Details

analyze442.0ms (9.6%)

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 (50.2%)

Results

1.0s	1425×	body	1024	valid
918.0ms	5791×	body	128	valid
278.0ms	689×	body	512	valid
102.0ms	348×	body	256	valid
5.0ms	3×	body	2048	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess48.0ms (1%)

Algorithm

2×	egg-herbie

Rules

792×	`fma-neg_binary64`
611×	`fma-def_binary64`
200×	`cancel-sign-sub-inv_binary64`
156×	`distribute-rgt-in_binary64`
142×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	56
1	57	56
2	128	56
3	237	56
4	428	56
5	697	56
6	1220	56
7	2086	56
8	2733	56
9	3116	56
10	3148	56
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

228×	`fma-def_binary64`
171×	`fma-neg_binary64`
68×	`cancel-sign-sub-inv_binary64`
44×	`distribute-rgt-in_binary64`
42×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	18	14
2	38	14
3	67	14
4	118	14
5	183	14
6	324	14
7	531	14
8	681	14
9	846	14
10	950	14
11	960	14

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 45 to 26 computations (42.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series46.0ms (1%)

Counts

3 → 84

Calls

21 calls:

24.0ms	(*.f64 z (sin.f64 y))	z	-inf
3.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))	z	-inf
1.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))	x	inf
1.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))	x	-inf
1.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))	x	0

rewrite71.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`log-prod_binary64`
460×	`fma-def_binary64`
217×	`fma-neg_binary64`
194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	202	26
2	2964	26

Stop Event

1×	node limit

Counts

3 → 193

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

498×	`sub-neg_binary64`
497×	`fma-neg_binary64`
267×	`*-commutative_binary64`
204×	`distribute-lft-neg-in_binary64`
202×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	830
1	183	822
2	533	806
3	1888	800
4	4555	800

Stop Event

1×	node limit

Counts

277 → 223

prune166.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	217	6	223
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	218	6	224

Error

0.0b

Counts

224 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (neg.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	1.7b	(fma.f64 (*.f64 (neg.f64 z) (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	43.4b	(fma.f64 (+.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (-.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (fma.f64 (neg.f64 z) (sin.f64 y) (*.f64 z (sin.f64 y))))
	14.1b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	26.1b	(-.f64 (pow.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) 2) (*.f64 z (sin.f64 y)))

Compiler

Compiled 4145 to 1175 computations (71.7% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series14.0ms (0.3%)

Counts

1 → 36

Calls

9 calls:

2.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))	z	inf
2.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))	z	0
2.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))	z	-inf
2.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))	x	0
2.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))	x	inf

rewrite37.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

866×	`expm1-log1p-u_binary64`
571×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
94×	`log1p-expm1-u_binary64`
93×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	190	12
2	2537	12

Stop Event

1×	node limit

Counts

1 → 25

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

976×	`fma-neg_binary64`
765×	`cancel-sign-sub-inv_binary64`
471×	`fma-def_binary64`
203×	`associate-l_binary64`
196×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	457
1	88	457
2	224	455
3	649	445
4	2352	445

Stop Event

1×	node limit

Counts

61 → 40

prune71.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	92	6	98

Error

0.0b

Counts

98 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (neg.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	1.7b	(fma.f64 (*.f64 (neg.f64 z) (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	43.4b	(fma.f64 (+.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (-.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (fma.f64 (neg.f64 z) (sin.f64 y) (*.f64 z (sin.f64 y))))
	14.1b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
▶	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	26.1b	(-.f64 (pow.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) 2) (*.f64 z (sin.f64 y)))

Compiler

Compiled 1478 to 565 computations (61.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)
✓	6.8b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series180.0ms (3.9%)

Counts

3 → 52

Calls

21 calls:

29.0ms	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))	z	-inf
26.0ms	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)	y	-inf
25.0ms	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)	y	inf
23.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))	y	-inf
21.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))	y	inf

rewrite66.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

465×	`fma-def_binary64`
226×	`fma-neg_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
162×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	261	28
2	3411	28

Stop Event

1×	node limit

Counts

3 → 162

simplify34.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

976×	`fma-neg_binary64`
762×	`cancel-sign-sub-inv_binary64`
471×	`fma-def_binary64`
202×	`associate-l_binary64`
196×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	569
1	94	569
2	235	567
3	669	557
4	2391	557

