Details

analyze1.4s (12.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample48.0ms (0.4%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
2.0ms	18×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	20	26
2	24	26
3	24	26

prune5.0ms (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

25.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.9b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))

Compiler

Compiled 66 to 32 computations (51.5% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y.re y.re (*.f64 y.im y.im))
✓	0.5b	(fma.f64 x.re y.re (*.f64 x.im y.im))
✓	25.4b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))

rewrite67.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`fma-udef_binary64`

Counts

3 → 112

Calls

3 calls:

21.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))
20.0ms	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
17.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

series348.0ms (3.1%)

Counts

3 → 120

Calls

3 calls:

241.0ms	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
66.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))
40.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

simplify332.0ms (3%)

Algorithm

1×	egg-herbie

Rules

934×	`times-frac_binary64`
487×	`associate-/l*_binary64`
337×	`fma-def_binary64`
276×	`fma-neg_binary64`
265×	`cancel-sign-sub-inv_binary64`

Counts

232 → 398

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	4312
1	353	4093
2	1282	3957
3	4874	3957
4	5009	3957

prune219.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	389	9	398
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	390	9	399

Error

5.4b

Counts

399 → 9

Alt Table

Status	Error	Program
▶	24.1b	(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
	26.1b	(.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
	42.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2))) 3))
	40.9b	(/.f64 (.f64 y.im x.im) (fma.f64 y.re y.re (.f64 y.im y.im)))
	34.7b	(fma.f64 (/.f64 y.im (pow.f64 y.re 2)) x.im (/.f64 x.re y.re))
	37.5b	(/.f64 x.re y.re)
	34.7b	(fma.f64 (/.f64 x.re (pow.f64 y.im 2)) y.re (/.f64 x.im y.im))
	45.3b	(/.f64 (pow.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 x.im y.im))) 2) (fma.f64 y.re y.re (.f64 y.im y.im)))
	39.0b	(/.f64 x.im y.im)

Compiler

Compiled 3770 to 1024 computations (72.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y.im y.im (pow.f64 y.re 2))
✓	1.6b	(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
✓	16.9b	(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))
✓	17.2b	(/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2)))

rewrite107.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
16×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 158

Calls

4 calls:

26.0ms	(/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2)))
23.0ms	(fma.f64 y.im y.im (pow.f64 y.re 2))
23.0ms	(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))
18.0ms	(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))

series500.0ms (4.5%)

Counts

4 → 132

Calls

4 calls:

259.0ms	(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
157.0ms	(/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2)))
45.0ms	(fma.f64 y.im y.im (pow.f64 y.re 2))
37.0ms	(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))

simplify467.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-neg_binary64`
419×	`cancel-sign-sub-inv_binary64`
395×	`fma-def_binary64`
287×	`associate-/r/_binary64`
231×	`associate-/l/_binary64`

Counts

290 → 483

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	220	6780
1	540	6490
2	1967	6352
3	4894	6352
4	5274	6352

prune499.0ms (4.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	480	3	483
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	483	9	492

Error

5.4b

Counts

492 → 9

Alt Table

Status	Error	Program
▶	22.8b	(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (.f64 (/.f64 y.re (.f64 (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))) (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))))) (/.f64 x.re (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))))))
	26.1b	(.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
	41.7b	(fma.f64 (/.f64 y.im (pow.f64 y.re 2)) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
	24.3b	(fma.f64 (.f64 y.im (/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2)))) x.im (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
	42.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2))) 3))
	37.5b	(/.f64 x.re y.re)
	34.7b	(fma.f64 (/.f64 x.re (pow.f64 y.im 2)) y.re (/.f64 x.im y.im))
	45.3b	(/.f64 (pow.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 x.im y.im))) 2) (fma.f64 y.re y.re (.f64 y.im y.im)))
	39.0b	(/.f64 x.im y.im)

Compiler

Compiled 7510 to 3942 computations (47.5% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	16.9b	(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))
	28.8b	(cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2)))
	28.8b	(cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2)))
✓	28.8b	(cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cube-cbrt_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`pow1/3_binary64`
3×	`log1p-expm1-u_binary64`
3×	`expm1-log1p-u_binary64`

Counts

1 → 30

Calls

1 calls:

18.0ms

(cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2)))

series73.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

72.0ms

(cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2)))

simplify136.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

771×	`fma-neg_binary64`
665×	`distribute-rgt-neg-in_binary64`
444×	`cancel-sign-sub-inv_binary64`
418×	`unswap-sqr_binary64`
273×	`associate-r_binary64`

Counts

54 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	1273
1	198	1255
2	500	1231
3	1740	1231
4	3733	1231
5	5238	1231

prune580.0ms (5.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	483	1	484
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	484	9	493

Error

5.4b

Counts

493 → 9

Alt Table

Status	Error	Program
✓	22.8b	(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (.f64 (/.f64 y.re (.f64 (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))) (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))))) (/.f64 x.re (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))))))
	26.1b	(.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
	42.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2))) 3))
▶	24.3b	(fma.f64 (.f64 y.im (/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2)))) x.im (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
	37.5b	(/.f64 x.re y.re)
	34.7b	(fma.f64 (/.f64 x.re (pow.f64 y.im 2)) y.re (/.f64 x.im y.im))
	45.3b	(/.f64 (pow.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 x.im y.im))) 2) (fma.f64 y.re y.re (.f64 y.im y.im)))
	39.0b	(/.f64 x.im y.im)
	40.4b	(fma.f64 (/.f64 y.im (pow.f64 y.re 2)) x.im (.f64 (/.f64 y.re (.f64 (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))) (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))))) (/.f64 x.re (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))))))

