Details

analyze566.0ms (3.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.5%	0.2%	5
6.2%	93.5%	0.2%	6
6.2%	81.1%	12.7%	7
9.4%	71.7%	18.9%	8
9.4%	51.4%	39.2%	9
9.4%	36.2%	54.4%	10
9.4%	36.2%	54.4%	11
9.4%	31%	59.7%	12
10.9%	26.8%	62.3%	13
10.9%	20.5%	68.6%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample3.1s (19%)

Infinites

0.5% of outputs are infinite.

Symmetry

(sort x y)

Results

1.8s	12665×	body	128	invalid
1.2s	8256×	body	128	valid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify211.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

2140×	`distribute-rgt-in_binary64`
556×	`associate--r+_binary64`
551×	`associate-+l+_binary64`
551×	`unsub-neg_binary64`
546×	`associate-+r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	23
2	72	23
3	160	23
4	426	23
5	1097	23
6	1994	23
7	1981	23
8	1956	23
9	1972	23
10	1987	23
11	2037	23
12	2044	23
13	2248	23
14	2651	23
15	2447	23
16	2459	23
17	2465	23
18	2465	23
19	2557	23
20	4649	23
21	4720	23
22	4802	23
23	4878	23
24	7643	23

prune4.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
	0.2b	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))

Compiler

Compiled 118 to 76 computations (35.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
✓	0.1b	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
✓	0.1b	(*.f64 (-.f64 a 1/2) (log.f64 t))
✓	0.6b	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

series1.6s (10%)

Counts

4 → 164

Calls

4 calls:

823.0ms	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
344.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
335.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
127.0ms	(*.f64 (-.f64 a 1/2) (log.f64 t))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`*-un-lft-identity_binary64`
48×	`pow1_binary64`
45×	`add-sqr-sqrt_binary64`
42×	`prod-diff_binary64`
42×	`log-pow_binary64`

Counts

4 → 176

Calls

4 calls:

11.0ms	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
8.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
7.0ms	(*.f64 (-.f64 a 1/2) (log.f64 t))
5.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

simplify138.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

450×	`associate--l+_binary64`
371×	`associate-+l+_binary64`
360×	`associate--r+_binary64`
318×	`fma-def_binary64`
286×	`sub-neg_binary64`

Counts

340 → 368

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	469	7429
1	1396	6861
2	5156	6861

prune395.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	362	6	368
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	364	6	370

Error

0.0b

Counts

370 → 6

Alt Table

Status	Error	Program
	0.2b	(+.f64 (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t) (.f64 (-.f64 a 1/2) (log.f64 t)))
	51.3b	(log.f64 (.f64 (pow.f64 t (+.f64 a -1/2)) (/.f64 (.f64 z (+.f64 y x)) (exp.f64 t))))
	0.2b	(+.f64 (fma.f64 (+.f64 a -1/2) (.f64 2 (log.f64 (cbrt.f64 t))) (-.f64 (+.f64 (log.f64 z) (log.f64 (+.f64 y x))) t)) (.f64 (log.f64 (cbrt.f64 t)) (-.f64 a 1/2)))
	0.3b	(-.f64 (+.f64 (log.f64 z) (.f64 a (log.f64 t))) (+.f64 t (+.f64 (log.f64 (/.f64 1 y)) (.f64 1/2 (log.f64 t)))))
▶	0.2b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t)))) (fma.f64 a (neg.f64 (log.f64 t)) t))
	31.5b	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/2)) (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/2)) (log.f64 t))))

Compiler

Compiled 10394 to 3997 computations (61.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t)))) (fma.f64 a (neg.f64 (log.f64 t)) t))
✓	0.1b	(fma.f64 a (neg.f64 (log.f64 t)) t)
✓	0.5b	(+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t)))
✓	0.5b	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t))))

series2.3s (13.9%)

Counts

4 → 156

Calls

4 calls:

952.0ms	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t))))
874.0ms	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t)))) (fma.f64 a (neg.f64 (log.f64 t)) t))
395.0ms	(+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t)))
48.0ms	(fma.f64 a (neg.f64 (log.f64 t)) t)

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
15×	`prod-diff_binary64`
13×	`log-prod_binary64`

Counts

4 → 109

Calls

4 calls:

11.0ms	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t)))) (fma.f64 a (neg.f64 (log.f64 t)) t))
6.0ms	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t))))
3.0ms	(+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t)))
0.0ms	(fma.f64 a (neg.f64 (log.f64 t)) t)

simplify163.0ms (1%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-neg_binary64`
390×	`associate-+l+_binary64`
384×	`associate--l+_binary64`
353×	`associate--r+_binary64`
317×	`+-commutative_binary64`

Counts

265 → 294

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	377	6874
1	1161	5987
2	4514	5987
3	4960	5987

prune322.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	291	3	294
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	292	8	300

Error

0.0b

Counts

300 → 8

Alt Table

Status	Error	Program
	0.2b	(+.f64 (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t) (.f64 (-.f64 a 1/2) (log.f64 t)))
	15.3b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 -1/2 (log.f64 t)))) (.f64 (sqrt.f64 (fma.f64 a (neg.f64 (log.f64 t)) t)) (sqrt.f64 (fma.f64 a (neg.f64 (log.f64 t)) t))))
✓	0.2b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t)))) (fma.f64 a (neg.f64 (log.f64 t)) t))
▶	0.2b	(-.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (+.f64 (fma.f64 (log.f64 t) -1/2 (log.f64 z)) (log.f64 (cbrt.f64 (+.f64 x y))))) (fma.f64 a (neg.f64 (log.f64 t)) t))
	51.3b	(log.f64 (.f64 (pow.f64 t (+.f64 a -1/2)) (/.f64 (.f64 z (+.f64 y x)) (exp.f64 t))))
	0.2b	(+.f64 (fma.f64 (+.f64 a -1/2) (.f64 2 (log.f64 (cbrt.f64 t))) (-.f64 (+.f64 (log.f64 z) (log.f64 (+.f64 y x))) t)) (.f64 (log.f64 (cbrt.f64 t)) (-.f64 a 1/2)))
	31.5b	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/2)) (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/2)) (log.f64 t))))
	0.3b	(-.f64 (-.f64 (log.f64 z) (-.f64 (*.f64 1/2 (log.f64 t)) (log.f64 y))) (fma.f64 a (neg.f64 (log.f64 t)) t))

Compiler

Compiled 8759 to 3220 computations (63.2% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 (log.f64 t) -1/2 (log.f64 z))
✓	0.5b	(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))
✓	0.6b	(cbrt.f64 (+.f64 x y))
✓	0.6b	(cbrt.f64 (+.f64 y x))

series447.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

377.0ms	(fma.f64 (log.f64 t) -1/2 (log.f64 z))
26.0ms	(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))
22.0ms	(cbrt.f64 (+.f64 x y))
22.0ms	(cbrt.f64 (+.f64 y x))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
32×	`cbrt-prod_binary64`
22×	`add-sqr-sqrt_binary64`
16×	`cbrt-div_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 97

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))
2.0ms	(cbrt.f64 (+.f64 y x))
2.0ms	(cbrt.f64 (+.f64 x y))
0.0ms	(fma.f64 (log.f64 t) -1/2 (log.f64 z))

simplify129.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

604×	`fma-def_binary64`
401×	`fma-neg_binary64`
348×	`times-frac_binary64`
243×	`associate-/l*_binary64`
204×	`associate-/r*_binary64`

Counts

193 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	4462
1	631	4279
2	1753	3852
3	4761	3845
4	5034	3845

prune360.0ms (2.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	232	8	240

Error

0.0b

Counts

240 → 8

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t) (.f64 (-.f64 a 1/2) (log.f64 t)))
	15.3b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 -1/2 (log.f64 t)))) (.f64 (sqrt.f64 (fma.f64 a (neg.f64 (log.f64 t)) t)) (sqrt.f64 (fma.f64 a (neg.f64 (log.f64 t)) t))))
✓	0.2b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t)))) (fma.f64 a (neg.f64 (log.f64 t)) t))
✓	0.2b	(-.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (+.f64 (fma.f64 (log.f64 t) -1/2 (log.f64 z)) (log.f64 (cbrt.f64 (+.f64 x y))))) (fma.f64 a (neg.f64 (log.f64 t)) t))
	51.3b	(log.f64 (.f64 (pow.f64 t (+.f64 a -1/2)) (/.f64 (.f64 z (+.f64 y x)) (exp.f64 t))))
	0.2b	(+.f64 (fma.f64 (+.f64 a -1/2) (.f64 2 (log.f64 (cbrt.f64 t))) (-.f64 (+.f64 (log.f64 z) (log.f64 (+.f64 y x))) t)) (.f64 (log.f64 (cbrt.f64 t)) (-.f64 a 1/2)))
	31.5b	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/2)) (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/2)) (log.f64 t))))
	0.3b	(-.f64 (-.f64 (log.f64 z) (-.f64 (*.f64 1/2 (log.f64 t)) (log.f64 y))) (fma.f64 a (neg.f64 (log.f64 t)) t))

