Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.0s (17.8%)

Results

818.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 28 computations (36.4% saved)

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

649×	`fma-neg_binary64`
504×	`div-sub_binary64`
481×	`fma-def_binary64`
326×	`times-frac_binary64`
174×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	21	10
3	37	10
4	64	10
5	113	10
6	216	10
7	415	10
8	754	10
9	1183	10
10	1537	10
11	1612	10
12	1657	10
13	1684	10
14	1694	10
15	1702	10
16	1702	10
17	1600	10

prune2.0ms (0%)

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

62.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	62.0b	(/.f64 (-.f64 x lo) (-.f64 hi lo))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	62.0b	(/.f64 (-.f64 x lo) (-.f64 hi lo))

series17.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

17.0ms

(/.f64 (-.f64 x lo) (-.f64 hi lo))

rewrite112.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
728×	`fma-udef_binary64`
226×	`fma-neg_binary64`
166×	`expm1-udef_binary64`
166×	`log1p-udef_binary64`

Counts

1 → 69

Calls

1 calls:

111.0ms

(/.f64 (-.f64 x lo) (-.f64 hi lo))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	167	10
2	2530	10
3	4730	10
4	4517	10
5	5108	10

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

721×	`sub-neg_binary64`
402×	`associate--l+_binary64`
332×	`associate--r+_binary64`
330×	`fma-def_binary64`
301×	`associate-+l+_binary64`

Counts

105 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	1093
1	234	1075
2	842	919
3	4059	913
4	4904	898
5	5053	898

prune51.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	6	101

Error

51.6b

Counts

101 → 6

Alt Table

Status	Error	Program
	52.0b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
▶	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (/.f64 (-.f64 x lo) hi))
	57.2b	(-.f64 (*.f64 (/.f64 lo hi) (/.f64 (-.f64 x lo) hi)) (/.f64 (-.f64 lo x) hi))
	51.9b	(/.f64 (-.f64 x lo) hi)
	52.0b	(+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (-.f64 (-.f64 1 (/.f64 x lo)) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	58.5b	(+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (+.f64 (pow.f64 (/.f64 hi lo) 3) (-.f64 (-.f64 1 (/.f64 x lo)) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))))))

Compiler

Compiled 2519 to 890 computations (64.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (/.f64 (-.f64 x lo) hi))
✓	0.0b	(/.f64 (-.f64 x lo) hi)

series32.0ms (0.6%)

Counts

2 → 64

Calls

2 calls:

23.0ms	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (/.f64 (-.f64 x lo) hi))
9.0ms	(/.f64 (-.f64 x lo) hi)

rewrite99.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

415×	`fma-def_binary64`
233×	`egg-rr`
210×	`fma-neg_binary64`
199×	`log-div_binary64`
194×	`expm1-udef_binary64`

Counts

2 → 233

Calls

2 calls:

93.0ms	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (/.f64 (-.f64 x lo) hi))
93.0ms	(/.f64 (-.f64 x lo) hi)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	204	24
2	2994	24
3	4982	24
4	4992	24

simplify88.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

804×	`times-frac_binary64`
595×	`distribute-neg-frac_binary64`
395×	`div-sub_binary64`
374×	`associate-/l*_binary64`
321×	`neg-sub0_binary64`

Counts

297 → 246

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	876
1	69	795
2	151	735
3	341	729
4	835	729
5	3820	729
6	4619	729
7	4915	729

prune137.0ms (2.4%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	228	18	246
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	229	23	252

