Details

analyze460.0ms (7.2%)

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)

sample2.9s (45.1%)

Results

1.5s	2011×	body	1024	valid
759.0ms	4685×	body	128	valid
441.0ms	1043×	body	512	valid
145.0ms	513×	body	256	valid
6.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify20.0ms (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)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 y)
✓	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))

series30.0ms (0.5%)

Counts

4 → 88

Calls

4 calls:

13.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
9.0ms	(*.f64 x (cos.f64 y))
6.0ms	(*.f64 z (sin.f64 y))
2.0ms	(sin.f64 y)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

5.0ms	(-.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))
1.0ms	(sin.f64 y)

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-neg_binary64`
554×	`fma-def_binary64`
310×	`cancel-sign-sub-inv_binary64`
272×	`distribute-rgt-neg-in_binary64`
262×	`*-commutative_binary64`

Counts

153 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1664
1	369	1606
2	1144	1571
3	2501	1571
4	4543	1571
5	4875	1571

prune117.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	10	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Error

0.0b

Counts

128 → 10

Alt Table

Status	Error	Program
	32.0b	(.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)))))
	18.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	6.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
▶	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)))
	10.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (log.f64 (exp.f64 (sin.f64 y)))))
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	27.5b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 y) x) 3)) (.f64 z (sin.f64 y)))
	30.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	30.2b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	41.5b	(/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (+.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))

Compiler

Compiled 2312 to 797 computations (65.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(cbrt.f64 (cos.f64 y))

series408.0ms (6.4%)

Counts

3 → 48

Calls

3 calls:

225.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
174.0ms	(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)))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

9.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (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))

simplify107.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-def_binary64`
610×	`unswap-sqr_binary64`
426×	`fma-neg_binary64`
366×	`*-commutative_binary64`
361×	`log-prod_binary64`

Counts

129 → 133

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	129	1459
1	299	1232
2	1037	1167
3	1977	1123
4	4368	1105
5	4887	1105
6	4986	1105

prune208.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	218	10	228

Error

0.0b

Counts

228 → 10

Alt Table

Status	Error	Program
	18.9b	(-.f64 (.f64 (.f64 x (log.f64 (exp.f64 (pow.f64 (cos.f64 y) 2/3)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	10.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (log.f64 (exp.f64 (sin.f64 y)))))
	32.0b	(.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)))))
	18.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	6.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
✓	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)))
	27.5b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 y) x) 3)) (.f64 z (sin.f64 y)))
	30.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	30.2b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	41.5b	(/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (+.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))

Compiler

Compiled 5374 to 1526 computations (71.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 x (cos.f64 y))
✓	0.1b	(*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3)))
✓	0.4b	(pow.f64 (sin.f64 y) 3)
✓	17.8b	(cbrt.f64 (pow.f64 (sin.f64 y) 3))

series15.0ms (0.2%)

Counts

3 → 40

Calls

3 calls:

7.0ms	(*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3)))
5.0ms	(pow.f64 (sin.f64 y) 3)
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 y) 3))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 84

Calls

3 calls:

6.0ms	(*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3)))
3.0ms	(pow.f64 (sin.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 y) 3))

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

919×	`fma-neg_binary64`
751×	`fma-def_binary64`
318×	`*-commutative_binary64`
306×	`cancel-sign-sub-inv_binary64`
272×	`sub-neg_binary64`

Counts

124 → 127

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	128	1113
1	268	1030
2	907	996
3	1881	990
4	3895	987
5	4953	987
6	4920	987

prune155.0ms (2.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	162	12	174

Error

0.0b

Counts

174 → 12

Alt Table

Status	Error	Program
	18.9b	(-.f64 (.f64 (.f64 x (log.f64 (exp.f64 (pow.f64 (cos.f64 y) 2/3)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	10.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (log.f64 (exp.f64 (sin.f64 y)))))
	28.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 3) 1/3)))
	27.5b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 y) x) 3)) (.f64 z (sin.f64 y)))
	32.0b	(.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)))))
	18.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
✓	6.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
✓	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)))
▶	4.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (cbrt.f64 (.f64 (sin.f64 y) (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	6.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (cbrt.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 3)))))
	30.2b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	41.5b	(/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (+.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))

