Details

analyze84.0ms (4.3%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
56.2%	43.7%	0.1%	6
65.6%	34.3%	0.1%	7
76.5%	23.4%	0.1%	8
82%	18%	0.1%	9
87.8%	12.1%	0.1%	10
90.7%	9.2%	0.1%	11
93.8%	6.1%	0.1%	12
95.3%	4.6%	0.1%	13
96.8%	3.1%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample777.0ms (39.6%)

Results

761.0ms

8256×

body

128

valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess14.0ms (0.7%)

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)

simplify17.0ms (0.9%)

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 (0.1%)

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

15.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	15.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	15.4b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

series32.0ms (1.6%)

Counts

1 → 0

Calls

6 calls:

9.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))	a	-inf
9.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))	g	-inf
4.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))	a	0
3.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))	g	0
3.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))	a	inf

rewrite37.0ms (1.9%)

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

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

30 → 30

prune26.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	8	31

Error

0.2b

Counts

31 → 8

Alt Table

Status	Error	Program
✓	15.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	0.9b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	16.3b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g (/.f64 1/2 a)))) 3)
▶	0.8b	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (cbrt.f64 a))
	0.8b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
	15.4b	(/.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 445 to 340 computations (23.6% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series62.0ms (3.2%)

Counts

3 → 0

Calls

12 calls:

13.0ms	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (cbrt.f64 a))	a	-inf
9.0ms	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (cbrt.f64 a))	g	-inf
9.0ms	(cbrt.f64 (*.f64 g 1/2))	g	-inf
8.0ms	(cbrt.f64 a)	a	-inf
4.0ms	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (cbrt.f64 a))	g	0

rewrite50.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

758×	`log1p-expm1-u_binary64`
758×	`expm1-log1p-u_binary64`
139×	`log1p-udef_binary64`
80×	`egg-rr`
78×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	163	18
2	2038	18

Stop Event

1×	node limit

Counts

3 → 80

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

80 → 80

prune54.0ms (2.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	75	13	88

Error

0.1b

Counts

88 → 13

Alt Table

Status	Error	Program
	0.8b	(.f64 (cbrt.f64 g) (/.f64 1 (cbrt.f64 (.f64 2 a))))
	1.5b	(*.f64 (/.f64 (cbrt.f64 g) (pow.f64 (cbrt.f64 (cbrt.f64 a)) 2)) (/.f64 (cbrt.f64 1/2) (cbrt.f64 (cbrt.f64 a))))
	16.3b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g (/.f64 1/2 a)))) 3)
	1.5b	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (pow.f64 (cbrt.f64 (cbrt.f64 a)) 3))
✓	15.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	0.8b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
	15.4b	(pow.f64 (cbrt.f64 (/.f64 a (*.f64 g 1/2))) -1)
	40.7b	(pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 g (/.f64 a 1/2)))) 2)
	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 1/2) (/.f64 1 (cbrt.f64 a))))
	1.5b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 g 1/2))) 2) (.f64 (cbrt.f64 (cbrt.f64 (.f64 g 1/2))) (/.f64 1 (cbrt.f64 a))))
▶	0.8b	(.f64 (cbrt.f64 (.f64 g 1/2)) (/.f64 1 (cbrt.f64 a)))
	1.5b	(/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g 1/2))) 3) (cbrt.f64 a))

Compiler

Compiled 1208 to 880 computations (27.2% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (cbrt.f64 a))
✓	0.4b	(.f64 (cbrt.f64 (.f64 g 1/2)) (/.f64 1 (cbrt.f64 a)))
	0.6b	(cbrt.f64 (*.f64 g 1/2))
	0.6b	(cbrt.f64 a)

series50.0ms (2.6%)

Counts

2 → 0

Calls

9 calls:

15.0ms	(.f64 (cbrt.f64 (.f64 g 1/2)) (/.f64 1 (cbrt.f64 a)))	a	-inf
9.0ms	(.f64 (cbrt.f64 (.f64 g 1/2)) (/.f64 1 (cbrt.f64 a)))	g	-inf
9.0ms	(/.f64 1 (cbrt.f64 a))	a	-inf
5.0ms	(.f64 (cbrt.f64 (.f64 g 1/2)) (/.f64 1 (cbrt.f64 a)))	g	inf
3.0ms	(.f64 (cbrt.f64 (.f64 g 1/2)) (/.f64 1 (cbrt.f64 a)))	g	0

rewrite52.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

788×	`log1p-expm1-u_binary64`
788×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
86×	`add-cbrt-cube_binary64`
84×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	197	15
2	2253	15

