Details

analyze4.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.8%	0.1%	0.1%	12
99.8%	0%	0.1%	13
99.8%	0%	0.2%	14

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample814.0ms (56.8%)

Results

800.0ms	8251×	body	128	valid
1.0ms	3×	body	512	valid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 22 to 20 computations (9.1% saved)

preprocess17.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	16	5
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 9 computations (10% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	16	5

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 841/108 x 4/29)
▶	0.1b	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))

Compiler

Compiled 44 to 38 computations (13.6% saved)

localize7.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
✓	0.2b	(*.f64 (/.f64 841 108) x)

series3.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

0.0ms	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))	x	inf
0.0ms	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))	x	-inf
0.0ms	(*.f64 (/.f64 841 108) x)	x	0
0.0ms	(*.f64 (/.f64 841 108) x)	x	inf
0.0ms	(*.f64 (/.f64 841 108) x)	x	-inf

rewrite43.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

858×	`log1p-expm1-u_binary64`
858×	`expm1-log1p-u_binary64`
158×	`prod-diff_binary64`
96×	`add-cbrt-cube_binary64`
96×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	218	9
2	2252	9

Stop Event

1×	node limit

Counts

2 → 47

simplify8.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	120
1	8	102
2	10	102

Stop Event

1×

saturated

Counts

71 → 50

prune46.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	47	5	52

Error

0.0b

Counts

52 → 5

Alt Table

Status	Error	Program
	17.6b	(.f64 (+.f64 (.f64 (*.f64 x x) 707281/11664) -16/841) (/.f64 1 (fma.f64 841/108 x -4/29)))
▶	0.7b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3) (/.f64 4 29))
✓	0.1b	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
	17.6b	(/.f64 (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841) (fma.f64 841/108 x -4/29))
	17.7b	(fma.f64 (cbrt.f64 (.f64 (.f64 x x) 707281/11664)) (cbrt.f64 (*.f64 841/108 x)) 4/29)

Compiler

Compiled 617 to 500 computations (19% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3) (/.f64 4 29))
✓	0.2b	(*.f64 841/108 x)
✓	0.6b	(cbrt.f64 (*.f64 841/108 x))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)

series98.0ms (6.9%)

Counts

4 → 12

Calls

12 calls:

34.0ms	(+.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3) (/.f64 4 29))	x	-inf
19.0ms	(pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)	x	-inf
9.0ms	(cbrt.f64 (*.f64 841/108 x))	x	-inf
8.0ms	(pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)	x	inf
6.0ms	(+.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3) (/.f64 4 29))	x	0

rewrite59.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

892×	`log1p-expm1-u_binary64`
892×	`expm1-log1p-u_binary64`
210×	`prod-diff_binary64`
103×	`egg-rr`
97×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	237	19
2	2411	19

Stop Event

1×	node limit

Counts

4 → 103

simplify10.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	72
1	8	54
2	10	54

Stop Event

1×

saturated

Counts

115 → 96

prune57.0ms (4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	99	2	101

Error

Counts

101 → 2

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (*.f64 (pow.f64 (cbrt.f64 841/108) 3) x) (/.f64 4 29))
✓	0.1b	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))

Compiler

Compiled 1213 to 993 computations (18.1% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (pow.f64 (cbrt.f64 841/108) 3) x) (/.f64 4 29))
✓	0.2b	(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)
✓	1.0b	(pow.f64 (cbrt.f64 841/108) 3)

series3.0ms (0.2%)

Counts

3 → 24

Calls

6 calls:

1.0ms	(+.f64 (*.f64 (pow.f64 (cbrt.f64 841/108) 3) x) (/.f64 4 29))	x	-inf
1.0ms	(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)	x	0
1.0ms	(+.f64 (*.f64 (pow.f64 (cbrt.f64 841/108) 3) x) (/.f64 4 29))	x	inf
1.0ms	(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)	x	-inf
0.0ms	(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)	x	inf

rewrite45.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

874×	`log1p-expm1-u_binary64`
874×	`expm1-log1p-u_binary64`
158×	`prod-diff_binary64`
97×	`add-sqr-sqrt_binary64`
97×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	10
1	237	10
2	2326	10

Stop Event

1×	node limit

Counts

3 → 48

simplify8.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	120
1	8	102
2	10	102

Stop Event

1×

saturated

Counts

72 → 51

prune25.0ms (1.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	51	2	53

Error

Counts

53 → 2

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 (*.f64 (pow.f64 (cbrt.f64 841/108) 3) x) (/.f64 4 29))
✓	0.1b	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))

Compiler

Compiled 531 to 434 computations (18.3% saved)

regimes122.0ms (8.5%)

Accuracy

Total 0.1b remaining (93.4%)

Threshold costs 0.1b (93.4%)

Counts

40 → 1

Compiler

Compiled 1250 to 1055 computations (15.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	5
1	10	5

Stop Event

1×

saturated

end40.0ms (2.8%)

Stop Event

1×

done

Compiler

Compiled 31 to 27 computations (12.9% saved)

Details

analyze4.0ms (0.3%)

sample814.0ms (56.8%)

preprocess17.0ms (1.2%)

simplify6.0ms (0.4%)

prune3.0ms (0.2%)

localize7.0ms (0.5%)

series3.0ms (0.2%)

rewrite43.0ms (3%)

simplify8.0ms (0.6%)

prune46.0ms (3.2%)

localize6.0ms (0.4%)

series98.0ms (6.9%)

rewrite59.0ms (4.1%)

simplify10.0ms (0.7%)

prune57.0ms (4%)

localize6.0ms (0.4%)

series3.0ms (0.2%)

rewrite45.0ms (3.1%)

simplify8.0ms (0.6%)

prune25.0ms (1.7%)

regimes122.0ms (8.5%)

simplify2.0ms (0.1%)

end40.0ms (2.8%)

Profiling