Details

analyze350.0ms (14.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
25%	75%	0%	4
37.5%	50%	12.5%	5
43.7%	37.5%	18.8%	6
46.9%	31.2%	21.9%	7
46.9%	29.7%	23.5%	8
46.9%	28.9%	24.3%	9
47.2%	28.1%	24.6%	10
47.3%	27.8%	24.8%	11
47.4%	27.7%	24.9%	12
47.4%	27.6%	24.9%	13
47.5%	27.6%	25%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample791.0ms (33.5%)

Results

745.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 21 to 17 computations (19% saved)

simplify24.0ms (1%)

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)

simplify71.0ms (3%)

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

prune37.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	4	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	5	39

Error

0.0b

Counts

39 → 5

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.5b	(.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)))
	0.5b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x -3/25 -253/1000)) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) 1)
	9.1b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 x -3/25 -253/1000) (fma.f64 x -3/25 -253/1000)) (fma.f64 x -3/25 -253/1000))) 1)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 535 to 415 computations (22.4% saved)

localize7.0ms (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)
✓	0.4b	(*.f64 3/25 (pow.f64 x 2))

series8.0ms (0.3%)

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))
2.0ms	(*.f64 253/1000 x)

rewrite14.0ms (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)

simplify87.0ms (3.7%)

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

prune106.0ms (4.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	90	7	97

Error

0.0b

Counts

97 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	0.4b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))
▶	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.3b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.5b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x -3/25 -253/1000)) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) 1)
	0.7b	(-.f64 1 (+.f64 (.f64 (.f64 3/25 (.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))) (.f64 253/1000 x)))
	9.1b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 x -3/25 -253/1000) (fma.f64 x -3/25 -253/1000)) (fma.f64 x -3/25 -253/1000))) 1)

Compiler

Compiled 1723 to 1374 computations (20.3% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series20.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

9.0ms	(.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))
3.0ms	(*.f64 x (sqrt.f64 3/25))

rewrite23.0ms (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:

7.0ms	(+.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))

simplify76.0ms (3.2%)

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

prune166.0ms (7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	3	1	4
Picked	0	1	1
Done	0	2	2
Total	154	5	159

Error

0.0b

Counts

159 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	0.4b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))
✓	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.3b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
▶	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 (.f64 x (fabs.f64 (cbrt.f64 3/25))) (sqrt.f64 (cbrt.f64 3/25)))) (*.f64 253/1000 x)))

Compiler

Compiled 3094 to 2454 computations (20.7% saved)

localize16.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 253/1000 x)
✓	0.2b	(.f64 (.f64 x (fabs.f64 (cbrt.f64 3/25))) (sqrt.f64 (cbrt.f64 3/25)))
✓	0.3b	(.f64 (.f64 x (sqrt.f64 3/25)) (.f64 (.f64 x (fabs.f64 (cbrt.f64 3/25))) (sqrt.f64 (cbrt.f64 3/25))))
✓	0.4b	(*.f64 x (fabs.f64 (cbrt.f64 3/25)))

series31.0ms (1.3%)

Counts

3 → 36

Calls

3 calls:

16.0ms

(*.f64 (*.f64 x (sqrt.f64 3/25)) (*.f64 (*.f64 x (fabs.f64 (cbrt.f64 3/25))) (sqrt.f64 (cbrt.f64 3/25))))

11.0ms

(*.f64 (*.f64 x (fabs.f64 (cbrt.f64 3/25))) (sqrt.f64 (cbrt.f64 3/25)))

3.0ms

(*.f64 x (fabs.f64 (cbrt.f64 3/25)))

rewrite27.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
31×	`pow1_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 88

Calls

3 calls:

11.0ms

(*.f64 (*.f64 x (sqrt.f64 3/25)) (*.f64 (*.f64 x (fabs.f64 (cbrt.f64 3/25))) (sqrt.f64 (cbrt.f64 3/25))))

6.0ms

(*.f64 (*.f64 x (fabs.f64 (cbrt.f64 3/25))) (sqrt.f64 (cbrt.f64 3/25)))

4.0ms

(*.f64 x (fabs.f64 (cbrt.f64 3/25)))

simplify114.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

534×	`sqr-pow_binary64`
513×	`*-commutative_binary64`
347×	`associate-l_binary64`
321×	`fma-def_binary64`
297×	`associate-r_binary64`

Counts

124 → 123

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	129	2347
1	289	1696
2	960	1692
3	1538	1692
4	2610	1688
5	3829	1688
6	5058	1688

prune168.0ms (7.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	145	5	150

Error

0.0b

Counts

150 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	0.4b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))
✓	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.3b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 (.f64 x (fabs.f64 (cbrt.f64 3/25))) (sqrt.f64 (cbrt.f64 3/25)))) (*.f64 253/1000 x)))

Compiler

Compiled 3905 to 3320 computations (15% saved)

regimes129.0ms (5.4%)

Accuracy

Total 0.1b remaining (92.9%)

Threshold costs 0.1b (92.9%)

Counts

41 → 1

Compiler

Compiled 1780 to 1434 computations (19.4% saved)

simplify2.0ms (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

end78.0ms (3.3%)

Compiler: Compiled 89 to 73 computations (18% saved)

Details

analyze350.0ms (14.8%)

sample791.0ms (33.5%)

simplify24.0ms (1%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify71.0ms (3%)

prune37.0ms (1.6%)

localize7.0ms (0.3%)

series8.0ms (0.3%)

rewrite14.0ms (0.6%)

simplify87.0ms (3.7%)

prune106.0ms (4.5%)

localize7.0ms (0.3%)

series20.0ms (0.8%)

rewrite23.0ms (1%)

simplify76.0ms (3.2%)

prune166.0ms (7%)

localize16.0ms (0.7%)

series31.0ms (1.3%)

rewrite27.0ms (1.2%)

simplify114.0ms (4.8%)

prune168.0ms (7.1%)

regimes129.0ms (5.4%)

simplify2.0ms (0.1%)

end78.0ms (3.3%)

Profiling