Error

51.6b

Counts

252 → 23

Alt Table

Status	Error	Program
	52.0b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (*.f64 (/.f64 (sqrt.f64 (-.f64 x lo)) 1) (/.f64 (sqrt.f64 (-.f64 x lo)) hi)))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (cbrt.f64 (/.f64 (-.f64 x lo) hi)) (pow.f64 (cbrt.f64 (/.f64 (-.f64 x lo) hi)) 2) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2) (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) (sqrt.f64 hi)) (/.f64 (cbrt.f64 (-.f64 x lo)) (sqrt.f64 hi))))
▶	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) (*.f64 (cbrt.f64 (-.f64 x lo)) (/.f64 1 hi)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2) (/.f64 lo hi))))
	51.9b	(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 x hi) (/.f64 lo hi)) 3) (pow.f64 (/.f64 (-.f64 x lo) hi) 3)) (fma.f64 (.f64 (/.f64 x hi) (/.f64 lo hi)) (.f64 (/.f64 x hi) (/.f64 lo hi)) (-.f64 (pow.f64 (/.f64 (-.f64 x lo) hi) 2) (.f64 (*.f64 (/.f64 x hi) (/.f64 lo hi)) (/.f64 (-.f64 x lo) hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) (*.f64 (cbrt.f64 (-.f64 x lo)) (/.f64 1 hi)) (fma.f64 (neg.f64 (/.f64 1 hi)) lo (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (*.f64 (/.f64 1 (sqrt.f64 hi)) (/.f64 (-.f64 x lo) (sqrt.f64 hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (sqrt.f64 (-.f64 x lo)) (*.f64 (sqrt.f64 (-.f64 x lo)) (/.f64 1 hi)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2) (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (log.f64 (/.f64 (exp.f64 (/.f64 x hi)) (+.f64 1 (expm1.f64 (/.f64 lo hi))))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (sqrt.f64 (-.f64 x lo)) (*.f64 (sqrt.f64 (-.f64 x lo)) (/.f64 1 hi)) (fma.f64 (neg.f64 (/.f64 1 hi)) lo (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (log.f64 (+.f64 1 (expm1.f64 (/.f64 (-.f64 x lo) hi)))))
	57.2b	(-.f64 (*.f64 (/.f64 lo hi) (/.f64 (-.f64 x lo) hi)) (/.f64 (-.f64 lo x) hi))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) (sqrt.f64 hi)) (/.f64 (cbrt.f64 (-.f64 x lo)) (sqrt.f64 hi)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2) (/.f64 lo hi))))
	51.9b	(/.f64 (-.f64 x lo) hi)
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) (sqrt.f64 hi)) (/.f64 (cbrt.f64 (-.f64 x lo)) (sqrt.f64 hi)) (fma.f64 (neg.f64 (/.f64 1 hi)) lo (/.f64 lo hi))))
	52.0b	(+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (-.f64 (-.f64 1 (/.f64 x lo)) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) 1) (/.f64 (cbrt.f64 (-.f64 x lo)) hi) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2) (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (pow.f64 (sqrt.f64 (/.f64 (-.f64 x lo) hi)) 2))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (-.f64 x lo) (/.f64 1 hi) (fma.f64 (neg.f64 (/.f64 1 hi)) lo (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 x lo) hi))) 1))
	58.5b	(+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (+.f64 (pow.f64 (/.f64 hi lo) 3) (-.f64 (-.f64 1 (/.f64 x lo)) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))))))

Compiler

Compiled 7176 to 1963 computations (72.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(cbrt.f64 hi)
✓	0.4b	(pow.f64 (cbrt.f64 (/.f64 lo hi)) 2)
✓	0.5b	(cbrt.f64 (/.f64 lo hi))
✓	60.4b	(cbrt.f64 (*.f64 hi hi))

series735.0ms (12.7%)

Counts

4 → 72

Calls

4 calls:

347.0ms	(pow.f64 (cbrt.f64 (/.f64 lo hi)) 2)
330.0ms	(cbrt.f64 (/.f64 lo hi))
29.0ms	(cbrt.f64 hi)
29.0ms	(cbrt.f64 (*.f64 hi hi))

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

774×	`log1p-expm1-u_binary64`
774×	`expm1-log1p-u_binary64`
151×	`log1p-udef_binary64`
108×	`egg-rr`
90×	`add-sqr-sqrt_binary64`

Counts

4 → 108

Calls

4 calls:

51.0ms	(cbrt.f64 hi)
51.0ms	(pow.f64 (cbrt.f64 (/.f64 lo hi)) 2)
51.0ms	(cbrt.f64 (/.f64 lo hi))
51.0ms	(cbrt.f64 (*.f64 hi hi))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	196	24
2	2048	24
3	5009	24

simplify113.0ms (2%)

Algorithm

1×	egg-herbie

Rules

750×	`fma-def_binary64`
562×	`associate-l_binary64`
506×	`associate-r_binary64`
488×	`div-sub_binary64`
378×	`fma-neg_binary64`

