Details

analyze605.0ms (11.7%)

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
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12
76.5%	23.4%	0.1%	13
81.9%	17.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.9s (55.2%)

Results

1.5s	2035×	body	1024	valid
738.0ms	4688×	body	128	valid
433.0ms	987×	body	512	valid
162.0ms	542×	body	256	valid
6.0ms	4×	body	2048	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess17.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

16×	`fma-def_binary64`
8×	`*-commutative_binary64`
4×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	38	48
2	50	48
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

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 (sin.f64 y)) (.f64 z (cos.f64 y)))

Compiler

Compiled 44 to 25 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

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

rewrite38.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

673×	`log1p-expm1-u_binary64`
673×	`expm1-log1p-u_binary64`
396×	`log-prod_binary64`
145×	`expm1-udef_binary64`
145×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	155	12
2	1852	12

Stop Event

1×	node limit

Counts

2 → 36

simplify35.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-neg-in_binary64`
501×	`fma-neg_binary64`
324×	`*-commutative_binary64`
276×	`sub-neg_binary64`
268×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	392
1	138	383
2	427	365
3	1656	363
4	3900	363

Stop Event

1×	node limit

Counts

84 → 52

prune33.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	6	53

Error

0.1b

Counts

53 → 6

Alt Table

Status	Error	Program
▶	0.5b	(+.f64 (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 3) (.f64 z (cos.f64 y)))
✓	0.1b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
	31.0b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	31.2b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	23.9b	(+.f64 (cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (sin.f64 y) 3))) (.f64 z (cos.f64 y)))
	29.8b	(+.f64 (pow.f64 (sqrt.f64 (.f64 x (sin.f64 y))) 2) (.f64 z (cos.f64 y)))

Compiler

Compiled 938 to 434 computations (53.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (cos.f64 y))
	0.1b	(*.f64 x (sin.f64 y))
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3)
✓	9.9b	(cbrt.f64 (*.f64 x (sin.f64 y)))

series177.0ms (3.4%)

Counts

2 → 16

Calls

12 calls:

52.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3)	y	inf
26.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3)	y	-inf
25.0ms	(cbrt.f64 (*.f64 x (sin.f64 y)))	y	-inf
22.0ms	(cbrt.f64 (*.f64 x (sin.f64 y)))	y	inf
19.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3)	x	-inf

rewrite39.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

596×	`log1p-expm1-u_binary64`
596×	`expm1-log1p-u_binary64`
319×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	159	14
2	1674	14

Stop Event

1×	node limit

Counts

2 → 63

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

730×	`sqr-pow_binary64`
370×	`cube-prod_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
283×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	112
1	14	112
2	19	112
3	28	112
4	50	112
5	139	112
6	519	112
7	1180	112
8	1270	112
9	1406	112
10	1567	112
11	1798	112
12	2123	112
13	2547	112
14	3050	112
15	3650	112
16	4375	112
17	4698	112
18	4984	112

Stop Event

1×	node limit

Counts

79 → 65

prune125.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	109	8	117
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	112	11	123

Error

0.0b

Counts

123 → 11

Alt Table

Status	Error	Program
	0.6b	(+.f64 (.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (*.f64 z (cos.f64 y)))
	31.0b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	30.9b	(+.f64 (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) x)) (*.f64 z (cos.f64 y)))
	31.2b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	0.6b	(+.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))
✓	0.1b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
	0.7b	(+.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sin.f64 y)))) 2)) (cbrt.f64 (cbrt.f64 (.f64 x (sin.f64 y))))) (.f64 z (cos.f64 y)))
	29.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.6b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) x)) (*.f64 z (cos.f64 y)))
▶	0.5b	(+.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2))) (.f64 z (cos.f64 y)))
	0.5b	(+.f64 (.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2)) (.f64 z (cos.f64 y)))

Compiler

Compiled 2379 to 1005 computations (57.8% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2)
✓	0.6b	(cbrt.f64 x)
✓	0.7b	(cbrt.f64 (sin.f64 y))
	9.9b	(cbrt.f64 (*.f64 x (sin.f64 y)))

series130.0ms (2.5%)

Counts

3 → 16

Calls

12 calls:

24.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2)	y	inf
24.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2)	y	-inf
20.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2)	x	-inf
19.0ms	(cbrt.f64 (sin.f64 y))	y	-inf
19.0ms	(cbrt.f64 (sin.f64 y))	y	inf

rewrite46.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

726×	`log1p-expm1-u_binary64`
726×	`expm1-log1p-u_binary64`
153×	`expm1-udef_binary64`
153×	`log1p-udef_binary64`
89×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	193	19
2	2102	19

