Details

analyze488.0ms (10.5%)

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)

sample39.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	194×	body	128	valid
8.0ms	22×	body	4096	valid
4.0ms	15×	body	1024	valid
4.0ms	14×	body	2048	valid
1.0ms	7×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify11.0ms (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 → 1

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

12.4b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	12.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	37.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 70 to 51 computations (27.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(hypot.f64 re im)
0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
1.0b	(+.f64 re (hypot.f64 re im))

rewrite98.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

12.2b

Rules

17×	`add-cube-cbrt_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64`
10×	`add-log-exp_binary64`
9×	`flip3-+_binary64`

Counts

3 → 113

Calls

3 calls:

12.0ms	(+.f64 re (hypot.f64 re im))
12.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
9.0ms	(hypot.f64 re im)

Compiler

Compiled 1536 to 755 computations (50.8% saved)

series99.0ms (2.1%)

Error

6.5b

Counts

3 → 45

Calls

3 calls:

30.0ms	(hypot.f64 re im)
29.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
23.0ms	(+.f64 re (hypot.f64 re im))

Compiler

Compiled 1835 to 1498 computations (18.4% saved)

simplify106.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-neg_binary64`
512×	`fma-def_binary64`
418×	`associate-/l*_binary64`
387×	`associate-/r*_binary64`
257×	`*-commutative_binary64`

Counts

158 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	1818
1	426	1748
2	1398	1721
3	4275	1721
4	4971	1721
5	4911	1721

prune38.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	7	67
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	61	8	69

Error

6.5b

Counts

69 → 8

Alt Table

Status	Error	Program
	45.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (+.f64 (pow.f64 re 3) (pow.f64 (hypot.f64 re im) 3)) (fma.f64 re re (*.f64 (hypot.f64 re im) (-.f64 (hypot.f64 re im) re)))))))
▶	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	31.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (/.f64 (*.f64 re re) (-.f64 re (hypot.f64 re im))) (/.f64 (hypot.f64 re im) (+.f64 (/.f64 re (hypot.f64 re im)) -1))))))
✓	12.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	48.3b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))))
	53.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))

Compiler

Compiled 1184 to 715 computations (39.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 re im)
0.2b	(sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))))
0.5b	(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
8.3b	(+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

rewrite139.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

6.5b

Rules

27×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
21×	`pow1/2_binary64`
15×	`pow1_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 164

Calls

4 calls:

16.0ms	(+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))
15.0ms	(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
11.0ms	(sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))))
11.0ms	(hypot.f64 re im)

Compiler

Compiled 3172 to 1106 computations (65.1% saved)

series140.0ms (3%)

Error

6.5b

Counts

4 → 65

Calls

4 calls:

33.0ms	(hypot.f64 re im)
31.0ms	(sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))))
29.0ms	(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
23.0ms	(+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

Compiler

Compiled 2869 to 2256 computations (21.4% saved)

simplify122.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
466×	`associate-/l*_binary64`
425×	`associate-/r*_binary64`
383×	`fma-neg_binary64`
261×	`cancel-sign-sub-inv_binary64`

Counts

229 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	2488
1	479	2358
2	1633	2307
3	4511	2297
4	5052	2297

prune97.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	137	8	145

Error

6.5b

Counts

145 → 8

Alt Table

Status	Error	Program
	31.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (/.f64 (*.f64 re re) (-.f64 re (hypot.f64 re im))) (/.f64 (hypot.f64 re im) (+.f64 (/.f64 re (hypot.f64 re im)) -1))))))
✓	12.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	38.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) 2)) (cbrt.f64 (hypot.f64 re im)))) (sqrt.f64 (hypot.f64 re im)))))))
▶	16.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (cbrt.f64 (sqrt.f64 (hypot.f64 re im))))))))
	48.3b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))))
	53.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))

Compiler

Compiled 2172 to 1219 computations (43.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (sqrt.f64 (hypot.f64 re im)))
0.5b	(cbrt.f64 (sqrt.f64 (hypot.f64 re im)))
1.0b	(pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5)
13.4b	(+.f64 re (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))))

rewrite117.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

6.5b

Rules

29×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`pow1/3_binary64`
12×	`add-log-exp_binary64`
12×	`log1p-expm1-u_binary64`

Counts

4 → 141

Calls

4 calls:

15.0ms	(+.f64 re (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))))
13.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5)
12.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 re im)))
10.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 re im)))

Compiler

Compiled 3000 to 1329 computations (55.7% saved)

series187.0ms (4%)

Error

6.5b

Counts

4 → 52

Calls

4 calls:

62.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5)
40.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 re im)))
39.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 re im)))
26.0ms	(+.f64 re (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))))

Compiler

Compiled 3018 to 2412 computations (20.1% saved)

simplify105.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

818×	`times-frac_binary64`
454×	`fma-def_binary64`
375×	`fma-neg_binary64`
187×	`cancel-sign-sub-inv_binary64`
179×	`distribute-rgt-neg-in_binary64`

Counts

193 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	2360
1	455	2269
2	1444	1966
3	4146	1917
4	4815	1917

prune52.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	94	9	103

Error

6.5b

Counts

103 → 9

Alt Table

Status	Error	Program
	38.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) 2)) (cbrt.f64 (hypot.f64 re im)))) (sqrt.f64 (hypot.f64 re im)))))))
▶	16.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) 6)))))))
	16.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) 6)) (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))))))))))
✓	12.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
✓	16.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (cbrt.f64 (sqrt.f64 (hypot.f64 re im))))))))
	48.3b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))))
	53.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))

Compiler

Compiled 1852 to 1053 computations (43.1% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))))
1.0b	(pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5)
1.1b	(pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) 6)
12.9b	(+.f64 re (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) 6))))

rewrite142.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

6.5b

Rules

30×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`add-log-exp_binary64`
12×	`log1p-expm1-u_binary64`
12×	`expm1-log1p-u_binary64`

Counts

4 → 146

Calls

4 calls:

18.0ms	(+.f64 re (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) 6))))
14.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5)
13.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) 6)
11.0ms	(cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))))

Compiler

Compiled 3789 to 1864 computations (50.8% saved)

series220.0ms (4.7%)

Error

6.5b

Counts

4 → 46

Calls

4 calls:

74.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5)
71.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) 6)
31.0ms	(cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))))
24.0ms	(+.f64 re (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) 6))))

Compiler

Compiled 2772 to 2243 computations (19.1% saved)

simplify174.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

862×	`times-frac_binary64`
446×	`fma-def_binary64`
350×	`fma-neg_binary64`
223×	`log-prod_binary64`
205×	`unswap-sqr_binary64`

Counts

192 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	3205
1	509	2771
2	1527	2610
3	4242	2249
4	4754	2249
5	4979	2249
6	4863	2249

prune56.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	6	6
Picked	0	1	1
Done	1	1	2
Total	97	9	106

Error

6.5b

Counts

106 → 9

Alt Table

Status	Error	Program
	53.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	19.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 6)))))))
	38.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) 2)) (cbrt.f64 (hypot.f64 re im)))) (sqrt.f64 (hypot.f64 re im)))))))
	16.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) 6)))))))
	16.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))) 5) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im)))) 6)) (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 re im))))))))))
	12.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	48.3b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))))

Compiler

Compiled 1876 to 1080 computations (42.4% saved)

regimes857.0ms (18.3%)

Accuracy

Total 2.8b remaining (26.9%)

Threshold costs 0b (0%)

Compiler

Compiled 12125 to 8130 computations (32.9% saved)

bsearch3.0ms (0.1%)

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
8×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	112
1	57	112
2	68	112
3	71	112
4	73	112
5	71	112

end1.0ms (0%)

Compiler: Compiled 76 to 40 computations (47.4% saved)

sample1.3s (28.4%)

Algorithm

1×

intervals

Results

386.0ms	6037×	body	128	valid
200.0ms	526×	body	4096	valid
196.0ms	639×	body	2048	valid
122.0ms	454×	body	1024	valid
40.0ms	229×	body	512	valid
13.0ms	115×	body	256	valid

Compiler

Compiled 265 to 177 computations (33.2% saved)

Details

analyze488.0ms (10.5%)

sample39.0ms (0.8%)

simplify11.0ms (0.2%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

rewrite98.0ms (2.1%)

series99.0ms (2.1%)

simplify106.0ms (2.3%)

prune38.0ms (0.8%)

localize9.0ms (0.2%)

rewrite139.0ms (3%)

series140.0ms (3%)

simplify122.0ms (2.6%)

prune97.0ms (2.1%)

localize13.0ms (0.3%)

rewrite117.0ms (2.5%)

series187.0ms (4%)

simplify105.0ms (2.3%)

prune52.0ms (1.1%)

localize18.0ms (0.4%)

rewrite142.0ms (3%)

series220.0ms (4.7%)

simplify174.0ms (3.7%)

prune56.0ms (1.2%)

regimes857.0ms (18.3%)

bsearch3.0ms (0.1%)

simplify7.0ms (0.2%)

end1.0ms (0%)

sample1.3s (28.4%)

Profiling