Details

analyze2.5s (14.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample88.0ms (0.5%)

Algorithm

1×

intervals

Results

37.0ms	256×	body	128	valid
20.0ms	110×	body	128	invalid
6.0ms	58×	body	128	nan

Compiler

Compiled 40 to 28 computations (30% saved)

simplify169.0ms (1%)

Algorithm

1×	egg-herbie

Rules

614×	`*-commutative_binary64`
613×	`associate-l_binary64`
526×	`sqr-pow_binary64`
394×	`associate-*r/_binary64`
380×	`cube-prod_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	18
2	55	17
3	104	17
4	225	17
5	591	17
6	1774	17
7	2466	17
8	2534	17
9	2692	17
10	2908	17
11	3166	17
12	3656	17
13	4497	17
14	5019	17

prune6.0ms (0%)

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

2.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	2.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cube-cbrt_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 81

Calls

2 calls:

27.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
23.0ms	(*.f64 a (pow.f64 k m))

series1.9s (11.1%)

Counts

2 → 72

Calls

2 calls:

1.1s	(*.f64 a (pow.f64 k m))
816.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

simplify179.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-def_binary64`
452×	`fma-neg_binary64`
375×	`unswap-sqr_binary64`
292×	`prod-exp_binary64`
267×	`cancel-sign-sub-inv_binary64`

Counts

153 → 249

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	2633
1	508	2404
2	1893	2184
3	3976	2158
4	5142	2158

prune221.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	246	3	249
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	246	4	250

Error

2.1b

Counts

250 → 4

Alt Table

Status	Error	Program
✓	2.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
	15.0b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) 2)
▶	2.2b	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
	11.3b	(/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 2)) (cbrt.f64 (*.f64 a (pow.f64 k m)))) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 2817 to 1523 computations (45.9% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.1b	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
✓	2.1b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`pow-to-exp_binary64`

Counts

2 → 89

Calls

2 calls:

25.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))
24.0ms	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)

series2.1s (12.5%)

Counts

2 → 72

Calls

2 calls:

1.1s	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
932.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

simplify280.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

323×	`times-frac_binary64`
314×	`associate-r_binary64`
255×	`associate-/l*_binary64`
235×	`fma-neg_binary64`
222×	`associate-+r+_binary64`

Counts

161 → 273

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	346	5376
1	1022	4839
2	4411	4688
3	4981	4688
4	5012	4688

prune566.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	389	1	390
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	389	5	394

Error

0.0b

Counts

394 → 5

Alt Table

Status	Error	Program
✓	2.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
	15.0b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) 2)
✓	2.2b	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
	26.3b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 (/.f64 1 k) (neg.f64 m)) k) (.f64 (.f64 (/.f64 a (pow.f64 k 3)) (pow.f64 (/.f64 1 k) (neg.f64 m))) -10))
▶	11.3b	(/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 2)) (cbrt.f64 (*.f64 a (pow.f64 k m)))) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 7168 to 4248 computations (40.7% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 2)) (cbrt.f64 (*.f64 a (pow.f64 k m))))
✓	0.6b	(cbrt.f64 (*.f64 a (pow.f64 k m)))
✓	2.2b	(/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 2)) (cbrt.f64 (*.f64 a (pow.f64 k m)))) (fma.f64 k (+.f64 k 10) 1))
✓	15.8b	(cbrt.f64 (pow.f64 (*.f64 a (pow.f64 k m)) 2))

rewrite120.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-cube-cbrt_binary64`
22×	`pow1/3_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
12×	`add-cbrt-cube_binary64`

Counts

4 → 145

Calls

4 calls:

32.0ms	(/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 2)) (cbrt.f64 (*.f64 a (pow.f64 k m)))) (fma.f64 k (+.f64 k 10) 1))
27.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 2)) (cbrt.f64 (*.f64 a (pow.f64 k m))))
23.0ms	(cbrt.f64 (*.f64 a (pow.f64 k m)))
21.0ms	(cbrt.f64 (pow.f64 (*.f64 a (pow.f64 k m)) 2))

series5.2s (30.9%)

Counts

4 → 144

Calls

4 calls:

