Details

analyze115.0ms (2.3%)

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
12.5%	87.4%	0.1%	5
46.8%	53.1%	0.1%	6
70.2%	29.7%	0.1%	7
76.5%	23.4%	0.1%	8
83.5%	16.4%	0.1%	9
87%	12.9%	0.1%	10
91.1%	8.8%	0.1%	11
93.2%	6.7%	0.1%	12
95.4%	4.5%	0.1%	13
96.5%	3.4%	0.1%	14

Compiler

Compiled 20 to 10 computations (50% saved)

sample1.1s (21%)

Symmetry

(sort x y)

Results

954.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 29 computations (50.8% saved)

simplify143.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

985×	`associate-/l*_binary64`
659×	`distribute-lft-out_binary64`
601×	`*-commutative_binary64`
469×	`distribute-rgt-out_binary64`
356×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	39	25
2	135	23
3	474	23
4	1536	23
5	2122	23
6	2589	23
7	2567	23
8	2620	23
9	2677	23
10	2770	23
11	3956	23
12	4088	23
13	4454	23
14	4983	23
15	4968	23
16	4961	23

prune4.0ms (0.1%)

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

17.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.4b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
▶	17.4b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

Compiler

Compiled 109 to 47 computations (56.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
✓	0.0b	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
✓	17.2b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

series51.0ms (1%)

Counts

3 → 72

Calls

3 calls:

34.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
12.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
5.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

rewrite57.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`flip-+_binary64`
60×	`frac-times_binary64`
60×	`flip3-+_binary64`
31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 146

Calls

3 calls:

16.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
13.0ms	(*.f64 (+.f64 x y) (+.f64 x y))
12.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))

simplify136.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

650×	`times-frac_binary64`
389×	`fma-def_binary64`
369×	`distribute-rgt-in_binary64`
363×	`associate-/l*_binary64`
348×	`distribute-lft-in_binary64`

Counts

218 → 276

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	448	7281
1	1472	6637
2	5162	6637

prune250.0ms (4.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	267	9	276
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	269	9	278

Error

3.3b

Counts

278 → 9

Alt Table

Status	Error	Program
	51.3b	(/.f64 (.f64 x y) (/.f64 (.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (+.f64 x y) 1)) (.f64 (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y))) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y))))))
	34.6b	(/.f64 x (*.f64 y (+.f64 1 y)))
▶	5.7b	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
	25.2b	(/.f64 (.f64 x y) (cbrt.f64 (pow.f64 (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 x (+.f64 y 1))) 3)))
	51.6b	(exp.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 y)) (+.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 (+.f64 x y))) (log.f64 (+.f64 (+.f64 x y) 1)))))
	5.7b	(/.f64 (.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) y) (+.f64 (+.f64 x y) 1))
	9.5b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))) (-.f64 (+.f64 x y) 1))
	30.4b	(/.f64 y (*.f64 (+.f64 1 x) x))
	19.7b	(/.f64 (.f64 x y) (/.f64 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 x y)) (+.f64 (+.f64 x y) 1)) (-.f64 x y)))

Compiler

Compiled 10418 to 4384 computations (57.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
✓	0.0b	(/.f64 y (+.f64 (+.f64 x y) 1))
✓	0.1b	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
✓	16.3b	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))

series56.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

34.0ms	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
11.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
10.0ms	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
36×	`add-sqr-sqrt_binary64`
31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 136

Calls

3 calls:

18.0ms	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
6.0ms	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))
5.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))

simplify118.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

364×	`times-frac_binary64`
346×	`associate-/r*_binary64`
278×	`fma-def_binary64`
267×	`associate-/l*_binary64`
240×	`associate-*r/_binary64`

Counts

208 → 271

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	481	6928
1	1467	6405
2	5014	6405

prune349.0ms (6.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	316	6	322
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	323	8	331

Error

0.0b

Counts

331 → 8

Alt Table

Status	Error	Program
	9.5b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))) (-.f64 (+.f64 x y) 1))
	0.7b	(.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y)) (/.f64 (cbrt.f64 x) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
	19.7b	(/.f64 (.f64 x y) (/.f64 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 x y)) (+.f64 (+.f64 x y) 1)) (-.f64 x y)))
▶	0.2b	(.f64 (/.f64 1 (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))))
	5.7b	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 1 (/.f64 (+.f64 (+.f64 x y) 1) y)))
	15.6b	(.f64 (.f64 (/.f64 x (.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 x y))) (-.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
	5.7b	(.f64 (.f64 x (/.f64 1 (*.f64 (+.f64 x y) (+.f64 x y)))) (/.f64 y (+.f64 (+.f64 x y) 1)))
	6.1b	(.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (.f64 (+.f64 x y) (cbrt.f64 (+.f64 x y))))) (/.f64 y (+.f64 (+.f64 x y) 1)))

Compiler

Compiled 10792 to 4716 computations (56.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x y))
	0.0b	(/.f64 y (+.f64 (+.f64 x y) 1))
✓	0.0b	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
✓	0.2b	(.f64 (/.f64 1 (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))))

series65.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

33.0ms	(.f64 (/.f64 1 (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))))
25.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
7.0ms	(/.f64 1 (+.f64 x y))

rewrite57.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-exp-log_binary64`
72×	`*-un-lft-identity_binary64`
58×	`add-cbrt-cube_binary64`
55×	`times-frac_binary64`
49×	`add-sqr-sqrt_binary64`

