Details

analyze869.0ms (12.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample93.0ms (1.3%)

Algorithm

1×

intervals

Results

29.0ms	191×	body	128	valid
14.0ms	24×	body	2048	valid
12.0ms	14×	body	4096	valid
7.0ms	14×	body	1024	valid
7.0ms	256×	pre	128	true
3.0ms	9×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

203×	`fma-def_binary64`
142×	`fma-neg_binary64`
51×	`distribute-rgt-in_binary64`
42×	`cancel-sign-sub-inv_binary64`
28×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

prune7.0ms (0.1%)

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

14.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.0b	(hypot.f64 re im)
✓	1.2b	(-.f64 (hypot.f64 re im) re)

series143.0ms (2%)

Counts

3 → 56

Calls

3 calls:

93.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
25.0ms	(-.f64 (hypot.f64 re im) re)
24.0ms	(hypot.f64 re im)

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
6×	`pow1_binary64`

Counts

3 → 55

Calls

3 calls:

13.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
6.0ms	(-.f64 (hypot.f64 re im) re)
1.0ms	(hypot.f64 re im)

simplify148.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

994×	`fma-neg_binary64`
747×	`times-frac_binary64`
413×	`cancel-sign-sub-inv_binary64`
173×	`fma-def_binary64`
158×	`sub-neg_binary64`

Counts

111 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	2332
1	611	2069
2	2078	1999
3	4466	1989
4	5015	1989

prune173.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	6	137

Error

0.1b

Counts

137 → 6

Alt Table

Status	Error	Program
	18.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re))))))
✓	14.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
▶	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	53.6b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16))))
	46.7b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
	54.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 3341 to 2190 computations (34.5% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (hypot.f64 re im))
	0.0b	(hypot.f64 re im)
✓	0.0b	(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))
✓	16.2b	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

series290.0ms (4.1%)

Counts

3 → 26

Calls

3 calls:

173.0ms

(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))

79.0ms

(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

37.0ms

(sqrt.f64 (hypot.f64 re im))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

3 → 38

Calls

3 calls:

4.0ms

(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))

2.0ms

(sqrt.f64 (hypot.f64 re im))

1.0ms

(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

simplify112.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

630×	`fma-def_binary64`
337×	`associate-/l*_binary64`
311×	`times-frac_binary64`
291×	`fma-neg_binary64`
289×	`cancel-sign-sub-inv_binary64`

Counts

64 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	1414
1	518	1316
2	1585	1263
3	4927	1261
4	5024	1261

prune260.0ms (3.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	207	6	213

Error

0.1b

Counts

213 → 6

Alt Table

Status	Error	Program
▶	18.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re))))))
✓	14.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
✓	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	53.6b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16))))
	46.7b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
	54.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 5690 to 3323 computations (41.6% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re)))))
	0.0b	(hypot.f64 re im)
	1.2b	(-.f64 (hypot.f64 re im) re)
✓	4.3b	(exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re)))

series114.0ms (1.6%)

Counts

2 → 32

Calls

2 calls:

90.0ms	(sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re)))))
23.0ms	(exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`pow1_binary64`
5×	`exp-sum_binary64`
5×	`log-prod_binary64`

Counts

2 → 36

Calls

2 calls:

10.0ms	(sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re)))))
6.0ms	(exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re)))

simplify118.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-def_binary64`
421×	`fma-neg_binary64`
337×	`associate-/l*_binary64`
311×	`times-frac_binary64`
242×	`cancel-sign-sub-inv_binary64`

Counts

68 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	1545
1	522	1490
2	1587	1435
3	4988	1431
4	5171	1431

prune210.0ms (3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	204	6	210

Error

0.1b

Counts

210 → 6

Alt Table

Status	Error	Program
✓	18.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re))))))
✓	14.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
✓	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	53.6b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16))))
▶	46.7b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
	54.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 4845 to 3097 computations (36.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 re))
✓	0.1b	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
✓	0.4b	(*.f64 (sqrt.f64 2) im)
✓	0.5b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))

series84.0ms (1.2%)

