Details

analyze36.0ms (0.9%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample771.0ms (18.7%)

Results

758.0ms

8256×

body

128

valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess20.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

4×	`associate-/r*_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	16	18
2	20	18
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 8 to 6 computations (25% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`associate-/r*_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	12	9

Stop Event

1×

saturated

Counts

1 → 1

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

14.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.1b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	13.8b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

series345.0ms (8.4%)

Counts

1 → 24

Calls

6 calls:

64.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))	g	0
63.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))	g	-inf
60.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))	g	inf
55.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))	a	-inf
53.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))	a	inf

rewrite38.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`
115×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	146	9
2	1871	9

Stop Event

1×	node limit

Counts

1 → 30

simplify36.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

403×	`fma-def_binary64`
359×	`fma-neg_binary64`
343×	`div-sub_binary64`
310×	`times-frac_binary64`
268×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	472
1	82	472
2	164	448
3	449	312
4	1208	280
5	2965	280

Stop Event

1×	node limit

Counts

54 → 37

prune32.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	28	9	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	9	38

Error

0.1b

Counts

38 → 9

Alt Table

Status	Error	Program
	0.9b	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (cbrt.f64 a))
	14.2b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
	14.1b	(.f64 (cbrt.f64 (.f64 g (/.f64 1/2 a))) 1)
	14.9b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g (/.f64 1/2 a)))) 3)
	0.8b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	0.8b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
	13.7b	(/.f64 1 (cbrt.f64 (*.f64 2 (/.f64 a g))))
	0.8b	(.f64 (cbrt.f64 g) (/.f64 1 (cbrt.f64 (.f64 2 a))))
▶	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))

Compiler

Compiled 557 to 430 computations (22.8% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
✓	0.5b	(cbrt.f64 g)
✓	0.6b	(cbrt.f64 (/.f64 1/2 a))

series399.0ms (9.7%)

Counts

3 → 48

Calls

12 calls:

66.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))	g	-inf
58.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))	g	0
57.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))	g	inf
57.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))	a	-inf
49.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))	a	0

rewrite42.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

687×	`log1p-expm1-u_binary64`
687×	`expm1-log1p-u_binary64`
138×	`expm1-udef_binary64`
138×	`log1p-udef_binary64`
127×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	164	18
2	1927	18

Stop Event

1×	node limit

Counts

3 → 65

simplify46.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

476×	`times-frac_binary64`
417×	`fma-def_binary64`
347×	`fma-neg_binary64`
346×	`div-sub_binary64`
289×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	50	680
1	115	680
2	231	624
3	580	512
4	1684	472
5	3538	472

Stop Event

1×	node limit

Counts

113 → 79

prune52.0ms (1.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	74	14	88

Error

0.1b

Counts

88 → 14

Alt Table

Status	Error	Program
	0.9b	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (cbrt.f64 a))
	14.2b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
▶	0.8b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))
	1.5b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 g)) 3) (cbrt.f64 (/.f64 1/2 a)))
	4.4b	(.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 g) 2) 1/3) (cbrt.f64 (cbrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))
	1.5b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 g)) (pow.f64 (cbrt.f64 (cbrt.f64 g)) 2)) (cbrt.f64 (/.f64 1/2 a)))
	1.5b	(*.f64 (cbrt.f64 g) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 1/2 a))) 3))
	14.9b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g (/.f64 1/2 a)))) 3)
	0.9b	(*.f64 (cbrt.f64 g) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
	0.8b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
	13.7b	(/.f64 1 (cbrt.f64 (*.f64 2 (/.f64 a g))))
	14.1b	(cbrt.f64 (*.f64 (/.f64 1/2 a) g))
	0.8b	(.f64 (cbrt.f64 g) (/.f64 1 (cbrt.f64 (.f64 2 a))))
✓	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))

Compiler

Compiled 1127 to 821 computations (27.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2))
	0.5b	(cbrt.f64 g)
✓	0.6b	(cbrt.f64 (/.f64 -1 a))

series535.0ms (13%)

Counts

3 → 48

Calls

12 calls:

81.0ms	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))	g	-inf
78.0ms	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))	g	0
76.0ms	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))	g	inf
72.0ms	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))	a	0
68.0ms	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))	a	inf

rewrite58.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

878×	`log1p-expm1-u_binary64`
878×	`expm1-log1p-u_binary64`
101×	`add-sqr-sqrt_binary64`
96×	`add-cbrt-cube_binary64`
95×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	217	21
2	2470	21

Stop Event

1×	node limit

Counts

3 → 59

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

506×	`unswap-sqr_binary64`
386×	`associate-l_binary64`
344×	`fma-neg_binary64`
283×	`associate-r_binary64`
224×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	50	860
1	118	860
2	254	836
3	704	696
4	2493	628
5	4949	628

Stop Event

1×	node limit

Counts

107 → 74

prune62.0ms (1.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	3	9	12
Picked	0	1	1
Done	0	1	1
Total	97	15	112

