Details

analyze78.0ms (1.4%)

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
25%	74.9%	0.1%	3
37.5%	62.4%	0.1%	4
56.2%	43.7%	0.1%	5
62.4%	37.5%	0.1%	6
71.8%	28.1%	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 (20%)

Symmetry

(sort x y)

Results

932.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 29 computations (50.8% saved)

simplify200.0ms (3.6%)

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

prune3.0ms (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

18.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	18.2b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
▶	18.2b	(/.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)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
✓	0.1b	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
✓	18.0b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

series78.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

60.0ms	(/.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))
6.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

rewrite62.0ms (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:

24.0ms	(/.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))
10.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify130.0ms (2.3%)

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

prune349.0ms (6.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	269	7	276
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	271	7	278

Error

4.2b

Counts

278 → 7

Alt Table

Status	Error	Program
	18.2b	(/.f64 (.f64 x y) (.f64 (pow.f64 (+.f64 x y) 2) (+.f64 (+.f64 x y) 1)))
	7.4b	(/.f64 (.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) y) (+.f64 (+.f64 x y) 1))
	15.3b	(/.f64 (/.f64 (.f64 x y) (.f64 (+.f64 x y) (+.f64 x y))) (+.f64 (+.f64 x y) 1))
	9.1b	(.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))
	35.6b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 4)))) (+.f64 (.f64 (+.f64 x y) (+.f64 x y)) (-.f64 (.f64 1 1) (*.f64 (+.f64 x y) 1))))
▶	7.4b	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
	52.0b	(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)))))

Compiler

Compiled 10328 to 4330 computations (58.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 (+.f64 x y) 1))
	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
✓	0.1b	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
✓	19.9b	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))

series92.0ms (1.6%)

Counts

3 → 72

Calls

3 calls:

58.0ms	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
17.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))
16.0ms	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))

rewrite45.0ms (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:

20.0ms	(.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)))
6.0ms	(/.f64 y (+.f64 (+.f64 x y) 1))

simplify118.0ms (2.1%)

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

prune588.0ms (10.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	317	5	322
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	323	6	329

Error

0.0b

Counts

329 → 6

Alt Table

Status	Error	Program
	7.4b	(/.f64 (.f64 y (/.f64 x (.f64 (+.f64 x y) (+.f64 x y)))) (+.f64 (+.f64 x y) 1))
	11.0b	(/.f64 (.f64 x (/.f64 y (+.f64 (+.f64 x y) 1))) (.f64 (+.f64 x y) (+.f64 x y)))
▶	0.2b	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
	0.2b	(*.f64 (/.f64 1 (/.f64 (+.f64 x y) (/.f64 x (+.f64 x y)))) (/.f64 y (+.f64 (+.f64 x y) 1)))
	35.6b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 4)))) (+.f64 (.f64 (+.f64 x y) (+.f64 x y)) (-.f64 (.f64 1 1) (*.f64 (+.f64 x y) 1))))
	0.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y)) (*.f64 (/.f64 (cbrt.f64 x) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))))

Compiler

Compiled 10676 to 4656 computations (56.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series147.0ms (2.6%)

Counts

3 → 72

Calls

3 calls:

76.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
55.0ms	(/.f64 x (+.f64 x y))
16.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))

rewrite90.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
282×	`*-un-lft-identity_binary64`
152×	`add-sqr-sqrt_binary64`
131×	`add-cube-cbrt_binary64`
78×	`associate-l_binary64`

Counts

3 → 279

Calls

3 calls:

35.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
8.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
4.0ms	(/.f64 x (+.f64 x y))

simplify229.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-def_binary64`
469×	`associate-*l/_binary64`
364×	`associate-/l*_binary64`
330×	`associate-/r*_binary64`
326×	`associate-*r/_binary64`

Counts

351 → 392

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	551	10661
1	1683	9917
2	4764	9884
3	5226	9884

prune459.0ms (8.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	474	3	477
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	476	7	483