Stop Event

1×	node limit

Counts

214 → 179

prune214.0ms (4.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	201	8	209

Error

Counts

209 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (neg.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	1.7b	(fma.f64 (*.f64 (neg.f64 z) (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	43.4b	(fma.f64 (+.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (-.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (fma.f64 (neg.f64 z) (sin.f64 y) (*.f64 z (sin.f64 y))))
	14.1b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
	9.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 2))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 2)))))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	26.1b	(-.f64 (pow.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) 2) (*.f64 z (sin.f64 y)))
▶	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z)))

Compiler

Compiled 3798 to 1189 computations (68.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2))
✓	0.3b	(.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z))
✓	0.5b	(pow.f64 (cbrt.f64 z) 2)
✓	0.6b	(cbrt.f64 z)

series170.0ms (3.7%)

Counts

4 → 36

Calls

18 calls:

52.0ms	(.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z))	z	-inf
25.0ms	(*.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2))	y	-inf
23.0ms	(*.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2))	y	inf
19.0ms	(pow.f64 (cbrt.f64 z) 2)	z	-inf
15.0ms	(*.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2))	z	-inf

rewrite45.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

705×	`log1p-expm1-u_binary64`
705×	`expm1-log1p-u_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`
85×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	179	26
2	2034	26

Stop Event

1×	node limit

Counts

4 → 71

simplify29.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

717×	`fma-neg_binary64`
443×	`*-commutative_binary64`
321×	`distribute-rgt-neg-in_binary64`
319×	`distribute-lft-neg-in_binary64`
216×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	422
1	129	386
2	445	356
3	2040	356

Stop Event

1×	node limit

Counts

107 → 90

prune141.0ms (3.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	113	8	121

Error

Counts

121 → 8

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 z) 2) (sin.f64 y))) 3) (cbrt.f64 z)))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z)))
✓	0.1b	(fma.f64 z (neg.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	1.7b	(fma.f64 (*.f64 (neg.f64 z) (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	14.1b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
	9.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 2))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 2)))))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	26.1b	(-.f64 (pow.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) 2) (*.f64 z (sin.f64 y)))

Compiler

Compiled 2201 to 968 computations (56% saved)

regimes259.0ms (5.6%)

Accuracy

Total 0.0b remaining (57.7%)

Threshold costs 0.0b (57.7%)

Counts

71 → 1

Compiler

Compiled 4136 to 2710 computations (34.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	14
2	16	14
3	17	14

Stop Event

1×

saturated

end125.0ms (2.7%)

Stop Event

1×

fuel

Compiler

Compiled 170 to 116 computations (31.8% saved)

Iter	Nodes	Cost
0	9	14
1	18	14
2	38	14
3	67	14
4	118	14
5	183	14
6	324	14
7	531	14
8	681	14
9	846	14
10	950	14
11	960	14

Iter	Nodes	Cost
0	9	14
1	18	14
2	38	14
3	67	14
4	118	14
5	183	14
6	324	14
7	531	14
8	681	14
9	846	14
10	950	14
11	960	14

Details

analyze442.0ms (9.6%)

sample2.3s (50.2%)

preprocess48.0ms (1%)

simplify18.0ms (0.4%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series46.0ms (1%)

rewrite71.0ms (1.5%)

simplify51.0ms (1.1%)

prune166.0ms (3.6%)

localize8.0ms (0.2%)

series14.0ms (0.3%)

rewrite37.0ms (0.8%)

simplify30.0ms (0.7%)

prune71.0ms (1.5%)

localize9.0ms (0.2%)

series180.0ms (3.9%)

rewrite66.0ms (1.4%)

simplify34.0ms (0.7%)

prune214.0ms (4.6%)

localize13.0ms (0.3%)

series170.0ms (3.7%)

rewrite45.0ms (1%)

simplify29.0ms (0.6%)

prune141.0ms (3.1%)

regimes259.0ms (5.6%)

simplify4.0ms (0.1%)

end125.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	9	14
1	18	14
2	38	14
3	67	14
4	118	14
5	183	14
6	324	14
7	531	14
8	681	14
9	846	14
10	950	14
11	960	14