Counts

180 → 125

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	53	1016
1	120	1016
2	226	920
3	787	696
4	3148	632
5	4066	632
6	4426	616
7	4994	616
8	4899	616

prune112.0ms (1.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	161	6	167
Fresh	6	16	22
Picked	1	0	1
Done	0	0	0
Total	168	22	190

Error

51.6b

Counts

190 → 22

Alt Table

Status	Error	Program
	52.0b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (*.f64 (/.f64 (sqrt.f64 (-.f64 x lo)) 1) (/.f64 (sqrt.f64 (-.f64 x lo)) hi)))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (.f64 (cbrt.f64 -1) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (/.f64 1 hi)) (log.f64 (/.f64 -1 lo)))))) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (cbrt.f64 (/.f64 (-.f64 x lo) hi)) (pow.f64 (cbrt.f64 (/.f64 (-.f64 x lo) hi)) 2) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2) (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) (sqrt.f64 hi)) (/.f64 (cbrt.f64 (-.f64 x lo)) (sqrt.f64 hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) (*.f64 (cbrt.f64 (-.f64 x lo)) (/.f64 1 hi)) (fma.f64 (neg.f64 (/.f64 1 hi)) lo (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (*.f64 (/.f64 1 (sqrt.f64 hi)) (/.f64 (-.f64 x lo) (sqrt.f64 hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (/.f64 1 (/.f64 (cbrt.f64 hi) (cbrt.f64 lo))) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (sqrt.f64 (-.f64 x lo)) (*.f64 (sqrt.f64 (-.f64 x lo)) (/.f64 1 hi)) (fma.f64 (neg.f64 (/.f64 1 hi)) lo (/.f64 lo hi))))
	57.2b	(-.f64 (*.f64 (/.f64 lo hi) (/.f64 (-.f64 x lo) hi)) (/.f64 (-.f64 lo x) hi))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (/.f64 1 (cbrt.f64 (/.f64 hi lo))) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) (sqrt.f64 hi)) (/.f64 (cbrt.f64 (-.f64 x lo)) (sqrt.f64 hi)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2) (/.f64 lo hi))))
	51.9b	(/.f64 (-.f64 x lo) hi)
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))) 2)) 2)) (cbrt.f64 (/.f64 lo hi)))))
	52.0b	(+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (-.f64 (-.f64 1 (/.f64 x lo)) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) 1) (/.f64 (cbrt.f64 (-.f64 x lo)) hi) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2) (/.f64 lo hi))))
	58.5b	(+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (+.f64 (pow.f64 (/.f64 hi lo) 3) (-.f64 (-.f64 1 (/.f64 x lo)) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 lo) (/.f64 1 (cbrt.f64 hi))) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) (*.f64 (cbrt.f64 (-.f64 x lo)) (/.f64 1 hi)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2) (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (-.f64 x lo) (/.f64 1 hi) (fma.f64 (neg.f64 (/.f64 1 hi)) lo (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 x lo) hi))) 1))
▶	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))

Compiler

Compiled 7094 to 2671 computations (62.3% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 (/.f64 lo hi)))
	0.5b	(cbrt.f64 (/.f64 lo hi))
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))) 3)
	60.4b	(cbrt.f64 (*.f64 hi hi))

series1.5s (26.4%)

Counts

2 → 48

Calls

2 calls:

785.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))) 3)
741.0ms	(cbrt.f64 (cbrt.f64 (/.f64 lo hi)))

rewrite47.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

653×	`log1p-expm1-u_binary64`
653×	`expm1-log1p-u_binary64`
327×	`log-prod_binary64`
123×	`expm1-udef_binary64`
123×	`log1p-udef_binary64`

Counts

2 → 63

Calls

2 calls:

45.0ms	(cbrt.f64 (cbrt.f64 (/.f64 lo hi)))
45.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	149	14
2	1716	14
3	5110	14

simplify92.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

832×	`fma-def_binary64`
438×	`associate-l_binary64`
411×	`fma-neg_binary64`
394×	`prod-exp_binary64`
376×	`associate-r_binary64`

