Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample644.0ms (31.6%)

Infinites

33.9% of outputs are infinite.

Results

447.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify165.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

1514×	`fma-def_binary64`
1229×	`fma-neg_binary64`
587×	`distribute-rgt-neg-in_binary64`
552×	`cancel-sign-sub-inv_binary64`
522×	`sqr-pow_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	42	11
3	96	11
4	169	11
5	224	11
6	343	11
7	549	11
8	728	11
9	1208	11
10	1666	11
11	2306	11
12	2905	11
13	3028	11
14	3233	11
15	3418	11
16	4282	11
17	3230	11
18	3595	11
19	4713	11
20	4755	11

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x x) (fma.f64 x -2 3))

Compiler

Compiled 36 to 23 computations (36.1% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x x) (fma.f64 x -2 3))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (*.f64 x x) (fma.f64 x -2 3))

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 23

Calls

1 calls:

4.0ms

(*.f64 (*.f64 x x) (fma.f64 x -2 3))

simplify69.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1057×	`fma-def_binary64`
450×	`associate-l_binary64`
439×	`times-frac_binary64`
381×	`exp-prod_binary64`
334×	`associate-r_binary64`

Counts

35 → 37

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	539
1	122	424
2	381	424
3	1373	424
4	2370	424
5	3834	424
6	5293	424

prune33.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	32	5	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	5	38

Error

0.0b

Counts

38 → 5

Alt Table

Status	Error	Program
	17.5b	(.f64 (.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x -2 3))) (sqrt.f64 (fma.f64 x -2 3)))
	0.7b	(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3))))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))))
▶	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	9.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	17.8b	(cbrt.f64 (pow.f64 (.f64 x (.f64 x (fma.f64 x -2 3))) 3))

Compiler

Compiled 648 to 425 computations (34.4% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (fma.f64 x -2 3))
✓	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))
2.0ms	(*.f64 x (fma.f64 x -2 3))

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 46

Calls

2 calls:

4.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))
3.0ms	(*.f64 x (fma.f64 x -2 3))

simplify74.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
444×	`unswap-sqr_binary64`
444×	`times-frac_binary64`
351×	`*-commutative_binary64`
216×	`exp-prod_binary64`

Counts

70 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	970
1	152	752
2	484	752
3	1374	750
4	2163	750
5	4334	750
6	5493	750

prune69.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	69	6	75

Error

0.0b

Counts

75 → 6

Alt Table

Status	Error	Program
	32.6b	(.f64 (sqrt.f64 x) (.f64 (fma.f64 x -2 3) (pow.f64 x 3/2)))
	17.5b	(.f64 (.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x -2 3))) (sqrt.f64 (fma.f64 x -2 3)))
	0.7b	(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3))))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))))
▶	0.6b	(.f64 x (+.f64 (.f64 (.f64 x -2) x) (.f64 3 x)))
	9.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	9.1b	(.f64 x (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (fma.f64 x -2 3) (fma.f64 x -2 3)) (fma.f64 x -2 3)))))

Compiler

Compiled 1111 to 725 computations (34.7% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (+.f64 (.f64 (.f64 x -2) x) (.f64 3 x)))
✓	0.5b	(+.f64 (.f64 (.f64 x -2) x) (*.f64 3 x))

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(.f64 x (+.f64 (.f64 (.f64 x -2) x) (.f64 3 x)))
3.0ms	(+.f64 (.f64 (.f64 x -2) x) (*.f64 3 x))

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

7.0ms	(.f64 x (+.f64 (.f64 (.f64 x -2) x) (.f64 3 x)))
4.0ms	(+.f64 (.f64 (.f64 x -2) x) (*.f64 3 x))

simplify69.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

360×	`neg-mul-1_binary64`
359×	`neg-sub0_binary64`
359×	`fma-def_binary64`
277×	`*-commutative_binary64`
241×	`distribute-rgt-neg-out_binary64`