Error

0.1b

Counts

112 → 15

Alt Table

Status	Error	Program
	1.5b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 g)) 3) (cbrt.f64 (/.f64 1/2 a)))
	30.5b	(*.f64 (cbrt.f64 g) (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 1/2 a))) 2))
	0.9b	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (cbrt.f64 a))
	14.2b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
✓	0.8b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))
	1.5b	(.f64 (cbrt.f64 g) (.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (cbrt.f64 a))) 3) (cbrt.f64 -1/2)))
✓	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	1.5b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 g)) 3) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))
	14.3b	(cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 1/2 a) g)) 3))
	1.5b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 g)) (pow.f64 (cbrt.f64 (cbrt.f64 g)) 2)) (cbrt.f64 (/.f64 1/2 a)))
	14.9b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g (/.f64 1/2 a)))) 3)
▶	0.8b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
	13.7b	(/.f64 1 (cbrt.f64 (*.f64 2 (/.f64 a g))))
	14.1b	(cbrt.f64 (*.f64 (/.f64 1/2 a) g))
	0.8b	(.f64 (cbrt.f64 g) (/.f64 1 (cbrt.f64 (.f64 2 a))))

Compiler

Compiled 1506 to 1121 computations (25.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
✓	0.3b	(/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g))
	0.5b	(cbrt.f64 g)
✓	0.6b	(cbrt.f64 (*.f64 2 a))

series795.0ms (19.3%)

Counts

3 → 60

Calls

15 calls:

80.0ms	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))	a	-inf
76.0ms	(/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g))	g	-inf
71.0ms	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))	g	-inf
66.0ms	(/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g))	a	-inf
65.0ms	(/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g))	a	0

rewrite57.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

893×	`log1p-expm1-u_binary64`
893×	`expm1-log1p-u_binary64`
102×	`egg-rr`
95×	`add-sqr-sqrt_binary64`
90×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	204	24
2	2506	24

Stop Event

1×	node limit

Counts

3 → 102

simplify52.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

337×	`fma-def_binary64`
303×	`associate-/l*_binary64`
275×	`distribute-rgt-in_binary64`
206×	`exp-sum_binary64`
188×	`div-sub_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	68	1072
1	152	1072
2	321	1024
3	814	712
4	2280	704

Stop Event

1×	node limit

Counts

162 → 121

prune83.0ms (2%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	137	8	145
Fresh	5	7	12
Picked	0	1	1
Done	1	1	2
Total	143	17	160

Error

0.0b

Counts

160 → 17

Alt Table

Status	Error	Program
	1.5b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 g)) 3) (cbrt.f64 (/.f64 1/2 a)))
	1.1b	(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 2 a)) 2))) (/.f64 (cbrt.f64 g) (cbrt.f64 (cbrt.f64 (*.f64 2 a)))))
	0.9b	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (cbrt.f64 a))
	14.2b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
✓	0.8b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))
	1.4b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (pow.f64 (cbrt.f64 (cbrt.f64 g)) 3)))
	1.5b	(.f64 (cbrt.f64 g) (.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (cbrt.f64 a))) 3) (cbrt.f64 -1/2)))
	13.7b	(/.f64 1 (cbrt.f64 (*.f64 2 (/.f64 a g))))
	14.6b	(/.f64 (cbrt.f64 (/.f64 g a)) (cbrt.f64 2))
	1.2b	(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cbrt.f64 g) (cbrt.f64 a)))
	1.5b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 g)) 2) 1) (/.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (.f64 2 a))))
	14.9b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g (/.f64 1/2 a)))) 3)
	1.6b	(/.f64 1 (*.f64 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cbrt.f64 g)) 2)) (/.f64 (cbrt.f64 a) (cbrt.f64 (cbrt.f64 g)))))
✓	0.8b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
	14.3b	(cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 g (*.f64 2 a))) 3))
	1.2b	(/.f64 1 (/.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 a)) (cbrt.f64 g)))
	14.1b	(cbrt.f64 (*.f64 (/.f64 1/2 a) g))

Compiler

Compiled 2093 to 1543 computations (26.3% saved)

regimes365.0ms (8.9%)

Accuracy

Total 0.8b remaining (92.8%)

Threshold costs 0.8b (92.8%)

Counts

65 → 1

Compiler

Compiled 4771 to 3844 computations (19.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	13	16

Stop Event

1×

saturated

end196.0ms (4.7%)

Stop Event

1×

fuel

Compiler

Compiled 236 to 191 computations (19.1% saved)

Details

analyze36.0ms (0.9%)

sample771.0ms (18.7%)

preprocess20.0ms (0.5%)

simplify7.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series345.0ms (8.4%)

rewrite38.0ms (0.9%)

simplify36.0ms (0.9%)

prune32.0ms (0.8%)

localize5.0ms (0.1%)

series399.0ms (9.7%)

rewrite42.0ms (1%)

simplify46.0ms (1.1%)

prune52.0ms (1.3%)

localize8.0ms (0.2%)

series535.0ms (13%)

rewrite58.0ms (1.4%)

simplify66.0ms (1.6%)

prune62.0ms (1.5%)

localize7.0ms (0.2%)

series795.0ms (19.3%)

rewrite57.0ms (1.4%)

simplify52.0ms (1.3%)

prune83.0ms (2%)

regimes365.0ms (8.9%)

simplify2.0ms (0.1%)

end196.0ms (4.7%)

Profiling