Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
62.5%	6.2%	31.3%	6
65.6%	3.1%	31.3%	7
65.6%	1.6%	32.8%	8
66.4%	0.8%	32.8%	9
66.4%	0.4%	33.2%	10
66.6%	0.2%	33.2%	11
66.6%	0.1%	33.3%	12
66.6%	0%	33.4%	13
66.6%	0%	33.4%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample915.0ms (41.2%)

Results

728.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify163.0ms (7.3%)

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))

Compiler

Compiled 36 to 23 computations (36.1% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite6.0ms (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:

5.0ms

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

simplify69.0ms (3.1%)

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

prune36.0ms (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
	8.1b	(.f64 (.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x -2 3))) (sqrt.f64 (fma.f64 x -2 3)))
	0.6b	(.f64 (.f64 (.f64 x x) (.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))) (cbrt.f64 (fma.f64 x -2 3)))
	25.0b	(cbrt.f64 (pow.f64 (.f64 x (.f64 x (fma.f64 x -2 3))) 3))
	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
▶	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 632 to 417 computations (34% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 3))
✓	0.0b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.2b	(*.f64 3 (pow.f64 x 2))

series9.0ms (0.4%)

Counts

3 → 3

Calls

3 calls:

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

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

5.0ms	(*.f64 3 (pow.f64 x 2))
5.0ms	(*.f64 2 (pow.f64 x 3))
4.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

simplify116.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-def_binary64`
465×	`fma-neg_binary64`
389×	`exp-prod_binary64`
316×	`distribute-rgt-neg-in_binary64`
308×	`distribute-lft-neg-in_binary64`

Counts

81 → 114

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	1015
1	258	861
2	724	817
3	1848	788
4	3852	780
5	4761	780
6	4994	780
7	4715	780

prune105.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	4	0	4
Picked	0	1	1
Done	0	0	0
Total	114	5	119

Error

Counts

119 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 (.f64 3 x) x) (*.f64 2 (pow.f64 x 3)))
	48.8b	(/.f64 (fma.f64 27 (pow.f64 x 6) (.f64 (pow.f64 x 9) -8)) (fma.f64 3 (fma.f64 2 (pow.f64 x 5) (.f64 3 (pow.f64 x 4))) (*.f64 (pow.f64 x 6) 4)))
	0.8b	(-.f64 (.f64 (.f64 3 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 2)) (pow.f64 (cbrt.f64 x) 2)) (.f64 2 (pow.f64 x 3)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	0.2b	(-.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (pow.f64 x 2))) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 2063 to 1631 computations (20.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 2 (pow.f64 x 3))
✓	0.0b	(-.f64 (.f64 (.f64 3 x) x) (*.f64 2 (pow.f64 x 3)))
✓	0.2b	(.f64 (.f64 3 x) x)

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (.f64 (.f64 3 x) x) (*.f64 2 (pow.f64 x 3)))
2.0ms	(.f64 (.f64 3 x) x)

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r_binary64`

Counts

2 → 36

Calls

2 calls:

4.0ms	(-.f64 (.f64 (.f64 3 x) x) (*.f64 2 (pow.f64 x 3)))
4.0ms	(.f64 (.f64 3 x) x)

simplify88.0ms (4%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-def_binary64`
739×	`fma-neg_binary64`
354×	`times-frac_binary64`
295×	`*-commutative_binary64`
202×	`cancel-sign-sub-inv_binary64`

Counts

60 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	768
1	184	703
2	670	662
3	1542	613
4	3718	613
5	4938	613
6	5064	613

prune87.0ms (3.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	100	5	105

Error

Counts

105 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 (.f64 3 x) x) (*.f64 2 (pow.f64 x 3)))
	48.8b	(/.f64 (fma.f64 27 (pow.f64 x 6) (.f64 (pow.f64 x 9) -8)) (fma.f64 3 (fma.f64 2 (pow.f64 x 5) (.f64 3 (pow.f64 x 4))) (*.f64 (pow.f64 x 6) 4)))
	0.8b	(-.f64 (.f64 (.f64 3 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 2)) (pow.f64 (cbrt.f64 x) 2)) (.f64 2 (pow.f64 x 3)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
▶	0.2b	(-.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (pow.f64 x 2))) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 1798 to 1315 computations (26.9% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 2 (pow.f64 x 3))
✓	0.0b	(-.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (pow.f64 x 2))) (.f64 2 (pow.f64 x 3)))
✓	0.2b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (pow.f64 x 2)))
✓	0.3b	(*.f64 (cbrt.f64 3) (pow.f64 x 2))

series45.0ms (2%)

Counts

3 → 24

Calls

3 calls:

30.0ms

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (pow.f64 x 2)))

10.0ms

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

5.0ms

(*.f64 (cbrt.f64 3) (pow.f64 x 2))

rewrite25.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
21×	`prod-exp_binary64`
19×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
9×	`associate-r_binary64`

Counts

3 → 78

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (pow.f64 x 2)))

8.0ms

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

5.0ms

(*.f64 (cbrt.f64 3) (pow.f64 x 2))

simplify102.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-neg_binary64`
325×	`*-commutative_binary64`
292×	`fma-def_binary64`
257×	`cancel-sign-sub-inv_binary64`
238×	`exp-prod_binary64`

Counts

102 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1373
1	257	1152
2	881	1113
3	2048	1112
4	4454	1112
5	4965	1112
6	4848	1112

prune178.0ms (8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	2	0	2
Picked	0	1	1
Done	1	1	2
Total	161	4	165

Error

Counts

165 → 4

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 (.f64 x x) (+.f64 3 (*.f64 x -2))) 0)
	0.2b	(-.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 x (cbrt.f64 (sqrt.f64 3))) (.f64 x (cbrt.f64 (sqrt.f64 3))))) (.f64 2 (pow.f64 x 3)))
✓	0.1b	(-.f64 (.f64 (.f64 3 x) x) (*.f64 2 (pow.f64 x 3)))
✓	0.2b	(-.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (pow.f64 x 2))) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 3803 to 3242 computations (14.8% saved)

regimes122.0ms (5.5%)

Accuracy

Total 0.1b remaining (83%)

Threshold costs 0.1b (83%)

Counts

66 → 1

Compiler

Compiled 2066 to 1610 computations (22.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	18	16
2	26	16
3	30	16
4	33	16
5	34	16
6	33	16

end82.0ms (3.7%)

Compiler: Compiled 91 to 74 computations (18.7% saved)

Details

analyze5.0ms (0.2%)

sample915.0ms (41.2%)

simplify163.0ms (7.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite6.0ms (0.3%)

simplify69.0ms (3.1%)

prune36.0ms (1.6%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite16.0ms (0.7%)

simplify116.0ms (5.2%)

prune105.0ms (4.7%)

localize7.0ms (0.3%)

series6.0ms (0.3%)

rewrite9.0ms (0.4%)

simplify88.0ms (4%)

prune87.0ms (3.9%)

localize9.0ms (0.4%)

series45.0ms (2%)

rewrite25.0ms (1.1%)

simplify102.0ms (4.6%)

prune178.0ms (8%)

regimes122.0ms (5.5%)

simplify3.0ms (0.1%)

end82.0ms (3.7%)

Profiling