Stop Event

1×	node limit

Counts

3 → 63

simplify97.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2215×	`associate-l_binary64`
724×	`sqr-pow_binary64`
290×	`pow-sqr_binary64`
276×	`unswap-sqr_binary64`
248×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	152
1	28	152
2	56	152
3	137	152
4	512	152
5	1058	152
6	1149	152
7	1288	152
8	1461	152
9	1650	152
10	1886	152
11	2163	152
12	2483	152
13	2855	152
14	3264	152
15	3697	152
16	3893	152
17	3997	152
18	4069	152
19	4123	152

Stop Event

1×	node limit

Counts

79 → 66

prune131.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	95	11	106

Error

0.0b

Counts

106 → 11

Alt Table

Status	Error	Program
	0.6b	(+.f64 (.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (*.f64 z (cos.f64 y)))
	31.0b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	30.9b	(+.f64 (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) x)) (*.f64 z (cos.f64 y)))
	31.2b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	0.6b	(+.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))
✓	0.1b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
	18.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 (.f64 x x)))) (.f64 (cbrt.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2))) (.f64 z (cos.f64 y)))
	0.7b	(+.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sin.f64 y)))) 2)) (cbrt.f64 (cbrt.f64 (.f64 x (sin.f64 y))))) (.f64 z (cos.f64 y)))
	29.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))
✓	0.5b	(+.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2))) (.f64 z (cos.f64 y)))
▶	0.5b	(+.f64 (.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2)) (.f64 z (cos.f64 y)))

Compiler

Compiled 2617 to 1002 computations (61.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 x (sin.f64 y))
✓	0.3b	(.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2))
	0.4b	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2)
	9.9b	(cbrt.f64 (*.f64 x (sin.f64 y)))

series59.0ms (1.1%)

Counts

1 → 24

Calls

6 calls:

53.0ms	(.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2))	x	-inf
2.0ms	(.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2))	x	0
1.0ms	(.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2))	x	inf
1.0ms	(.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2))	y	0
1.0ms	(.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2))	y	inf

rewrite40.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`log1p-expm1-u_binary64`
616×	`expm1-log1p-u_binary64`
339×	`log-prod_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	6
1	180	6
2	1797	6

Stop Event

1×	node limit

Counts

1 → 18

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

466×	`fma-def_binary64`
360×	`cancel-sign-sub-inv_binary64`
323×	`associate-l_binary64`
317×	`distribute-rgt-neg-in_binary64`
296×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	202
1	76	194
2	233	184
3	845	180
4	3123	180
5	4353	180

Stop Event

1×	node limit

Counts

42 → 26

prune184.0ms (3.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	159	11	170

Error

0.0b

Counts

170 → 11

Alt Table

Status	Error	Program
	0.6b	(+.f64 (.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (*.f64 z (cos.f64 y)))
	31.0b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	30.9b	(+.f64 (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) x)) (*.f64 z (cos.f64 y)))
	31.2b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	0.6b	(+.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))
✓	0.1b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
	18.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 (.f64 x x)))) (.f64 (cbrt.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2))) (.f64 z (cos.f64 y)))
	0.7b	(+.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sin.f64 y)))) 2)) (cbrt.f64 (cbrt.f64 (.f64 x (sin.f64 y))))) (.f64 z (cos.f64 y)))
	29.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))
✓	0.5b	(+.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2))) (.f64 z (cos.f64 y)))
✓	0.5b	(+.f64 (.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 2)) (.f64 z (cos.f64 y)))

Compiler

Compiled 3696 to 1279 computations (65.4% saved)

regimes201.0ms (3.9%)

Accuracy

Total 0.1b remaining (48.5%)

Threshold costs 0.1b (48.5%)

Counts

42 → 1

Compiler

Compiled 3028 to 2162 computations (28.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	12	14

Stop Event

1×

saturated

end171.0ms (3.3%)

Stop Event

1×

fuel

Compiler

Compiled 240 to 155 computations (35.4% saved)

Details

analyze605.0ms (11.7%)

sample2.9s (55.2%)

preprocess17.0ms (0.3%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series15.0ms (0.3%)

rewrite38.0ms (0.7%)

simplify35.0ms (0.7%)

prune33.0ms (0.6%)

localize10.0ms (0.2%)

series177.0ms (3.4%)

rewrite39.0ms (0.8%)

simplify71.0ms (1.4%)

prune125.0ms (2.4%)

localize18.0ms (0.4%)

series130.0ms (2.5%)

rewrite46.0ms (0.9%)

simplify97.0ms (1.9%)

prune131.0ms (2.5%)

localize13.0ms (0.3%)

series59.0ms (1.1%)

rewrite40.0ms (0.8%)

simplify37.0ms (0.7%)

prune184.0ms (3.6%)

regimes201.0ms (3.9%)

simplify4.0ms (0.1%)

end171.0ms (3.3%)

Profiling