Details

analyze1.8s (31%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.9s (31.2%)

Results

823.0ms	6262×	body	128	valid
356.0ms	554×	body	4096	valid
341.0ms	642×	body	2048	valid
186.0ms	437×	body	1024	valid
85.0ms	252×	body	512	valid
28.0ms	109×	body	256	valid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify7.0ms (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

prune4.0ms (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

16.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.5b	(.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
✓	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.9b	(+.f64 re (hypot.f64 re im))

series62.0ms (1.1%)

Counts

2 → 32

Calls

2 calls:

48.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
14.0ms	(+.f64 re (hypot.f64 re im))

rewrite7.0ms (0.1%)

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))

simplify64.0ms (1.1%)

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

prune64.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Error

9.2b

Counts

80 → 6

Alt Table

Status	Error	Program
▶	16.5b	(.f64 1/2 (.f64 1 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))
	48.0b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	53.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	17.4b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))

Compiler

Compiled 1862 to 1277 computations (31.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
	0.9b	(+.f64 re (hypot.f64 re im))

prune55.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	79	6	85

Error

9.2b

Counts

85 → 6

Alt Table

Status	Error	Program
✓	16.5b	(.f64 1/2 (.f64 1 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))
	48.0b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	53.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
▶	17.4b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))

Compiler

Compiled 2006 to 1424 computations (29% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))
✓	0.4b	(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))
✓	0.4b	(cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))
	0.9b	(+.f64 re (hypot.f64 re im))

series200.0ms (3.4%)

Counts

3 → 56

Calls

3 calls:

68.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

67.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

64.0ms

(cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))

rewrite84.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
68×	`sqrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`

Counts

3 → 134

Calls

3 calls:

43.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

11.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

4.0ms

(cbrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))

simplify189.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

424×	`unswap-sqr_binary64`
421×	`associate-r_binary64`
366×	`associate-l_binary64`
292×	`*-commutative_binary64`
289×	`fma-neg_binary64`

Counts

190 → 280

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	488	8767
1	1237	8004
2	4072	7471
3	5472	7471

prune542.0ms (9.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	541	1	542
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	542	6	548

Error

9.2b

Counts

548 → 6

Alt Table

Status	Error	Program
✓	16.5b	(.f64 1/2 (.f64 1 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))
	48.0b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	53.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	18.6b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 26015 to 15756 computations (39.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 re)
✓	0.6b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
	0.9b	(+.f64 re (hypot.f64 re im))
✓	17.7b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series103.0ms (1.7%)

Counts

3 → 48

Calls

3 calls:

43.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
32.0ms	(cbrt.f64 re)
29.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

rewrite14.0ms (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:

6.0ms	(cbrt.f64 re)
5.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
0.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

simplify97.0ms (1.6%)

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

prune210.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	261	6	267

Error

9.2b

Counts

267 → 6

Alt Table

Status	Error	Program
✓	16.5b	(.f64 1/2 (.f64 1 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))
	48.0b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	53.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	18.6b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (cbrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 11150 to 5573 computations (50% saved)

regimes365.0ms (6.2%)

Accuracy

Total 4.3b remaining (36.1%)

Threshold costs 0b (0%)

Counts

38 → 2

Compiler

Compiled 5237 to 3748 computations (28.4% saved)

bsearch32.0ms (0.5%)

Steps

Iters	Range		Point
4	-1.5468733405504273e+99	-9.437159345461679e+98	-1.4762733248770277e+99

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	39
1	31	39
2	30	39

end97.0ms (1.6%)

Compiler: Compiled 148 to 112 computations (24.3% saved)

Details

analyze1.8s (31%)

sample1.9s (31.2%)

simplify7.0ms (0.1%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series62.0ms (1.1%)

rewrite7.0ms (0.1%)

simplify64.0ms (1.1%)

prune64.0ms (1.1%)

localize8.0ms (0.1%)

prune55.0ms (0.9%)

localize11.0ms (0.2%)

series200.0ms (3.4%)

rewrite84.0ms (1.4%)

simplify189.0ms (3.2%)

prune542.0ms (9.1%)

localize18.0ms (0.3%)

series103.0ms (1.7%)

rewrite14.0ms (0.2%)

simplify97.0ms (1.6%)

prune210.0ms (3.5%)

regimes365.0ms (6.2%)

bsearch32.0ms (0.5%)

simplify3.0ms (0%)

end97.0ms (1.6%)

Profiling