Stop Event

1×	node limit

Counts

2 → 51

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

51 → 51

prune69.0ms (3.5%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	92	16	108

Error

0.1b

Counts

108 → 16

Alt Table

Status	Error	Program
	0.9b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (/.f64 1 (cbrt.f64 a)))
	16.3b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g (/.f64 1/2 a)))) 3)
	0.9b	(/.f64 (cbrt.f64 g) (/.f64 (cbrt.f64 a) (cbrt.f64 1/2)))
	0.8b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
	1.1b	(/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 g 1/2)) 2)) (/.f64 (cbrt.f64 a) (cbrt.f64 (cbrt.f64 (.f64 g 1/2)))))
	15.4b	(pow.f64 (cbrt.f64 (/.f64 a (*.f64 g 1/2))) -1)
	0.8b	(.f64 (cbrt.f64 g) (/.f64 1 (cbrt.f64 (.f64 2 a))))
	1.5b	(*.f64 (/.f64 (cbrt.f64 g) (pow.f64 (cbrt.f64 (cbrt.f64 a)) 2)) (/.f64 (cbrt.f64 1/2) (cbrt.f64 (cbrt.f64 a))))
	30.9b	(.f64 (cbrt.f64 (.f64 g 1/2)) (sqrt.f64 (pow.f64 (cbrt.f64 a) -2)))
	1.5b	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (pow.f64 (cbrt.f64 (cbrt.f64 a)) 3))
✓	15.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	40.7b	(pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 g (/.f64 a 1/2)))) 2)
▶	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 1/2) (/.f64 1 (cbrt.f64 a))))
✓	0.8b	(.f64 (cbrt.f64 (.f64 g 1/2)) (/.f64 1 (cbrt.f64 a)))
	1.5b	(/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g 1/2))) 3) (cbrt.f64 a))

Compiler

Compiled 1473 to 1096 computations (25.6% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
✓	0.6b	(cbrt.f64 g)
✓	0.7b	(cbrt.f64 (/.f64 1/2 a))

series63.0ms (3.2%)

Counts

3 → 0

Calls

12 calls:

12.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))	g	-inf
10.0ms	(cbrt.f64 g)	g	-inf
9.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))	a	-inf
9.0ms	(cbrt.f64 (/.f64 1/2 a))	a	-inf
5.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))	a	0

rewrite43.0ms (2.2%)

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

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

65 → 65

prune39.0ms (2%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	3	10	13
Picked	0	1	1
Done	0	2	2
Total	65	16	81

Error

0.0b

Counts

81 → 16

Alt Table

Status	Error	Program
	0.9b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (/.f64 1 (cbrt.f64 a)))
	16.3b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g (/.f64 1/2 a)))) 3)
	1.1b	(/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 g 1/2)) 2)) (/.f64 (cbrt.f64 a) (cbrt.f64 (cbrt.f64 (.f64 g 1/2)))))
	15.4b	(pow.f64 (cbrt.f64 (/.f64 a (*.f64 g 1/2))) -1)
	1.6b	(*.f64 (cbrt.f64 g) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 1/2 a))) 3))
	1.5b	(/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 g 1/2))) 3) (cbrt.f64 a))
	0.8b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 1 a))))
	30.9b	(.f64 (cbrt.f64 (.f64 g 1/2)) (sqrt.f64 (pow.f64 (cbrt.f64 a) -2)))
	1.5b	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (pow.f64 (cbrt.f64 (cbrt.f64 a)) 3))
✓	15.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	0.8b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
	40.7b	(pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 g (/.f64 a 1/2)))) 2)
	1.5b	(*.f64 (/.f64 (cbrt.f64 g) (pow.f64 (cbrt.f64 (cbrt.f64 a)) 2)) (/.f64 (cbrt.f64 1/2) (cbrt.f64 (cbrt.f64 a))))
✓	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
✓	0.8b	(.f64 (cbrt.f64 (.f64 g 1/2)) (/.f64 1 (cbrt.f64 a)))
	0.8b	(*.f64 (cbrt.f64 g) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))

Compiler

Compiled 851 to 612 computations (28.1% saved)

regimes262.0ms (13.4%)

Accuracy

Total 0.7b remaining (91%)

Threshold costs 0.7b (91%)

Counts

50 → 1

Compiler

Compiled 3126 to 2492 computations (20.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11

Stop Event

1×

saturated

end170.0ms (8.7%)

Stop Event

1×

fuel

Compiler

Compiled 206 to 166 computations (19.4% saved)

Details

analyze84.0ms (4.3%)

sample777.0ms (39.6%)

preprocess14.0ms (0.7%)

simplify17.0ms (0.9%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series32.0ms (1.6%)

rewrite37.0ms (1.9%)

simplify6.0ms (0.3%)

prune26.0ms (1.3%)

localize6.0ms (0.3%)

series62.0ms (3.2%)

rewrite50.0ms (2.6%)

simplify9.0ms (0.5%)

prune54.0ms (2.8%)

localize7.0ms (0.4%)

series50.0ms (2.6%)

rewrite52.0ms (2.6%)

simplify7.0ms (0.3%)

prune69.0ms (3.5%)

localize7.0ms (0.4%)

series63.0ms (3.2%)

rewrite43.0ms (2.2%)

simplify7.0ms (0.3%)

prune39.0ms (2%)

regimes262.0ms (13.4%)

simplify2.0ms (0.1%)

end170.0ms (8.7%)

Profiling