Compiler

Compiled 3288 to 1617 computations (50.8% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (sin.f64 y) (sin.f64 y))
✓	0.3b	(.f64 (.f64 z (cbrt.f64 (*.f64 (sin.f64 y) (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))
✓	0.6b	(cbrt.f64 (sin.f64 y))
✓	12.2b	(cbrt.f64 (*.f64 (sin.f64 y) (sin.f64 y)))

series461.0ms (7.2%)

Counts

4 → 60

Calls

4 calls:

231.0ms	(cbrt.f64 (*.f64 (sin.f64 y) (sin.f64 y)))
177.0ms	(cbrt.f64 (sin.f64 y))
50.0ms	(.f64 (.f64 z (cbrt.f64 (*.f64 (sin.f64 y) (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))
3.0ms	(*.f64 (sin.f64 y) (sin.f64 y))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
11×	`add-exp-log_binary64`

Counts

4 → 78

Calls

4 calls:

5.0ms	(.f64 (.f64 z (cbrt.f64 (*.f64 (sin.f64 y) (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))
3.0ms	(*.f64 (sin.f64 y) (sin.f64 y))
2.0ms	(cbrt.f64 (*.f64 (sin.f64 y) (sin.f64 y)))
1.0ms	(cbrt.f64 (sin.f64 y))

simplify186.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-neg_binary64`
459×	`*-commutative_binary64`
345×	`cancel-sign-sub-inv_binary64`
279×	`exp-prod_binary64`
277×	`log-prod_binary64`

Counts

138 → 145

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	175	1603
1	425	1401
2	1415	1313
3	2838	1143
4	4415	1127
5	4652	1125
6	4840	1125
7	4878	1125

prune200.0ms (3.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	145	12	157

Error

0.0b

Counts

157 → 12

Alt Table

Status	Error	Program
	18.9b	(-.f64 (.f64 (.f64 x (log.f64 (exp.f64 (pow.f64 (cos.f64 y) 2/3)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	10.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (log.f64 (exp.f64 (sin.f64 y)))))
	28.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 3) 1/3)))
	27.5b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 y) x) 3)) (.f64 z (sin.f64 y)))
	32.0b	(.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)))))
	18.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
✓	6.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
✓	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)))
✓	4.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (cbrt.f64 (.f64 (sin.f64 y) (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	30.2b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	4.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
	41.5b	(/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (+.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))

Compiler

Compiled 3373 to 1149 computations (65.9% saved)

regimes667.0ms (10.4%)

Accuracy

Total 0.1b remaining (62.2%)

Threshold costs 0.1b (62.2%)

Counts

119 → 1

Compiler

Compiled 8552 to 5396 computations (36.9% saved)

simplify2.0ms (0%)

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	11	14
1	20	14
2	29	14
3	35	14
4	39	14
5	40	14
6	39	14

end182.0ms (2.8%)

Compiler: Compiled 268 to 159 computations (40.7% 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

analyze460.0ms (7.2%)

sample2.9s (45.1%)

simplify20.0ms (0.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series30.0ms (0.5%)

rewrite13.0ms (0.2%)

simplify96.0ms (1.5%)

prune117.0ms (1.8%)

localize11.0ms (0.2%)

series408.0ms (6.4%)

rewrite18.0ms (0.3%)

simplify107.0ms (1.7%)

prune208.0ms (3.3%)

localize10.0ms (0.2%)

series15.0ms (0.2%)

rewrite14.0ms (0.2%)

simplify91.0ms (1.4%)

prune155.0ms (2.4%)

localize22.0ms (0.3%)

series461.0ms (7.2%)

rewrite16.0ms (0.2%)

simplify186.0ms (2.9%)

prune200.0ms (3.1%)

regimes667.0ms (10.4%)

simplify2.0ms (0%)

end182.0ms (2.8%)

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