Details

analyze676.0ms (3.3%)

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
6.2%	93.6%	0.1%	6
12.5%	87.4%	0.1%	7
15.6%	84.3%	0.1%	8
18.7%	71.8%	9.5%	9
23.4%	56%	20.6%	10
26.3%	52.2%	21.5%	11
31%	40.1%	28.9%	12
35.6%	28.9%	35.5%	13
36.8%	27.5%	35.7%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.5s (7.2%)

Symmetry

(sort x y z)

Results

1.2s	8256×	body	128	valid
255.0ms	2376×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
8×	`+-commutative_binary64`
8×	`*-commutative_binary64`
5×	`distribute-rgt-out_binary64`
3×	`associate-+r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	23	16
2	43	16
3	59	16
4	61	16
5	62	16
6	62	16

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

18.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	18.1b	(.f64 2 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))
▶	18.1b	(.f64 2 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (.f64 y z))))

Compiler

Compiled 90 to 56 computations (37.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(+.f64 (.f64 x y) (.f64 x z))
✓	1.0b	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
✓	17.1b	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))

series126.0ms (0.6%)

Counts

3 → 84

Calls

3 calls:

110.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))
10.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
6.0ms	(+.f64 (.f64 x y) (.f64 x z))

rewrite103.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

812×	`fma-def_binary64`
462×	`fma-neg_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
203×	`egg-rr`

Counts

3 → 203

Calls

3 calls:

99.0ms	(+.f64 (.f64 x y) (.f64 x z))
99.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
99.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	222	31
2	3032	31
3	4992	31
4	5043	31
0	0	0
1	0	0

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

605×	`cancel-sign-sub-inv_binary64`
602×	`associate-l_binary64`
542×	`associate-r_binary64`
318×	`times-frac_binary64`
297×	`fma-neg_binary64`

Counts

287 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	1448
1	506	1389
2	1816	1344
3	4609	1344
4	5322	1344

prune554.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	220	12	232
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	222	12	234

Error

17.6b

Counts

234 → 12

Alt Table

Status	Error	Program
	39.6b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	18.6b	(.f64 2 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 3)))
	30.2b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) y) (*.f64 x (+.f64 y z)))))
	18.3b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
	18.6b	(.f64 2 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
▶	18.1b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))
	45.5b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	41.2b	(.f64 2 (sqrt.f64 (.f64 y x)))
	61.6b	(.f64 2 (sqrt.f64 (.f64 z x)))
	40.8b	(.f64 2 (sqrt.f64 (.f64 y z)))
	41.0b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) z) (*.f64 x (+.f64 y z)))))
	22.3b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))

Compiler

Compiled 5373 to 2276 computations (57.6% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (+.f64 y x))
✓	0.7b	(fma.f64 y x (*.f64 z (+.f64 y x)))
✓	17.1b	(sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))

series128.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

109.0ms	(sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))
11.0ms	(*.f64 z (+.f64 y x))
8.0ms	(fma.f64 y x (*.f64 z (+.f64 y x)))

rewrite58.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

887×	`expm1-log1p-u_binary64`
858×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
85×	`log1p-expm1-u_binary64`
83×	`add-log-exp_binary64`

Counts

3 → 78

Calls

3 calls:

57.0ms	(*.f64 z (+.f64 y x))
57.0ms	(fma.f64 y x (*.f64 z (+.f64 y x)))
57.0ms	(sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	31
1	173	31
2	2213	31
3	5472	31
0	0	0
1	0	0

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

605×	`cancel-sign-sub-inv_binary64`
602×	`associate-l_binary64`
542×	`associate-r_binary64`
318×	`times-frac_binary64`
297×	`fma-neg_binary64`

Counts

150 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	1364
1	503	1305
2	1812	1260
3	4605	1260
4	5318	1260

prune122.0ms (0.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	114	12	126

Error

17.6b

Counts

126 → 12

Alt Table

Status	Error	Program
	39.6b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	18.6b	(.f64 2 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 3)))
	45.5b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	40.0b	(.f64 2 (sqrt.f64 (.f64 x (+.f64 z y))))
	30.2b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) y) (*.f64 x (+.f64 y z)))))
▶	18.3b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
	18.6b	(.f64 2 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
✓	18.1b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))
	41.2b	(.f64 2 (sqrt.f64 (.f64 y x)))
	40.8b	(.f64 2 (sqrt.f64 (.f64 y z)))
	41.0b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) z) (*.f64 x (+.f64 y z)))))
	22.3b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))

Compiler

Compiled 2973 to 1478 computations (50.3% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 x (+.f64 y z) (*.f64 y z))
✓	0.5b	(pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4) 2)
✓	17.4b	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)

series146.0ms (0.7%)

Counts

3 → 108

Calls

3 calls:

83.0ms	(pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4) 2)
53.0ms	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)
9.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))

rewrite115.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

750×	`prod-diff_binary64`
542×	`fma-udef_binary64`
304×	`fma-def_binary64`
203×	`fma-neg_binary64`
194×	`expm1-udef_binary64`

Counts

3 → 82

Calls

3 calls:

113.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))
113.0ms	(pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4) 2)
113.0ms	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	240	38
2	2631	38
3	4734	38
4	4706	38
5	4972	38
0	0	0
1	0	0

simplify110.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

718×	`times-frac_binary64`
534×	`fma-def_binary64`
469×	`associate-/l*_binary64`
251×	`*-commutative_binary64`
132×	`cancel-sign-sub-inv_binary64`

Counts

190 → 223

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	622	6589
1	2078	6304
2	5199	6304

prune224.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	6	4	10
Picked	0	1	1
Done	0	1	1
Total	227	8	235

Error

1.9b

Counts

235 → 8

Alt Table

Status	Error	Program
	30.2b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) y) (*.f64 x (+.f64 y z)))))
✓	18.3b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
▶	18.6b	(.f64 2 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 3)))
	37.0b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
✓	18.1b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))
	32.9b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	41.0b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) z) (*.f64 x (+.f64 y z)))))
	22.3b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))

Compiler

Compiled 10340 to 5903 computations (42.9% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 x (+.f64 y z) (*.f64 y z))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 3)
✓	17.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 3))
✓	17.7b	(cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

series13.6s (65.6%)

Counts

3 → 84

Calls

3 calls:

13.4s	(pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 3)
114.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 3))
53.0ms	(cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

rewrite118.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

750×	`prod-diff_binary64`
532×	`fma-udef_binary64`
311×	`fma-def_binary64`
203×	`fma-neg_binary64`
180×	`expm1-udef_binary64`

Counts

3 → 114

Calls

3 calls:

116.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 3)
116.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 3))
116.0ms	(cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	213	37
2	2505	37
3	4710	37
4	4684	37
5	4955	37
0	0	0
1	0	0

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

484×	`fma-def_binary64`
435×	`associate-l_binary64`
418×	`times-frac_binary64`
320×	`associate-/r*_binary64`
290×	`associate-/l*_binary64`

Counts

198 → 230

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	531	5269
1	1725	5008
2	5559	5008

prune239.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	275	8	283

Error

1.9b

Counts

283 → 8

Alt Table

Status	Error	Program
	30.2b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) y) (*.f64 x (+.f64 y z)))))
✓	18.3b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
✓	18.6b	(.f64 2 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 3)))
	37.0b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
✓	18.1b	(.f64 2 (sqrt.f64 (fma.f64 y x (.f64 z (+.f64 y x)))))
	32.9b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	41.0b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) z) (*.f64 x (+.f64 y z)))))
	22.3b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))

Compiler

Compiled 9238 to 4859 computations (47.4% saved)

regimes1.2s (5.8%)

Accuracy

Total 2.4b remaining (52.9%)

Threshold costs 0b (0%)

Counts

60 → 6

Compiler

Compiled 6128 to 4196 computations (31.5% saved)

bsearch536.0ms (2.6%)

Steps

Iters	Range		Point
7	5.6660096666677866e+41	4.302850915418598e+43	4.247940556637857e+43
8	9.954176946213014e-236	1.0999934010201603e-232	1.010928485720324e-235
12	-8.324565990360531e-305	1.8793821612069284e-270	1.863229279770189e-270
10	-1.2192672032441498e-164	-3.690785170976697e-176	-7.079352293701776e-176
7	-28146690579458.563	-403390882349.5441	-27725273429553.94

Compiler

Compiled 4 to 3 computations (25% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
9×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	166
1	66	166
2	80	166
3	90	166
4	94	166
5	93	166

end879.0ms (4.2%)

Compiler: Compiled 587 to 397 computations (32.4% saved)

Details

analyze676.0ms (3.3%)

sample1.5s (7.2%)

simplify8.0ms (0%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series126.0ms (0.6%)

rewrite103.0ms (0.5%)

simplify79.0ms (0.4%)

prune554.0ms (2.7%)

localize9.0ms (0%)

series128.0ms (0.6%)

rewrite58.0ms (0.3%)

simplify66.0ms (0.3%)

prune122.0ms (0.6%)

localize13.0ms (0.1%)

series146.0ms (0.7%)

rewrite115.0ms (0.6%)

simplify110.0ms (0.5%)

prune224.0ms (1.1%)

localize10.0ms (0%)

series13.6s (65.6%)

rewrite118.0ms (0.6%)

simplify99.0ms (0.5%)

prune239.0ms (1.2%)

regimes1.2s (5.8%)

bsearch536.0ms (2.6%)

simplify12.0ms (0.1%)

end879.0ms (4.2%)

Profiling