Compiler

Compiled 10050 to 3680 computations (63.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (-.f64 a 1/2) (log.f64 t))
✓	0.4b	(+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
✓	0.5b	(+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z))))
✓	0.6b	(cbrt.f64 z)

series1.7s (10.5%)

Counts

3 → 84

Calls

3 calls:

849.0ms	(+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z))))
826.0ms	(+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
32.0ms	(cbrt.f64 z)

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`log-prod_binary64`
18×	`associate-+r+_binary64`
18×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 76

Calls

3 calls:

6.0ms	(+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z))))
6.0ms	(+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
1.0ms	(cbrt.f64 z)

simplify114.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

548×	`distribute-rgt-in_binary64`
516×	`fma-neg_binary64`
447×	`distribute-lft-in_binary64`
292×	`times-frac_binary64`
276×	`sub-neg_binary64`

Counts

160 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	3227
1	755	2853
2	2450	2596
3	4340	2560
4	5020	2560

prune498.0ms (3.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	274	8	282

Error

0.0b

Counts

282 → 8

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t) (.f64 (-.f64 a 1/2) (log.f64 t)))
	15.3b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 -1/2 (log.f64 t)))) (.f64 (sqrt.f64 (fma.f64 a (neg.f64 (log.f64 t)) t)) (sqrt.f64 (fma.f64 a (neg.f64 (log.f64 t)) t))))
✓	0.2b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 -1/2 (log.f64 t)))) (fma.f64 a (neg.f64 (log.f64 t)) t))
✓	0.2b	(-.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (+.f64 (fma.f64 (log.f64 t) -1/2 (log.f64 z)) (log.f64 (cbrt.f64 (+.f64 x y))))) (fma.f64 a (neg.f64 (log.f64 t)) t))
	51.3b	(log.f64 (.f64 (pow.f64 t (+.f64 a -1/2)) (/.f64 (.f64 z (+.f64 y x)) (exp.f64 t))))
	0.2b	(+.f64 (fma.f64 (+.f64 a -1/2) (.f64 2 (log.f64 (cbrt.f64 t))) (-.f64 (+.f64 (log.f64 z) (log.f64 (+.f64 y x))) t)) (.f64 (log.f64 (cbrt.f64 t)) (-.f64 a 1/2)))
	31.5b	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/2)) (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/2)) (log.f64 t))))
	0.3b	(-.f64 (-.f64 (log.f64 z) (-.f64 (*.f64 1/2 (log.f64 t)) (log.f64 y))) (fma.f64 a (neg.f64 (log.f64 t)) t))

Compiler

Compiled 8403 to 3979 computations (52.6% saved)

regimes3.9s (24%)

Accuracy

Total 0.2b remaining (88%)

Threshold costs 0.2b (88%)

Counts

211 → 1

Compiler

Compiled 71087 to 49062 computations (31% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	27	37
2	32	37
3	35	37
4	36	37
5	36	37

end147.0ms (0.9%)

Remove: (sort x y)
Compiler: Compiled 334 to 213 computations (36.2% saved)

Details

analyze566.0ms (3.5%)

sample3.1s (19%)

simplify211.0ms (1.3%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series1.6s (10%)

rewrite45.0ms (0.3%)

simplify138.0ms (0.8%)

prune395.0ms (2.4%)

localize16.0ms (0.1%)

series2.3s (13.9%)

rewrite29.0ms (0.2%)

simplify163.0ms (1%)

prune322.0ms (2%)

localize23.0ms (0.1%)

series447.0ms (2.7%)

rewrite19.0ms (0.1%)

simplify129.0ms (0.8%)

prune360.0ms (2.2%)

localize18.0ms (0.1%)

series1.7s (10.5%)

rewrite17.0ms (0.1%)

simplify114.0ms (0.7%)

prune498.0ms (3.1%)

regimes3.9s (24%)

simplify4.0ms (0%)

end147.0ms (0.9%)

Profiling