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)

sample46.0ms (2.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify25.0ms (1.3%)

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

prune4.0ms (0.2%)

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

Compiler

Compiled 53 to 41 computations (22.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(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 (fma.f64 x -3/25 -253/1000) 1)
0.0ms	(fma.f64 x -3/25 -253/1000)

simplify75.0ms (4%)

Algorithm

1×	egg-herbie

Rules

549×	`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

prune41.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	32	6	38
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	34	6	40

Error

0.0b

Counts

40 → 6

Alt Table

Status	Error	Program
	51.6b	(fma.f64 x (*.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) (sqrt.f64 (fma.f64 x -3/25 -253/1000))) 1)
	7.7b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
	0.1b	(*.f64 1 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1))
	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)))
	14.4b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1) 3))
▶	0.1b	(+.f64 (neg.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))) 1)

Compiler

Compiled 541 to 418 computations (22.7% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (neg.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))) 1)
✓	0.1b	(*.f64 253/1000 x)
✓	0.1b	(fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))

series7.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

3.0ms	(fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))
2.0ms	(+.f64 (neg.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))) 1)
2.0ms	(*.f64 253/1000 x)

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
10×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 58

Calls

3 calls:

5.0ms	(+.f64 (neg.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))) 1)
3.0ms	(*.f64 253/1000 x)
0.0ms	(fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))

simplify86.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-neg_binary64`
389×	`times-frac_binary64`
263×	`associate-l_binary64`
251×	`distribute-rgt-neg-out_binary64`
242×	`unsub-neg_binary64`

Counts

82 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	931
1	185	804
2	469	696
3	2036	650
4	4136	650
5	5081	650

prune90.0ms (4.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	89	6	95

Error

0.0b

Counts

95 → 6

Alt Table

Status	Error	Program
	7.7b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
	21.6b	(fma.f64 (sqrt.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))) (neg.f64 (sqrt.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x)))) 1)
▶	0.1b	(*.f64 1 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1))
	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)))
	14.4b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1) 3))
✓	0.1b	(+.f64 (neg.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))) 1)

Compiler

Compiled 1561 to 1100 computations (29.5% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

prune59.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	38	6	44

Error

0.0b

Counts

44 → 6

Alt Table

Status	Error	Program
	7.7b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
	21.6b	(fma.f64 (sqrt.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))) (neg.f64 (sqrt.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x)))) 1)
✓	0.1b	(*.f64 1 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1))
▶	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)))
	14.4b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1) 3))
✓	0.1b	(+.f64 (neg.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))) 1)

Compiler

Compiled 609 to 483 computations (20.7% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
✓	0.2b	(.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)))
✓	0.2b	(*.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)))
✓	0.2b	(cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1))

series16.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

7.0ms

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

6.0ms

(*.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)))

3.0ms

(*.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)))

rewrite21.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

9.0ms

(*.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)))

5.0ms

(*.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)))

1.0ms

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

simplify142.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
358×	`associate-l_binary64`
358×	`fma-def_binary64`
283×	`associate-r_binary64`
219×	`sub-neg_binary64`

Counts

129 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	3216
1	428	2859
2	1114	2332
3	3679	2128
4	4899	2128
5	4973	2128

prune499.0ms (26.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	309	1	310
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	309	7	316

Error

Counts

316 → 7

Alt Table

Status	Error	Program
	7.7b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
	21.6b	(fma.f64 (sqrt.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))) (neg.f64 (sqrt.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x)))) 1)
✓	0.1b	(*.f64 1 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1))
✓	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)))
	14.4b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1) 3))
	0.8b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1))) 6) (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1)))
✓	0.1b	(+.f64 (neg.f64 (fma.f64 3/25 (.f64 x x) (.f64 253/1000 x))) 1)

Compiler

Compiled 10304 to 8195 computations (20.5% saved)

regimes217.0ms (11.5%)

Accuracy

Total 0.2b remaining (88.2%)

Threshold costs 0.2b (88.2%)

Counts

60 → 1

Compiler

Compiled 2808 to 2225 computations (20.8% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	17	14
2	20	14
3	21	14
4	20	14

end1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample510.0ms (27%)

Algorithm

1×

intervals

Results

245.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 137 to 106 computations (22.6% saved)

Details

analyze4.0ms (0.2%)

sample46.0ms (2.4%)

simplify25.0ms (1.3%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify75.0ms (4%)

prune41.0ms (2.2%)

localize8.0ms (0.4%)

series7.0ms (0.4%)

rewrite11.0ms (0.6%)

simplify86.0ms (4.5%)

prune90.0ms (4.8%)

localize6.0ms (0.3%)

prune59.0ms (3.1%)

localize8.0ms (0.4%)

series16.0ms (0.9%)

rewrite21.0ms (1.1%)

simplify142.0ms (7.5%)

prune499.0ms (26.4%)

regimes217.0ms (11.5%)

simplify3.0ms (0.2%)

end1.0ms (0%)

sample510.0ms (27%)

Profiling