Details

analyze4.0ms (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
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	24.9%	13
75%	0%	25%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample746.0ms (35.8%)

Results

700.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify25.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

271×	`fma-def_binary64`
257×	`fma-neg_binary64`
76×	`cancel-sign-sub-inv_binary64`
55×	`sub-neg_binary64`
32×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	54	11
3	122	11
4	222	9
5	361	9
6	423	9
7	587	9
8	645	9
9	664	9
10	593	9

prune3.0ms (0.1%)

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 x (fma.f64 x -3/25 -253/1000) 1)
▶	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 x 3/25))))

Compiler

Compiled 53 to 41 computations (22.6% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 253/1000 (*.f64 x 3/25))
✓	0.2b	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))
✓	0.3b	(*.f64 x 3/25)

series6.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))
2.0ms	(+.f64 253/1000 (*.f64 x 3/25))
2.0ms	(*.f64 x 3/25)

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`

Counts

3 → 60

Calls

3 calls:

4.0ms	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))
4.0ms	(*.f64 x 3/25)
2.0ms	(+.f64 253/1000 (*.f64 x 3/25))

simplify74.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

747×	`associate-+l+_binary64`
687×	`fma-def_binary64`
673×	`associate-+r+_binary64`
364×	`unswap-sqr_binary64`
295×	`*-commutative_binary64`

Counts

96 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	864
1	207	699
2	630	692
3	1515	690
4	2469	690
5	4451	690
6	5059	690

prune116.0ms (5.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	99	7	106

Error

Counts

106 → 7

Alt Table

Status	Error	Program
	9.8b	(-.f64 1 (/.f64 (.f64 x (+.f64 (pow.f64 253/1000 3) (pow.f64 (.f64 x 3/25) 3))) (+.f64 (.f64 253/1000 253/1000) (-.f64 (.f64 (.f64 x 3/25) (.f64 x 3/25)) (.f64 253/1000 (.f64 x 3/25))))))
	22.2b	(-.f64 1 (.f64 (sqrt.f64 (.f64 x (fma.f64 3/25 x 253/1000))) (sqrt.f64 (*.f64 x (fma.f64 3/25 x 253/1000)))))
	6.4b	(-.f64 1 (.f64 x (+.f64 253/1000 (cbrt.f64 (pow.f64 (.f64 3/25 x) 3)))))
	0.4b	(-.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 x (fma.f64 3/25 x 253/1000))) (cbrt.f64 (.f64 x (fma.f64 3/25 x 253/1000)))) (cbrt.f64 (*.f64 x (fma.f64 3/25 x 253/1000)))))
▶	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.4b	(-.f64 1 (.f64 (.f64 x (.f64 (cbrt.f64 (fma.f64 3/25 x 253/1000)) (cbrt.f64 (fma.f64 3/25 x 253/1000)))) (cbrt.f64 (+.f64 253/1000 (.f64 x 3/25)))))
	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 (*.f64 x (sqrt.f64 3/25)) (sqrt.f64 3/25)))))

Compiler

Compiled 1719 to 1348 computations (21.6% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
✓	0.1b	(*.f64 253/1000 x)
✓	0.2b	(*.f64 3/25 (pow.f64 x 2))

series9.0ms (0.4%)

Counts

3 → 3

Calls

3 calls:

5.0ms	(*.f64 3/25 (pow.f64 x 2))
3.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
1.0ms	(*.f64 253/1000 x)

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`associate-r_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 63

Calls

3 calls:

5.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
4.0ms	(*.f64 3/25 (pow.f64 x 2))
3.0ms	(*.f64 253/1000 x)

simplify85.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
484×	`associate-l_binary64`
452×	`distribute-rgt-out_binary64`
388×	`associate-r_binary64`
351×	`cancel-sign-sub-inv_binary64`

Counts

66 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	705
1	226	611
2	573	582
3	2216	580
4	4154	580
5	4978	580
6	4929	580

prune113.0ms (5.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	93	6	99

Error

Counts

99 → 6

Alt Table

Status	Error	Program
	0.1b	(-.f64 1 (+.f64 (.f64 (.f64 3/25 x) x) (*.f64 253/1000 x)))
	9.8b	(-.f64 1 (/.f64 (.f64 x (+.f64 (pow.f64 253/1000 3) (pow.f64 (.f64 x 3/25) 3))) (+.f64 (.f64 253/1000 253/1000) (-.f64 (.f64 (.f64 x 3/25) (.f64 x 3/25)) (.f64 253/1000 (.f64 x 3/25))))))
	0.4b	(-.f64 1 (+.f64 (.f64 (.f64 3/25 (.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)) (.f64 253/1000 x)))
▶	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))
	6.4b	(-.f64 1 (.f64 x (+.f64 253/1000 (cbrt.f64 (pow.f64 (.f64 3/25 x) 3)))))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))