Counts

4 → 0

Calls

4 calls:

53.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
13.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
11.0ms	(sqrt.f64 (/.f64 1 re))
7.0ms	(*.f64 (sqrt.f64 2) im)

rewrite115.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`sqrt-prod_binary64`
32×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
22×	`pow1_binary64`

Counts

4 → 114

Calls

4 calls:

66.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
23.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
8.0ms	(*.f64 (sqrt.f64 2) im)
5.0ms	(sqrt.f64 (/.f64 1 re))

simplify176.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-/l*_binary64`
416×	`*-commutative_binary64`
403×	`unswap-sqr_binary64`
271×	`sqr-pow_binary64`
214×	`associate-l_binary64`

Counts

114 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	121	1600
1	239	1498
2	789	1498
3	1286	1498
4	2620	1498
5	3060	1498
6	4473	1498
7	5012	1498

prune187.0ms (2.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	1	1	2
Picked	1	0	1
Done	0	3	3
Total	118	11	129

Error

0.0b

Counts

129 → 11

Alt Table

Status	Error	Program
	46.7b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 re)))
	46.7b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re))))
✓	18.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (-.f64 (hypot.f64 re im) re))))))
✓	14.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	46.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re))))
	54.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	46.7b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 re))) (sqrt.f64 (sqrt.f64 (/.f64 1 re))))))
✓	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	46.8b	(.f64 1/2 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))) (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)))) (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)))) (sqrt.f64 (/.f64 1 re))))
	46.8b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (*.f64 (fabs.f64 (cbrt.f64 (/.f64 1 re))) (sqrt.f64 (cbrt.f64 (/.f64 1 re))))))
	46.8b	(.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 re))) (cbrt.f64 (sqrt.f64 (/.f64 1 re))))) (cbrt.f64 (sqrt.f64 (/.f64 1 re)))))

Compiler

Compiled 2747 to 2323 computations (15.4% saved)

regimes1.1s (16%)

Accuracy

Total 7.4b remaining (98.4%)

Threshold costs 0b (0%)

Counts

89 → 2

Compiler

Compiled 12624 to 10769 computations (14.7% saved)

bsearch35.0ms (0.5%)

Steps

Iters	Range		Point
9	5.304916424123851e-15	2.358782368906144e-7	2.3291133550561322e-7

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	52
1	36	52
2	40	52
3	42	52
4	43	52
5	42	52

end1.0ms (0%)

Compiler: Compiled 35 to 29 computations (17.1% saved)

sample2.6s (37.1%)

Algorithm

1×

intervals

Results

612.0ms	6042×	body	128	valid
342.0ms	552×	body	4096	valid
319.0ms	639×	body	2048	valid
196.0ms	385×	body	1024	valid
194.0ms	8000×	pre	128	true
76.0ms	249×	body	512	valid
24.0ms	133×	body	256	valid

Compiler

Compiled 285 to 238 computations (16.5% saved)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Details

analyze869.0ms (12.4%)

sample93.0ms (1.3%)

simplify38.0ms (0.5%)

prune7.0ms (0.1%)

localize13.0ms (0.2%)

series143.0ms (2%)

rewrite25.0ms (0.4%)

simplify148.0ms (2.1%)

prune173.0ms (2.5%)

localize19.0ms (0.3%)

series290.0ms (4.1%)

rewrite9.0ms (0.1%)

simplify112.0ms (1.6%)

prune260.0ms (3.7%)

localize19.0ms (0.3%)

series114.0ms (1.6%)

rewrite20.0ms (0.3%)

simplify118.0ms (1.7%)

prune210.0ms (3%)

localize19.0ms (0.3%)

series84.0ms (1.2%)

rewrite115.0ms (1.6%)

simplify176.0ms (2.5%)

prune187.0ms (2.7%)

regimes1.1s (16%)

bsearch35.0ms (0.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.6s (37.1%)

Profiling

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15