Counts

64 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	929
1	224	743
2	864	728
3	2507	723
4	4318	723
5	5149	723

prune64.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	74	7	81

Error

Counts

81 → 7

Alt Table

Status	Error	Program
	32.6b	(.f64 (sqrt.f64 x) (.f64 (fma.f64 x -2 3) (pow.f64 x 3/2)))
	17.5b	(.f64 (.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x -2 3))) (sqrt.f64 (fma.f64 x -2 3)))
▶	0.7b	(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3))))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))))
✓	0.6b	(.f64 x (+.f64 (.f64 (.f64 x -2) x) (.f64 3 x)))
	9.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	9.1b	(.f64 x (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (fma.f64 x -2 3) (fma.f64 x -2 3)) (fma.f64 x -2 3)))))
	1.1b	(.f64 (.f64 x (.f64 (cbrt.f64 (.f64 x (fma.f64 x -2 3))) (cbrt.f64 (.f64 x (fma.f64 x -2 3))))) (cbrt.f64 (+.f64 (.f64 (.f64 x -2) x) (.f64 3 x))))

Compiler

Compiled 1535 to 1052 computations (31.5% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3))))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))))
✓	0.3b	(.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (cbrt.f64 (.f64 x (*.f64 x (fma.f64 x -2 3)))))
✓	34.2b	(cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3))))

series18.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

7.0ms

(cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3))))

6.0ms

(*.f64 (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3)))) (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3)))))

4.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3)))) (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3))))) (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3)))))

rewrite19.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3)))) (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3))))) (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3)))))

6.0ms

(*.f64 (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3)))) (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3)))))

2.0ms

(cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x -2 3))))

simplify98.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-neg_binary64`
417×	`fma-def_binary64`
279×	`*-commutative_binary64`
254×	`cancel-sign-sub-inv_binary64`
179×	`exp-prod_binary64`

Counts

115 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	190	3105
1	474	2723
2	1415	2101
3	4103	2043
4	5016	2043

prune414.0ms (20.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	337	7	344

Error

Counts

344 → 7

Alt Table

Status	Error	Program
	32.6b	(.f64 (sqrt.f64 x) (.f64 (fma.f64 x -2 3) (pow.f64 x 3/2)))
	17.5b	(.f64 (.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x -2 3))) (sqrt.f64 (fma.f64 x -2 3)))
✓	0.7b	(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3))))) (cbrt.f64 (.f64 x (.f64 x (fma.f64 x -2 3)))))
✓	0.6b	(.f64 x (+.f64 (.f64 (.f64 x -2) x) (.f64 3 x)))
	9.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	9.1b	(.f64 x (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (fma.f64 x -2 3) (fma.f64 x -2 3)) (fma.f64 x -2 3)))))
	1.1b	(.f64 (.f64 x (.f64 (cbrt.f64 (.f64 x (fma.f64 x -2 3))) (cbrt.f64 (.f64 x (fma.f64 x -2 3))))) (cbrt.f64 (+.f64 (.f64 (.f64 x -2) x) (.f64 3 x))))

Compiler

Compiled 12612 to 9240 computations (26.7% saved)

regimes120.0ms (5.9%)

Accuracy

Total 0.1b remaining (92.6%)

Threshold costs 0.1b (92.6%)

Counts

68 → 1

Compiler

Compiled 1976 to 1388 computations (29.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	11
1	18	11
2	15	11

end106.0ms (5.2%)

Compiler: Compiled 153 to 110 computations (28.1% saved)

Details

analyze1.0ms (0%)

sample644.0ms (31.6%)

simplify165.0ms (8.1%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite5.0ms (0.3%)

simplify69.0ms (3.4%)

prune33.0ms (1.6%)

localize6.0ms (0.3%)

series6.0ms (0.3%)

rewrite8.0ms (0.4%)

simplify74.0ms (3.6%)

prune69.0ms (3.4%)

localize7.0ms (0.3%)

series7.0ms (0.3%)

rewrite13.0ms (0.6%)

simplify69.0ms (3.4%)

prune64.0ms (3.2%)

localize8.0ms (0.4%)

series18.0ms (0.9%)

rewrite19.0ms (0.9%)

simplify98.0ms (4.8%)

prune414.0ms (20.3%)

regimes120.0ms (5.9%)

simplify2.0ms (0.1%)

end106.0ms (5.2%)

Profiling