Compiler

Compiled 10608 to 6560 computations (38.2% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2)))
✓	1.6b	(fma.f64 (.f64 y.im (/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2)))) x.im (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
✓	16.9b	(*.f64 y.im (/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2))))
	17.2b	(/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2)))

rewrite98.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
13×	`pow1_binary64`

Counts

3 → 126

Calls

3 calls:

38.0ms

(*.f64 y.im (/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2))))

24.0ms

(/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2)))

22.0ms

(fma.f64 (*.f64 y.im (/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2)))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))

series328.0ms (2.9%)

Counts

3 → 96

Calls

3 calls:

265.0ms

(fma.f64 (*.f64 y.im (/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2)))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))

32.0ms

(*.f64 y.im (/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2))))

30.0ms

(/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2)))

simplify549.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

785×	`associate-/l*_binary64`
313×	`cancel-sign-sub-inv_binary64`
308×	`associate-/r/_binary64`
273×	`fma-def_binary64`
192×	`associate-/l/_binary64`

Counts

222 → 350

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	5579
1	447	5285
2	1712	5161
3	5575	5161

prune540.0ms (4.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	488	1	489
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	488	10	498

Error

5.2b

Counts

498 → 10

Alt Table

Status	Error	Program
✓	22.8b	(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (.f64 (/.f64 y.re (.f64 (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))) (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))))) (/.f64 x.re (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))))))
	26.1b	(.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
	39.5b	(fma.f64 (.f64 (fabs.f64 (/.f64 (sqrt.f64 y.im) (hypot.f64 y.im y.re))) (fabs.f64 (/.f64 (sqrt.f64 y.im) (hypot.f64 y.im y.re)))) x.im (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
	42.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2))) 3))
✓	24.3b	(fma.f64 (.f64 y.im (/.f64 1 (fma.f64 y.im y.im (pow.f64 y.re 2)))) x.im (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
	37.5b	(/.f64 x.re y.re)
	34.7b	(fma.f64 (/.f64 x.re (pow.f64 y.im 2)) y.re (/.f64 x.im y.im))
	45.3b	(/.f64 (pow.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 x.im y.im))) 2) (fma.f64 y.re y.re (.f64 y.im y.im)))
	39.0b	(/.f64 x.im y.im)
	40.4b	(fma.f64 (/.f64 y.im (pow.f64 y.re 2)) x.im (.f64 (/.f64 y.re (.f64 (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))) (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))))) (/.f64 x.re (cbrt.f64 (fma.f64 y.im y.im (pow.f64 y.re 2))))))

Compiler

Compiled 8075 to 4492 computations (44.4% saved)

regimes2.9s (26.1%)

Accuracy

Total 9.2b remaining (68%)

Threshold costs 0b (0%)

Compiler

Compiled 14288 to 8899 computations (37.7% saved)

bsearch92.0ms (0.8%)

Steps

Iters	Range	Point
5	2.4680245409095543e+30	6.420824084845101e+30	4.7526766511788395e+30
6	-9.088419335841466e-83	-1.1186950646027973e-83	-1.138134009878751e-83
10	-2.8871365287463673e+167	-4.468354710374448e+153	-6.889595916751356e+153

Iters

Range

Point

2.4680245409095543e+30

6.420824084845101e+30

4.7526766511788395e+30

-9.088419335841466e-83

-1.1186950646027973e-83

-1.138134009878751e-83

-2.8871365287463673e+167

-4.468354710374448e+153

-6.889595916751356e+153

Compiler

Compiled 5 to 4 computations (20% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`sqr-abs_binary64`
1×	`fabs-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	184
1	47	184
2	47	184

end3.0ms (0%)

Compiler: Compiled 101 to 55 computations (45.5% saved)

sample1.7s (15.4%)

Algorithm

1×

intervals

Results

786.0ms	8000×	body	128	valid
49.0ms	486×	body	128	invalid

Compiler

Compiled 348 to 206 computations (40.8% saved)

Details

analyze1.4s (12.6%)

sample48.0ms (0.4%)

simplify24.0ms (0.2%)

prune5.0ms (0%)

localize15.0ms (0.1%)

rewrite67.0ms (0.6%)

series348.0ms (3.1%)

simplify332.0ms (3%)

prune219.0ms (2%)

localize20.0ms (0.2%)

rewrite107.0ms (1%)

series500.0ms (4.5%)

simplify467.0ms (4.2%)

prune499.0ms (4.5%)

localize30.0ms (0.3%)

rewrite20.0ms (0.2%)

series73.0ms (0.6%)

simplify136.0ms (1.2%)

prune580.0ms (5.2%)

localize30.0ms (0.3%)

rewrite98.0ms (0.9%)

series328.0ms (2.9%)

simplify549.0ms (4.9%)

prune540.0ms (4.8%)

regimes2.9s (26.1%)

bsearch92.0ms (0.8%)

simplify11.0ms (0.1%)

end3.0ms (0%)

sample1.7s (15.4%)

Profiling