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)

sample798.0ms (42.1%)

Results

751.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify27.0ms (1.4%)

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

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	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 33 to 25 computations (24.2% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
✓	0.1b	(fma.f64 x -3/25 -253/1000)

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
2.0ms	(fma.f64 x -3/25 -253/1000)

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 x -3/25 -253/1000)
0.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

simplify70.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-l_binary64`
533×	`fma-neg_binary64`
477×	`associate-r_binary64`
446×	`unsub-neg_binary64`
418×	`times-frac_binary64`

Counts

44 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	455
1	77	344
2	166	341
3	592	341
4	2915	341
5	4504	341
6	5515	341

prune35.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	4	39

Error

0.0b

Counts

39 → 4

Alt Table

Status	Error	Program
	0.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1))) (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1)))
	12.1b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1) 3))
▶	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 477 to 369 computations (22.6% 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))

series7.0ms (0.4%)

Counts

3 → 3

Calls

3 calls:

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

rewrite13.0ms (0.7%)

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

simplify88.0ms (4.7%)

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

prune91.0ms (4.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	91	5	96

Error

Counts

96 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
▶	0.1b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	12.1b	(-.f64 1 (+.f64 (cbrt.f64 (.f64 27/15625 (pow.f64 x 6))) (.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)))

Compiler

Compiled 1623 to 1294 computations (20.3% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (sqrt.f64 3/25))
✓	0.0b	(+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x))
	0.1b	(*.f64 253/1000 x)
✓	0.3b	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))

series21.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

10.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))
7.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x))
4.0ms	(*.f64 x (sqrt.f64 3/25))

rewrite20.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`pow1_binary64`
18×	`pow-prod-down_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

3 → 74

Calls

3 calls:

6.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x))
6.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))
5.0ms	(*.f64 x (sqrt.f64 3/25))

simplify73.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-neg_binary64`
341×	`distribute-lft-out_binary64`
340×	`fma-def_binary64`
326×	`cancel-sign-sub-inv_binary64`
315×	`unswap-sqr_binary64`

Counts

110 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	981
1	223	899
2	797	829
3	2066	829
4	4718	829
5	5053	829

prune146.0ms (7.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	152	5	157

Error

Counts

157 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	12.1b	(-.f64 1 (+.f64 (cbrt.f64 (.f64 27/15625 (pow.f64 x 6))) (.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)))

Compiler

Compiled 3078 to 2440 computations (20.7% 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)))

series21.0ms (1.1%)

Counts

3 → 24

Calls

3 calls:

9.0ms	(+.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 (1.1%)

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))

simplify95.0ms (5%)

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 (7.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	133	5	138

Error

Counts

138 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	12.1b	(-.f64 1 (+.f64 (cbrt.f64 (.f64 27/15625 (pow.f64 x 6))) (.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)))

Compiler

Compiled 2745 to 2302 computations (16.1% saved)

regimes111.0ms (5.9%)

Accuracy

Total 0.1b remaining (88.2%)

Threshold costs 0.1b (88.2%)

Counts

36 → 1

Compiler

Compiled 1438 to 1158 computations (19.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
2	8	9

end74.0ms (3.9%)

Compiler: Compiled 81 to 66 computations (18.5% saved)

Details

analyze4.0ms (0.2%)

sample798.0ms (42.1%)

simplify27.0ms (1.4%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify70.0ms (3.7%)

prune35.0ms (1.8%)

localize6.0ms (0.3%)

series7.0ms (0.4%)

rewrite13.0ms (0.7%)

simplify88.0ms (4.7%)

prune91.0ms (4.8%)

localize7.0ms (0.4%)

series21.0ms (1.1%)

rewrite20.0ms (1.1%)

simplify73.0ms (3.8%)

prune146.0ms (7.7%)

localize9.0ms (0.5%)

series21.0ms (1.1%)

rewrite21.0ms (1.1%)

simplify95.0ms (5%)

prune143.0ms (7.5%)

regimes111.0ms (5.9%)

simplify3.0ms (0.1%)

end74.0ms (3.9%)

Profiling