2.5s	(cbrt.f64 (pow.f64 (*.f64 a (pow.f64 k m)) 2))
1.7s	(cbrt.f64 (*.f64 a (pow.f64 k m)))
555.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 2)) (cbrt.f64 (*.f64 a (pow.f64 k m))))
409.0ms	(/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 2)) (cbrt.f64 (*.f64 a (pow.f64 k m)))) (fma.f64 k (+.f64 k 10) 1))

simplify195.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-neg_binary64`
325×	`cancel-sign-sub-inv_binary64`
291×	`log-prod_binary64`
280×	`associate-r_binary64`
216×	`prod-exp_binary64`

Counts

289 → 504

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	308	5497
1	786	4508
2	2756	3802
3	3866	3753
4	4903	3753
5	5148	3753

prune294.0ms (1.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	503	1	504
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	504	5	509

Error

0.0b

Counts

509 → 5

Alt Table

Status	Error	Program
✓	2.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
▶	15.0b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) 2)
✓	2.2b	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
	25.0b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	11.3b	(/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 2)) (cbrt.f64 (*.f64 a (pow.f64 k m)))) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 7004 to 3505 computations (50% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.1b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) 2)
	2.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
✓	8.7b	(sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1)))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cube-cbrt_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`pow1_binary64`
6×	`add-cbrt-cube_binary64`
6×	`log1p-expm1-u_binary64`

Counts

2 → 80

Calls

2 calls:

11.0ms	(pow.f64 (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) 2)
10.0ms	(sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1)))

series227.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

134.0ms	(pow.f64 (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) 2)
93.0ms	(sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1)))

simplify196.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-neg_binary64`
459×	`cancel-sign-sub-inv_binary64`
319×	`times-frac_binary64`
190×	`distribute-rgt-neg-in_binary64`
183×	`associate-r_binary64`

Counts

128 → 219

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	241	3381
1	630	2917
2	2074	2484
3	4030	2431
4	4832	2431
5	4974	2431
6	4891	2431

prune224.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	584	1	585
Fresh	0	1	1
Picked	1	0	1
Done	1	2	3
Total	586	4	590

Error

0.0b

Counts

590 → 4

Alt Table

Status	Error	Program
	25.3b	(pow.f64 (/.f64 (sqrt.f64 (*.f64 a (pow.f64 k m))) k) 2)
	25.0b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	2.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
✓	2.2b	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)

Compiler

Compiled 7139 to 4234 computations (40.7% saved)

regimes179.0ms (1.1%)

Accuracy

Total 0.0b remaining (56.8%)

Threshold costs 0.0b (56.8%)

Compiler

Compiled 2820 to 1930 computations (31.6% saved)

bsearch11.0ms (0.1%)

Steps

Iters	Range		Point
3	1.3851549757423743e+23	4.521787758671721e+23	2.2014896057993437e+23

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	52
1	29	52
2	28	52

end1.0ms (0%)

Compiler: Compiled 39 to 22 computations (43.6% saved)

sample2.0s (11.9%)

Algorithm

1×

intervals

Results

779.0ms	8000×	body	128	valid
430.0ms	3248×	body	128	invalid
130.0ms	1930×	body	128	nan

Compiler

Compiled 129 to 82 computations (36.4% saved)

Details

analyze2.5s (14.7%)

sample88.0ms (0.5%)

simplify169.0ms (1%)

prune6.0ms (0%)

localize15.0ms (0.1%)

rewrite59.0ms (0.4%)

series1.9s (11.1%)

simplify179.0ms (1.1%)

prune221.0ms (1.3%)

localize17.0ms (0.1%)

rewrite58.0ms (0.3%)

series2.1s (12.5%)

simplify280.0ms (1.7%)

prune566.0ms (3.4%)

localize26.0ms (0.2%)

rewrite120.0ms (0.7%)

series5.2s (30.9%)

simplify195.0ms (1.2%)

prune294.0ms (1.8%)

localize10.0ms (0.1%)

rewrite27.0ms (0.2%)

series227.0ms (1.4%)

simplify196.0ms (1.2%)

prune224.0ms (1.3%)

regimes179.0ms (1.1%)

bsearch11.0ms (0.1%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.0s (11.9%)

Profiling