Error

Counts

483 → 7

Alt Table

Status	Error	Program
	0.2b	(*.f64 (/.f64 1 (/.f64 (+.f64 x y) (/.f64 x (+.f64 x y)))) (/.f64 y (+.f64 (+.f64 x y) 1)))
	0.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))) (cbrt.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)))) (*.f64 (cbrt.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1))))
	7.4b	(/.f64 (.f64 y (/.f64 x (.f64 (+.f64 x y) (+.f64 x y)))) (+.f64 (+.f64 x y) 1))
	11.0b	(/.f64 (.f64 x (/.f64 y (+.f64 (+.f64 x y) 1))) (.f64 (+.f64 x y) (+.f64 x y)))
▶	0.1b	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))) (+.f64 x y))
	11.0b	(.f64 (.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (sqrt.f64 (/.f64 y (+.f64 (+.f64 x y) 1)))) (sqrt.f64 (/.f64 y (+.f64 (+.f64 x y) 1))))
	0.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y)) (*.f64 (/.f64 (cbrt.f64 x) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))))

Compiler

Compiled 15779 to 5805 computations (63.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series93.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

53.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))) (+.f64 x y))
39.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
35×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`

Counts

2 → 101

Calls

2 calls:

17.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1)))
14.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1))) (+.f64 x y))

simplify134.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-def_binary64`
436×	`times-frac_binary64`
370×	`associate-/l*_binary64`
357×	`associate-/r*_binary64`
249×	`associate-*l/_binary64`

Counts

149 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	493	6433
1	1571	5945
2	4855	5909
3	5471	5909

prune398.0ms (7.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	352	2	354
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	355	6	361

Error

Counts

361 → 6

Alt Table

Status	Error	Program
	11.0b	(/.f64 (.f64 x (/.f64 y (+.f64 (+.f64 x y) 1))) (.f64 (+.f64 x y) (+.f64 x y)))
	0.4b	(/.f64 (/.f64 x (+.f64 x y)) (/.f64 (+.f64 x y) (/.f64 y (+.f64 (+.f64 x y) 1))))
	7.4b	(/.f64 (.f64 y (/.f64 x (.f64 (+.f64 x y) (+.f64 x y)))) (+.f64 (+.f64 x y) 1))
	0.2b	(*.f64 (/.f64 1 (/.f64 (+.f64 x y) (/.f64 x (+.f64 x y)))) (/.f64 y (+.f64 (+.f64 x y) 1)))
	0.1b	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 x y) x)) (/.f64 y (+.f64 (+.f64 x y) 1))) (+.f64 x y))
	11.0b	(.f64 (.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (sqrt.f64 (/.f64 y (+.f64 (+.f64 x y) 1)))) (sqrt.f64 (/.f64 y (+.f64 (+.f64 x y) 1))))

Compiler

Compiled 12125 to 5755 computations (52.5% saved)

regimes910.0ms (16.4%)

Accuracy

Total 0.1b remaining (70.7%)

Threshold costs 0.1b (70.7%)

Counts

178 → 1

Compiler

Compiled 11999 to 6461 computations (46.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	15	25
2	14	25

end163.0ms (2.9%)

Remove: (sort x y)
Compiler: Compiled 204 to 100 computations (51% saved)

Details

analyze78.0ms (1.4%)

sample1.1s (20%)

simplify200.0ms (3.6%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series78.0ms (1.4%)

rewrite62.0ms (1.1%)

simplify130.0ms (2.3%)

prune349.0ms (6.3%)

localize13.0ms (0.2%)

series92.0ms (1.6%)

rewrite45.0ms (0.8%)

simplify118.0ms (2.1%)

prune588.0ms (10.6%)

localize8.0ms (0.1%)

series147.0ms (2.6%)

rewrite90.0ms (1.6%)

simplify229.0ms (4.1%)

prune459.0ms (8.2%)

localize8.0ms (0.1%)

series93.0ms (1.7%)

rewrite43.0ms (0.8%)

simplify134.0ms (2.4%)

prune398.0ms (7.1%)

regimes910.0ms (16.4%)

simplify4.0ms (0.1%)

end163.0ms (2.9%)

Profiling