Details

analyze331.0ms (5.4%)

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)

sample112.0ms (1.8%)

Algorithm

1×

intervals

Results

32.0ms	64×	body	1024	valid
12.0ms	147×	body	128	valid
8.0ms	27×	body	512	valid
3.0ms	18×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% 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)

localize10.0ms (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 x (cos.f64 y))
✓	0.1b	(*.f64 z (sin.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)))
7.0ms	(*.f64 z (sin.f64 y))
7.0ms	(*.f64 x (cos.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:

4.0ms	(*.f64 x (cos.f64 y))
3.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
3.0ms	(*.f64 z (sin.f64 y))

simplify85.0ms (1.4%)

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

prune96.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	12	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	12	111

Error

0.0b

Counts

111 → 12

Alt Table

Status	Error	Program
	17.9b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	27.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.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))))
	33.1b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.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)))
▶	0.4b	(-.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)))
	28.7b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	18.3b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.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)))
	35.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (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))))
	37.3b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 2136 to 724 computations (66.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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))

series1.0s (17%)

Counts

4 → 72

Calls

4 calls:

569.0ms	(.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
235.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
220.0ms	(cbrt.f64 (cos.f64 y))
10.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite26.0ms (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)))
7.0ms	(.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))

simplify121.0ms (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

prune269.0ms (4.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	221	11	232

Error

0.0b

Counts

232 → 11

Alt Table

Status	Error	Program
	17.9b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	27.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))))
▶	0.2b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	28.7b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.3b	(-.f64 (.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (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))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	33.1b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	18.3b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 z (sin.f64 y)))))
	35.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	37.3b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 5413 to 1620 computations (70.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
✓	0.2b	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
✓	0.2b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))

series579.0ms (9.5%)

Counts

3 → 52

Calls

3 calls:

566.0ms	(*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
9.0ms	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
3.0ms	(pow.f64 (cos.f64 y) 2)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`unpow-prod-down_binary64`
18×	`associate-r_binary64`
16×	`prod-exp_binary64`

Counts

3 → 85

Calls

3 calls:

7.0ms	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
6.0ms	(*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify98.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
568×	`unswap-sqr_binary64`
400×	`*-commutative_binary64`
390×	`cancel-sign-sub-inv_binary64`
289×	`log-prod_binary64`

Counts

137 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	1962
1	372	1687
2	1210	1550
3	2374	1550
4	4270	1550
5	4939	1550

prune181.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	165	11	176

Error

0.0b

Counts

176 → 11

Alt Table

Status	Error	Program
	17.9b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	27.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))))
✓	0.2b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	28.7b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
▶	0.3b	(-.f64 (.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (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))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	33.1b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	18.3b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 z (sin.f64 y)))))
	35.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	37.3b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 4182 to 2013 computations (51.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
	0.2b	(pow.f64 (cos.f64 y) 2)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
	0.3b	(cbrt.f64 (cos.f64 y))

series235.0ms (3.9%)

Counts

2 → 36

Calls

2 calls:

227.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
8.0ms	(.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`cbrt-prod_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 41

Calls

2 calls:

6.0ms	(.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
1.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

simplify124.0ms (2%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
495×	`fma-def_binary64`
412×	`unswap-sqr_binary64`
387×	`cancel-sign-sub-inv_binary64`
342×	`log-prod_binary64`

Counts

77 → 71

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	103	1073
1	237	917
2	780	880
3	1509	872
4	3224	715
5	3868	697
6	4385	697
7	4688	697
8	4928	697

prune137.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	126	11	137

Error

0.0b

Counts

137 → 11

Alt Table

Status	Error	Program
	17.9b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	27.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))))
✓	0.2b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	28.7b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	0.3b	(-.f64 (.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (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))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	33.1b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	18.3b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 z (sin.f64 y)))))
	35.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	37.3b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 2807 to 1285 computations (54.2% saved)

regimes307.0ms (5%)

Accuracy

Total 0.1b remaining (65.3%)

Threshold costs 0.1b (65.3%)

Counts

74 → 1

Compiler

Compiled 4992 to 3274 computations (34.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	11	14
1	21	14
2	30	14
3	36	14
4	40	14
5	41	14
6	40	14

end0.0ms (0%)

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

sample2.2s (36.4%)

Algorithm

1×

intervals

Results

1.0s	2002×	body	1024	valid
400.0ms	4514×	body	128	valid
250.0ms	967×	body	512	valid
98.0ms	512×	body	256	valid
5.0ms	5×	body	2048	valid

Compiler

Compiled 241 to 141 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

analyze331.0ms (5.4%)

sample112.0ms (1.8%)

simplify17.0ms (0.3%)

prune2.0ms (0%)

localize10.0ms (0.2%)

series31.0ms (0.5%)

rewrite12.0ms (0.2%)

simplify85.0ms (1.4%)

prune96.0ms (1.6%)

localize12.0ms (0.2%)

series1.0s (17%)

rewrite26.0ms (0.4%)

simplify121.0ms (2%)

prune269.0ms (4.4%)

localize13.0ms (0.2%)

series579.0ms (9.5%)

rewrite18.0ms (0.3%)

simplify98.0ms (1.6%)

prune181.0ms (3%)

localize12.0ms (0.2%)

series235.0ms (3.9%)

rewrite9.0ms (0.1%)

simplify124.0ms (2%)

prune137.0ms (2.3%)

regimes307.0ms (5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (36.4%)

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