Details

analyze179.0ms (8.7%)

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)

sample13.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify160.0ms (7.8%)

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)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series4.0ms (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))

simplify61.0ms (3%)

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

prune34.0ms (1.7%)

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
	9.8b	(.f64 (sqrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) (sqrt.f64 (.f64 (*.f64 x x) (fma.f64 x -2 3))))
	26.1b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (.f64 (fma.f64 x -2 3) (fma.f64 x -2 3)) (fma.f64 x -2 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)))
	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)))

Compiler

Compiled 672 to 435 computations (35.3% 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 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.2b	(*.f64 3 (pow.f64 x 2))

series10.0ms (0.5%)

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))

rewrite15.0ms (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 2 (pow.f64 x 3))
4.0ms	(*.f64 3 (pow.f64 x 2))
4.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

simplify110.0ms (5.3%)

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

prune111.0ms (5.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	114	5	119

Error

0.0b

Counts

119 → 5

Alt Table

Status	Error	Program
	9.8b	(.f64 (sqrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) (sqrt.f64 (.f64 (*.f64 x x) (fma.f64 x -2 3))))
	26.1b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (.f64 (fma.f64 x -2 3) (fma.f64 x -2 3)) (fma.f64 x -2 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)))
▶	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 2053 to 1607 computations (21.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

simplify71.0ms (3.5%)

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

prune79.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

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

Error

0.0b

Counts

75 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 x (.f64 (.f64 x (.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))) (cbrt.f64 (fma.f64 x -2 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)))
	9.8b	(.f64 (sqrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) (sqrt.f64 (.f64 (*.f64 x x) (fma.f64 x -2 3))))
	26.1b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (.f64 (fma.f64 x -2 3) (fma.f64 x -2 3)) (fma.f64 x -2 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 1098 to 715 computations (34.9% saved)

localize10.0ms (0.5%)

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)))
✓	0.1b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (pow.f64 x 2)))
✓	0.2b	(*.f64 (cbrt.f64 3) (pow.f64 x 2))

series31.0ms (1.5%)

Counts

3 → 24

Calls

3 calls:

14.0ms

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

12.0ms

(-.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))

rewrite27.0ms (1.3%)

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:

9.0ms

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

8.0ms

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

6.0ms

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

simplify103.0ms (5%)

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

prune238.0ms (11.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	160	6	166

Error

Counts

166 → 6

Alt Table

Status	Error	Program
	0.2b	(-.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (cbrt.f64 3) x) x)) (*.f64 2 (pow.f64 x 3)))
	9.8b	(.f64 (sqrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) (sqrt.f64 (.f64 (*.f64 x x) (fma.f64 x -2 3))))
	26.1b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (.f64 (fma.f64 x -2 3) (fma.f64 x -2 3)) (fma.f64 x -2 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)))
	0.2b	(-.f64 (expm1.f64 (log1p.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 3845 to 3267 computations (15% saved)

regimes245.0ms (11.9%)

Accuracy

Total 0.1b remaining (91.5%)

Threshold costs 0.1b (91.5%)

Counts

109 → 1

Compiler

Compiled 3362 to 2650 computations (21.2% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	10	14
2	10	14

end1.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

sample511.0ms (24.8%)

Algorithm

1×

intervals

Results

242.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 132 to 99 computations (25% saved)

Details

analyze179.0ms (8.7%)

sample13.0ms (0.6%)

simplify160.0ms (7.8%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite5.0ms (0.3%)

simplify61.0ms (3%)

prune34.0ms (1.7%)

localize7.0ms (0.3%)

series10.0ms (0.5%)

rewrite15.0ms (0.7%)

simplify110.0ms (5.3%)

prune111.0ms (5.4%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite8.0ms (0.4%)

simplify71.0ms (3.5%)

prune79.0ms (3.8%)

localize10.0ms (0.5%)

series31.0ms (1.5%)

rewrite27.0ms (1.3%)

simplify103.0ms (5%)

prune238.0ms (11.6%)

regimes245.0ms (11.9%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample511.0ms (24.8%)

Profiling