Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample995.0ms (33.2%)

Results

738.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify194.0ms (6.5%)

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)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite6.0ms (0.2%)

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))

simplify93.0ms (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

prune69.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	4	38

Error

0.0b

Counts

38 → 4

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) (cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)))) (cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))))
▶	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	5.3b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	0.4b	(.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 636 to 413 computations (35.1% saved)

localize9.0ms (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)))

series11.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))
5.0ms	(*.f64 x (fma.f64 x -2 3))

rewrite22.0ms (0.7%)

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:

10.0ms	(*.f64 x (fma.f64 x -2 3))
8.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))

simplify127.0ms (4.2%)

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

prune100.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	71	3	74

Error

0.0b

Counts

74 → 3

Alt Table

Status	Error	Program
▶	0.4b	(.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))))
✓	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	5.3b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 976 to 631 computations (35.3% saved)

localize21.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series41.0ms (1.4%)

Counts

4 → 48

Calls

4 calls:

14.0ms	(.f64 x (.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3))))
11.0ms	(*.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))
10.0ms	(cbrt.f64 (fma.f64 x -2 3))
6.0ms	(.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)))

rewrite47.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 102

Calls

4 calls:

17.0ms	(.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)))
10.0ms	(.f64 x (.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3))))
8.0ms	(*.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))
1.0ms	(cbrt.f64 (fma.f64 x -2 3))

simplify166.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

566×	`fma-def_binary64`
444×	`fma-neg_binary64`
364×	`cancel-sign-sub-inv_binary64`
245×	`distribute-rgt-in_binary64`
211×	`associate-r_binary64`

Counts

150 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	232	3622
1	602	3243
2	1960	2663
3	4950	2657
4	5242	2657

prune493.0ms (16.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	295	1	296
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	295	4	299

Error

Counts

299 → 4

Alt Table

Status	Error	Program
	13.8b	(.f64 x (.f64 (.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))) (cbrt.f64 (sqrt.f64 (fma.f64 x -2 3)))) (cbrt.f64 (sqrt.f64 (fma.f64 x -2 3)))))
▶	5.3b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.4b	(.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))))
✓	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))

Compiler

Compiled 9273 to 7398 computations (20.2% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 3))
✓	0.2b	(*.f64 3 (pow.f64 x 2))
✓	5.3b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

series14.0ms (0.5%)

Counts

3 → 3

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)))

rewrite28.0ms (0.9%)

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:

8.0ms	(*.f64 2 (pow.f64 x 3))
7.0ms	(*.f64 3 (pow.f64 x 2))
7.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

simplify150.0ms (5%)

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

prune104.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	114	4	118

Error

Counts

118 → 4

Alt Table

Status	Error	Program
	13.8b	(.f64 x (.f64 (.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))) (cbrt.f64 (sqrt.f64 (fma.f64 x -2 3)))) (cbrt.f64 (sqrt.f64 (fma.f64 x -2 3)))))
✓	5.3b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.4b	(.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))))
✓	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))

Compiler

Compiled 1962 to 1546 computations (21.2% saved)

regimes182.0ms (6.1%)

Accuracy

Total 0.1b remaining (86.1%)

Threshold costs 0.1b (86.1%)

Counts

78 → 1

Compiler

Compiled 2718 to 2098 computations (22.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	9	11
2	9	11

end100.0ms (3.3%)

Compiler: Compiled 91 to 69 computations (24.2% saved)

Details

analyze2.0ms (0.1%)

sample995.0ms (33.2%)

simplify194.0ms (6.5%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series4.0ms (0.1%)

rewrite6.0ms (0.2%)

simplify93.0ms (3.1%)

prune69.0ms (2.3%)

localize9.0ms (0.3%)

series11.0ms (0.4%)

rewrite22.0ms (0.7%)

simplify127.0ms (4.2%)

prune100.0ms (3.3%)

localize21.0ms (0.7%)

series41.0ms (1.4%)

rewrite47.0ms (1.6%)

simplify166.0ms (5.5%)

prune493.0ms (16.5%)

localize11.0ms (0.4%)

series14.0ms (0.5%)

rewrite28.0ms (0.9%)

simplify150.0ms (5%)

prune104.0ms (3.5%)

regimes182.0ms (6.1%)

simplify3.0ms (0.1%)

end100.0ms (3.3%)

Profiling