Counts

3 → 172

Calls

3 calls:

17.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
17.0ms	(.f64 (/.f64 1 (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))))
4.0ms	(/.f64 1 (+.f64 x y))

simplify164.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

969×	`fma-def_binary64`
368×	`times-frac_binary64`
339×	`associate-/r*_binary64`
336×	`associate-/l*_binary64`
293×	`associate-*r/_binary64`

Counts

244 → 305

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	544	8533
1	1671	7661
2	4906	7625
3	5541	7625

prune531.0ms (10.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	383	7	390
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	390	8	398

Error

0.0b

Counts

398 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 1 (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 (/.f64 y (*.f64 (cbrt.f64 (+.f64 x (+.f64 y 1))) (cbrt.f64 (+.f64 x (+.f64 y 1))))) (cbrt.f64 (+.f64 (+.f64 x y) 1)))))
	0.2b	(.f64 (/.f64 1 (+.f64 x y)) (.f64 x (/.f64 (/.f64 y (+.f64 x (+.f64 y 1))) (+.f64 x y))))
	35.6b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 x y))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 x y))) (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))))
	0.7b	(.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y)) (/.f64 (cbrt.f64 x) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
	13.8b	(.f64 (/.f64 1 (+.f64 x y)) (/.f64 (.f64 x y) (*.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))))
	0.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))) (+.f64 x y))) (cbrt.f64 (/.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))) (+.f64 x y)))) (cbrt.f64 (/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))) (+.f64 x y))))
	0.2b	(.f64 (/.f64 1 (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 1 (/.f64 (+.f64 x (+.f64 y 1)) y))))
▶	0.1b	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))) (+.f64 x y))

Compiler

Compiled 14126 to 7079 computations (49.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x y))
✓	0.0b	(/.f64 y (+.f64 x (+.f64 y 1)))
✓	0.0b	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1))))
✓	0.1b	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))) (+.f64 x y))

series79.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

34.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))) (+.f64 x y))
26.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1))))
11.0ms	(/.f64 y (+.f64 x (+.f64 y 1)))
8.0ms	(/.f64 x (+.f64 x y))

rewrite54.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity_binary64`
62×	`times-frac_binary64`
54×	`add-sqr-sqrt_binary64`
42×	`add-cube-cbrt_binary64`
38×	`add-cbrt-cube_binary64`

Counts

4 → 175

Calls

4 calls:

19.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1))))
12.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))) (+.f64 x y))
5.0ms	(/.f64 y (+.f64 x (+.f64 y 1)))
3.0ms	(/.f64 x (+.f64 x y))

simplify131.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

438×	`times-frac_binary64`
387×	`associate-/l*_binary64`
377×	`associate-/r*_binary64`
354×	`fma-def_binary64`
293×	`associate-*l/_binary64`

Counts

271 → 289

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	594	8980
1	1844	8389
2	5145	8389

prune361.0ms (7.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	286	3	289
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	290	7	297

Error

0.0b

Counts

297 → 7

Alt Table

Status	Error	Program
	35.6b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 x y))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 x y))) (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))))
	0.4b	(/.f64 (/.f64 x (+.f64 x y)) (/.f64 (+.f64 x y) (/.f64 y (+.f64 x (+.f64 y 1)))))
	0.7b	(.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y)) (/.f64 (cbrt.f64 x) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
	13.8b	(.f64 (/.f64 1 (+.f64 x y)) (/.f64 (.f64 x y) (*.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))))
	0.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))) (+.f64 x y))) (cbrt.f64 (/.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))) (+.f64 x y)))) (cbrt.f64 (/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))) (+.f64 x y))))
	0.5b	(/.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 (/.f64 y (.f64 (cbrt.f64 (+.f64 x (+.f64 y 1))) (cbrt.f64 (+.f64 x (+.f64 y 1))))) (cbrt.f64 (+.f64 x (+.f64 y 1))))) (+.f64 x y))
	0.1b	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 (/.f64 y (+.f64 x (+.f64 y 1))) (+.f64 x y)))

Compiler

Compiled 10556 to 5461 computations (48.3% saved)

regimes1.1s (22.3%)

Accuracy

Total 0.1b remaining (73.6%)

Threshold costs 0.1b (73.6%)

Counts

346 → 1

Compiler

Compiled 25502 to 13911 computations (45.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	19	29
2	18	29

end109.0ms (2.1%)

Remove: (sort x y)
Compiler: Compiled 290 to 155 computations (46.6% saved)

Details

analyze115.0ms (2.3%)

sample1.1s (21%)

simplify143.0ms (2.8%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series51.0ms (1%)

rewrite57.0ms (1.1%)

simplify136.0ms (2.7%)

prune250.0ms (4.9%)

localize7.0ms (0.1%)

series56.0ms (1.1%)

rewrite42.0ms (0.8%)

simplify118.0ms (2.3%)

prune349.0ms (6.8%)

localize8.0ms (0.2%)

series65.0ms (1.3%)

rewrite57.0ms (1.1%)

simplify164.0ms (3.2%)

prune531.0ms (10.4%)

localize8.0ms (0.2%)

series79.0ms (1.5%)

rewrite54.0ms (1.1%)

simplify131.0ms (2.6%)

prune361.0ms (7.1%)

regimes1.1s (22.3%)

simplify2.0ms (0%)

end109.0ms (2.1%)

Profiling