Compiler

Compiled 1707 to 1360 computations (20.3% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x))
	0.1b	(*.f64 253/1000 x)
✓	0.2b	(*.f64 (sqrt.f64 3/25) (pow.f64 x 2))
✓	0.2b	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))

series25.0ms (1.2%)

Counts

3 → 24

Calls

3 calls:

13.0ms	(+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x))
8.0ms	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))
4.0ms	(*.f64 (sqrt.f64 3/25) (pow.f64 x 2))

rewrite21.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
12×	`associate-l_binary64`
10×	`sqrt-prod_binary64`
10×	`add-cbrt-cube_binary64`

Counts

3 → 74

Calls

3 calls:

6.0ms	(*.f64 (sqrt.f64 3/25) (pow.f64 x 2))
6.0ms	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))
6.0ms	(+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x))

simplify97.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-neg_binary64`
382×	`unswap-sqr_binary64`
375×	`*-commutative_binary64`
290×	`fma-def_binary64`
219×	`distribute-rgt-in_binary64`

Counts

98 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	102	1180
1	255	1111
2	819	1068
3	1879	1040
4	3901	1000
5	4918	1000
6	4947	1000

prune143.0ms (6.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Status	Error	Program
	12.8b	(-.f64 1 (+.f64 (cbrt.f64 (.f64 (pow.f64 x 6) 27/15625)) (.f64 253/1000 x)))
▶	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 3/25 x))))
✓	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))
	6.4b	(-.f64 1 (.f64 x (+.f64 253/1000 (cbrt.f64 (pow.f64 (.f64 3/25 x) 3)))))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))

Compiler

Compiled 2780 to 2332 computations (16.1% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 253/1000 (*.f64 3/25 x))
✓	0.2b	(.f64 x (+.f64 253/1000 (.f64 3/25 x)))
✓	0.3b	(*.f64 3/25 x)

series6.0ms (0.3%)

Counts

3 → 15

Calls

3 calls:

3.0ms	(.f64 x (+.f64 253/1000 (.f64 3/25 x)))
2.0ms	(*.f64 3/25 x)
2.0ms	(+.f64 253/1000 (*.f64 3/25 x))

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`

Counts

3 → 60

Calls

3 calls:

5.0ms	(.f64 x (+.f64 253/1000 (.f64 3/25 x)))
3.0ms	(*.f64 3/25 x)
2.0ms	(+.f64 253/1000 (*.f64 3/25 x))

simplify105.0ms (5%)

Algorithm

1×	egg-herbie

Rules

474×	`associate-l_binary64`
364×	`associate-r_binary64`
355×	`+-commutative_binary64`
345×	`fma-neg_binary64`
281×	`distribute-rgt-out_binary64`

Counts

75 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	753
1	212	606
2	619	597
3	1832	597
4	2948	597
5	4090	597
6	4944	597
7	4870	597

prune94.0ms (4.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	101	5	106

Error

Counts

106 → 5

Alt Table

Status	Error	Program
	12.8b	(-.f64 1 (+.f64 (cbrt.f64 (.f64 (pow.f64 x 6) 27/15625)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (.f64 x (+.f64 253/1000 (.f64 3/25 x))))
✓	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))
	6.4b	(-.f64 1 (.f64 x (+.f64 253/1000 (cbrt.f64 (pow.f64 (.f64 3/25 x) 3)))))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))

Compiler

Compiled 1481 to 1166 computations (21.3% saved)

regimes266.0ms (12.8%)

Accuracy

Total 0.2b remaining (91.4%)

Threshold costs 0.2b (91.4%)

Counts

91 → 1

Compiler

Compiled 4034 to 3242 computations (19.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	15	14
2	19	14
3	21	14
4	22	14
5	21	14

end82.0ms (3.9%)

Compiler: Compiled 86 to 72 computations (16.3% saved)

Details

analyze4.0ms (0.2%)

sample746.0ms (35.8%)

simplify25.0ms (1.2%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite12.0ms (0.6%)

simplify74.0ms (3.6%)

prune116.0ms (5.6%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite13.0ms (0.6%)

simplify85.0ms (4.1%)

prune113.0ms (5.4%)

localize9.0ms (0.5%)

series25.0ms (1.2%)

rewrite21.0ms (1%)

simplify97.0ms (4.6%)

prune143.0ms (6.9%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite12.0ms (0.6%)

simplify105.0ms (5%)

prune94.0ms (4.5%)

regimes266.0ms (12.8%)

simplify2.0ms (0.1%)

end82.0ms (3.9%)

Profiling