Counts

111 → 78

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	51	872
1	116	872
2	231	872
3	763	768
4	2781	688
5	4359	592
6	4426	584
7	4801	584

prune141.0ms (2.4%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	174	15	189
Fresh	13	8	21
Picked	1	0	1
Done	0	0	0
Total	188	23	211

Error

51.6b

Counts

211 → 23

Alt Table

Status	Error	Program
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (.f64 (cbrt.f64 -1) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (/.f64 1 hi)) (log.f64 (/.f64 -1 lo)))))) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (cbrt.f64 (/.f64 (-.f64 x lo) hi)) (pow.f64 (cbrt.f64 (/.f64 (-.f64 x lo) hi)) 2) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 lo hi))) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 2) (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))) 3) 2)) (*.f64 (cbrt.f64 lo) (/.f64 1 (cbrt.f64 hi))))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (pow.f64 (cbrt.f64 (-.f64 x lo)) 2) (*.f64 (cbrt.f64 (-.f64 x lo)) (/.f64 1 hi)) (fma.f64 (neg.f64 (/.f64 1 hi)) lo (/.f64 lo hi))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (/.f64 lo hi)))) (cbrt.f64 (exp.f64 (cbrt.f64 (/.f64 lo hi)))))) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (/.f64 lo hi)))))) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (cbrt.f64 lo) (cbrt.f64 hi))) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (log.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))))) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))) 3) 2)) (/.f64 (cbrt.f64 lo) (cbrt.f64 hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi)))) 3) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(/.f64 (-.f64 x lo) hi)
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (/.f64 lo hi))))) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi)))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))))))) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	52.0b	(+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (-.f64 (-.f64 1 (/.f64 x lo)) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))))) (cbrt.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))))))) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))))))) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	52.0b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (cbrt.f64 -1) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (/.f64 1 hi)) (log.f64 (/.f64 -1 lo))))))) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 (pow.f64 (exp.f64 1/9) (-.f64 (log.f64 (neg.f64 lo)) (log.f64 hi))) (cbrt.f64 (cbrt.f64 -1))) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))))) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (/.f64 (cbrt.f64 (cbrt.f64 lo)) (cbrt.f64 (cbrt.f64 hi))) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi)))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi)))) 2)) 3) 2)) (cbrt.f64 (/.f64 lo hi)))))
	51.9b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (fma.f64 (/.f64 1 (cbrt.f64 (.f64 hi hi))) (/.f64 x (cbrt.f64 hi)) (.f64 (neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))) 3) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 lo hi))) 3))))
	57.2b	(-.f64 (*.f64 (/.f64 lo hi) (/.f64 (-.f64 x lo) hi)) (/.f64 (-.f64 lo x) hi))
	58.5b	(+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (+.f64 (pow.f64 (/.f64 hi lo) 3) (-.f64 (-.f64 1 (/.f64 x lo)) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))))))

Compiler

Compiled 7939 to 3091 computations (61.1% saved)

regimes655.0ms (11.3%)

Accuracy

Total 0.5b remaining (0.9%)

Threshold costs 0.5b (0.9%)

Counts

128 → 1

Compiler

Compiled 15650 to 8752 computations (44.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	64
1	41	64
2	51	64
3	65	64
4	73	64
5	78	64
6	80	64
7	79	64

end520.0ms (9%)

Compiler: Compiled 961 to 569 computations (40.8% saved)

Details

analyze2.0ms (0%)

sample1.0s (17.8%)

simplify85.0ms (1.5%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series17.0ms (0.3%)

rewrite112.0ms (1.9%)

simplify68.0ms (1.2%)

prune51.0ms (0.9%)

localize7.0ms (0.1%)

series32.0ms (0.6%)

rewrite99.0ms (1.7%)

simplify88.0ms (1.5%)

prune137.0ms (2.4%)

localize17.0ms (0.3%)

series735.0ms (12.7%)

rewrite53.0ms (0.9%)

simplify113.0ms (2%)

prune112.0ms (1.9%)

localize25.0ms (0.4%)

series1.5s (26.4%)

rewrite47.0ms (0.8%)

simplify92.0ms (1.6%)

prune141.0ms (2.4%)

regimes655.0ms (11.3%)

simplify5.0ms (0.1%)

end520.0ms (9%)

Profiling