Details

analyze467.0ms (10.2%)

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)

sample1.8s (38.7%)

Results

808.0ms	6318×	body	128	valid
327.0ms	651×	body	2048	valid
321.0ms	522×	body	4096	valid
180.0ms	436×	body	1024	valid
64.0ms	216×	body	512	valid
32.0ms	113×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify6.0ms (0.1%)

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

prune5.0ms (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

12.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.8b	(+.f64 re (hypot.f64 re im))

series57.0ms (1.2%)

Counts

2 → 32

Calls

2 calls:

44.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
13.0ms	(+.f64 re (hypot.f64 re im))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
2.0ms	(+.f64 re (hypot.f64 re im))

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
517×	`fma-def_binary64`
437×	`associate-r_binary64`
361×	`associate-l_binary64`
244×	`cancel-sign-sub-inv_binary64`

Counts

64 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	1270
1	435	1196
2	1255	1148
3	4683	1148
4	5413	1148

prune56.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	6	80

Error

6.7b

Counts

80 → 6

Alt Table

Status	Error	Program
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
▶	15.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	57.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
	54.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 1864 to 1282 computations (31.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (.f64 2 (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))
✓	0.5b	(cbrt.f64 re)
✓	14.7b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series169.0ms (3.7%)

Counts

4 → 56

Calls

4 calls:

68.0ms	(sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))
36.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
35.0ms	(cbrt.f64 re)
29.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 78

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
2.0ms	(sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))
1.0ms	(cbrt.f64 re)
0.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

simplify118.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
702×	`associate-/l*_binary64`
325×	`cancel-sign-sub-inv_binary64`
294×	`fma-neg_binary64`
220×	`unswap-sqr_binary64`

Counts

134 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	1923
1	518	1757
2	1867	1664
3	4667	1645
4	4862	1645
5	4985	1645
6	4962	1645

prune117.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	197	6	203

Error

6.7b

Counts

203 → 6

Alt Table

Status	Error	Program
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	57.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
	54.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	18.6b	(.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)))))))
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 4544 to 2402 computations (47.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
	0.5b	(cbrt.f64 re)
✓	4.9b	(exp.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))
	14.7b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series28.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

28.0ms

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

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`exp-prod_binary64`
3×	`exp-sum_binary64`
3×	`log-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 17

Calls

1 calls:

1.0ms

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

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

481×	`cancel-sign-sub-inv_binary64`
395×	`fma-neg_binary64`
298×	`associate-/r/_binary64`
273×	`associate-/l/_binary64`
216×	`times-frac_binary64`

Counts

41 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	775
1	207	536
2	544	530
3	2358	522
4	4699	522
5	4964	522

prune99.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	217	3	220
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	219	7	226

Error

6.7b

Counts

226 → 7

Alt Table

Status	Error	Program
▶	20.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (log.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))) (cbrt.f64 (log.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))))))
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (neg.f64 im))))))
	54.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) (fma.f64 1/8 (/.f64 im (/.f64 (*.f64 re re) im)) -1/2)))))
	57.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 4970 to 2570 computations (48.3% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 re)
✓	2.7b	(exp.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))))
✓	4.9b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (log.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))) (cbrt.f64 (log.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	14.7b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series525.0ms (11.5%)

Counts

2 → 48

Calls

2 calls:

315.0ms

(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))) (cbrt.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))

210.0ms

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

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow-unpow_binary64`
5×	`add-log-exp_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

3.0ms

(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))) (cbrt.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))

1.0ms

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

simplify109.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

446×	`fma-def_binary64`
356×	`associate-l_binary64`
306×	`associate-*r/_binary64`
266×	`times-frac_binary64`
236×	`associate-/r*_binary64`

Counts

85 → 155

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	549	7159
1	1741	5740
2	5482	5740

prune315.0ms (6.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	461	3	464
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	462	9	471

Error

6.7b

Counts

471 → 9

Alt Table

Status	Error	Program
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	54.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) (fma.f64 1/8 (/.f64 im (/.f64 (*.f64 re re) im)) -1/2)))))
	50.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (log.f64 im)))) (cbrt.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))))))
	49.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (neg.f64 im))))))
	57.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
	20.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))) (cbrt.f64 (log.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))) (cbrt.f64 (log.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))))
	58.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 3/2 (.f64 (+.f64 (cbrt.f64 -1) 1) (pow.f64 (/.f64 -1 re) (cbrt.f64 -1))) (.f64 (.f64 (cbrt.f64 -1) (/.f64 (.f64 (.f64 im im) (pow.f64 (/.f64 -1 re) (cbrt.f64 -1))) (.f64 re re))) -1/2)))))
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 26388 to 9498 computations (64% saved)

regimes299.0ms (6.6%)

Accuracy

Total 4.6b remaining (38.8%)

Threshold costs 0b (0%)

Counts

27 → 2

Compiler

Compiled 5203 to 3082 computations (40.8% saved)

bsearch76.0ms (1.7%)

Steps

Iters	Range		Point
10	-2.4370651620935205e+211	-8.823753745983514e+195	-2.926404548759696e+196

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	52
1	32	52
2	32	52

end152.0ms (3.3%)

Compiler: Compiled 296 to 194 computations (34.5% saved)

Details

analyze467.0ms (10.2%)

sample1.8s (38.7%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series57.0ms (1.2%)

rewrite7.0ms (0.2%)

simplify65.0ms (1.4%)

prune56.0ms (1.2%)

localize12.0ms (0.3%)

series169.0ms (3.7%)

rewrite10.0ms (0.2%)

simplify118.0ms (2.6%)

prune117.0ms (2.6%)

localize12.0ms (0.3%)

series28.0ms (0.6%)

rewrite2.0ms (0.1%)

simplify55.0ms (1.2%)

prune99.0ms (2.2%)

localize19.0ms (0.4%)

series525.0ms (11.5%)

rewrite7.0ms (0.2%)

simplify109.0ms (2.4%)

prune315.0ms (6.9%)

regimes299.0ms (6.6%)

bsearch76.0ms (1.7%)

simplify2.0ms (0.1%)

end152.0ms (3.3%)

Profiling