Details

analyze421.0ms (10.7%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.5s (39.5%)

Results

651.0ms	6219×	body	128	valid
330.0ms	574×	body	4096	valid
280.0ms	669×	body	2048	valid
167.0ms	435×	body	1024	valid
56.0ms	219×	body	512	valid
27.0ms	140×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	25	15
2	29	15
3	31	15
4	31	15

prune4.0ms (0.1%)

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

12.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	35.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.6b	(+.f64 re (hypot.f64 re im))

series12.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(+.f64 re (hypot.f64 re im))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 17

Calls

1 calls:

5.0ms

(+.f64 re (hypot.f64 re im))

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-neg_binary64`
513×	`cancel-sign-sub-inv_binary64`
257×	`associate-/r/_binary64`
248×	`distribute-rgt-neg-in_binary64`
241×	`distribute-lft-neg-in_binary64`

Counts

41 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	623
1	237	598
2	604	590
3	2282	590
4	4708	590
5	5107	590

prune39.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	45	5	50

Error

6.7b

Counts

50 → 5

Alt Table

Status	Error	Program
▶	14.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	46.4b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	28.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 re) (sqrt.f64 re) (hypot.f64 re im)))))

Compiler

Compiled 1008 to 676 computations (32.9% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 re)
✓	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
✓	13.8b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series100.0ms (2.6%)

Counts

3 → 48

Calls

3 calls:

44.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
31.0ms	(cbrt.f64 re)
25.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`

Counts

3 → 65

Calls

3 calls:

5.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
1.0ms	(cbrt.f64 re)
0.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

simplify104.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

749×	`times-frac_binary64`
486×	`fma-neg_binary64`
403×	`associate-/r*_binary64`
393×	`distribute-neg-frac_binary64`
314×	`fma-def_binary64`

Counts

113 → 127

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1156
1	267	1039
2	861	983
3	3718	968
4	4753	956
5	4987	956
6	4914	956

prune106.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	163	7	170

Error

6.7b

Counts

170 → 7

Alt Table

Status	Error	Program
	46.4b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	14.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
✓	14.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	17.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
	28.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 re) (sqrt.f64 re) (hypot.f64 re im)))))

Compiler

Compiled 3485 to 1689 computations (51.5% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 re)
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))
	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
	13.8b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series80.0ms (2%)

Counts

1 → 24

Calls

1 calls:

80.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`

Counts

1 → 42

Calls

1 calls:

5.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))

simplify70.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

340×	`times-frac_binary64`
298×	`associate-/l*_binary64`
234×	`associate-/r*_binary64`
233×	`cancel-sign-sub-inv_binary64`
226×	`associate-*l/_binary64`

Counts

66 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	2996
1	582	1940
2	1972	1780
3	4984	1780

prune405.0ms (10.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	600	1	601
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	601	7	608

Error

6.7b

Counts

608 → 7

Alt Table

Status	Error	Program
	46.4b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	14.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
✓	14.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
	28.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 re) (sqrt.f64 re) (hypot.f64 re im)))))

Compiler

Compiled 28728 to 7453 computations (74.1% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 re)
	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
	0.6b	(+.f64 re (hypot.f64 re im))
	13.8b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

prune256.0ms (6.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	377	1	378
Fresh	0	4	4
Picked	0	1	1
Done	1	1	2
Total	378	7	385

Error

6.7b

Counts

385 → 7

Alt Table

Status	Error	Program
✓	14.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (+.f64 (.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re)) (hypot.f64 re im)))))))
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
	46.4b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	28.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 re) (sqrt.f64 re) (hypot.f64 re im)))))

Compiler

Compiled 15735 to 4412 computations (72% saved)

regimes500.0ms (12.7%)

Accuracy

Total 3.1b remaining (29.5%)

Threshold costs 0b (0%)

Counts

43 → 3

Compiler

Compiled 7220 to 4210 computations (41.7% saved)

bsearch2.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	98
1	45	98
2	45	98

end123.0ms (3.1%)

Compiler: Compiled 275 to 159 computations (42.2% saved)

Details

analyze421.0ms (10.7%)

sample1.5s (39.5%)

simplify9.0ms (0.2%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series12.0ms (0.3%)

rewrite5.0ms (0.1%)

simplify62.0ms (1.6%)

prune39.0ms (1%)

localize11.0ms (0.3%)

series100.0ms (2.6%)

rewrite9.0ms (0.2%)

simplify104.0ms (2.6%)

prune106.0ms (2.7%)

localize15.0ms (0.4%)

series80.0ms (2%)

rewrite9.0ms (0.2%)

simplify70.0ms (1.8%)

prune405.0ms (10.3%)

localize17.0ms (0.4%)

prune256.0ms (6.5%)

regimes500.0ms (12.7%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end123.0ms (3.1%)

Profiling