	31.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 5220 to 1658 computations (68.2% saved)

regimes236.0ms (3.7%)

Accuracy

Total 0.1b remaining (60.9%)

Threshold costs 0.1b (60.9%)

Counts

56 → 1

Compiler

Compiled 4008 to 2432 computations (39.3% 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

end137.0ms (2.1%)

Compiler: Compiled 212 to 124 computations (41.5% 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

analyze436.0ms (6.8%)

sample3.0s (47.4%)

simplify17.0ms (0.3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series31.0ms (0.5%)

rewrite12.0ms (0.2%)

simplify93.0ms (1.5%)

prune110.0ms (1.7%)

localize8.0ms (0.1%)

series17.0ms (0.3%)

rewrite1.0ms (0%)

simplify66.0ms (1%)

prune65.0ms (1%)

localize11.0ms (0.2%)

series1.1s (17.6%)

rewrite27.0ms (0.4%)

simplify126.0ms (2%)

prune243.0ms (3.8%)

localize15.0ms (0.2%)

series251.0ms (3.9%)

rewrite7.0ms (0.1%)

simplify102.0ms (1.6%)

prune222.0ms (3.5%)

regimes236.0ms (3.7%)

simplify3.0ms (0%)

end137.0ms (2.1%)

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