Details

analyze371.0ms (4.8%)

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)

sample50.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms

256×

body

128

valid

Compiler

Compiled 41 to 21 computations (48.8% saved)

simplify171.0ms (2.2%)

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

prune6.0ms (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

20.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.2b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
▶	20.2b	(/.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)

localize14.0ms (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))
✓	20.0b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

series150.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

112.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
27.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
10.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

rewrite120.0ms (1.6%)

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:

34.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
30.0ms	(/.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))

simplify187.0ms (2.4%)

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

prune391.0ms (5.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	269	7	276
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	270	8	278

Error

3.5b

Counts

278 → 8

Alt Table

Status	Error	Program
	20.2b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
	11.2b	(/.f64 x (/.f64 (.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)) y))
▶	7.7b	(/.f64 (.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) y) (+.f64 (+.f64 x y) 1))
	20.2b	(/.f64 (.f64 x y) (.f64 (fma.f64 2 (.f64 x y) (fma.f64 x x (.f64 y y))) (+.f64 (+.f64 x y) 1)))
	9.3b	(.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))
	7.7b	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1)))
	34.5b	(/.f64 y (*.f64 (+.f64 1 x) x))
	48.6b	(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)))))

Compiler

Compiled 10320 to 4326 computations (58.1% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
✓	0.1b	(/.f64 (.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) y) (+.f64 (+.f64 x y) 1))
✓	8.2b	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) y)
✓	18.3b	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))

series165.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

114.0ms	(/.f64 (.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) y) (+.f64 (+.f64 x y) 1))
34.0ms	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) y)
17.0ms	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))

rewrite93.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
18×	`associate-/r/_binary64`
15×	`associate-l_binary64`

Counts

3 → 103

Calls

3 calls:

30.0ms	(/.f64 (.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) y) (+.f64 (+.f64 x y) 1))
19.0ms	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) y)
17.0ms	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))

simplify243.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

364×	`times-frac_binary64`
329×	`associate-/r*_binary64`
267×	`associate-/l*_binary64`
262×	`fma-def_binary64`
211×	`associate-r_binary64`

Counts

175 → 208

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	417	5783
1	1260	5241
2	4878	5241
3	4980	5241

prune547.0ms (7.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	252	7	259
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	259	8	267

Error

0.0b

Counts

267 → 8

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y) (+.f64 (+.f64 x y) 1))
	36.2b	(/.f64 (-.f64 (/.f64 y x) (*.f64 2 (/.f64 (pow.f64 y 2) (pow.f64 x 2)))) (+.f64 (+.f64 x y) 1))
	0.2b	(/.f64 (.f64 (.f64 (/.f64 1 (+.f64 x y)) (/.f64 x (+.f64 x y))) y) (+.f64 (+.f64 x y) 1))
	11.2b	(/.f64 x (/.f64 (.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)) y))
	7.7b	(/.f64 (/.f64 x (*.f64 (+.f64 x y) (+.f64 x y))) (/.f64 (+.f64 (+.f64 x y) 1) y))
	7.9b	(/.f64 1 (/.f64 (+.f64 (+.f64 x y) 1) (.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) y)))
	0.7b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y)) (*.f64 (/.f64 (cbrt.f64 x) (+.f64 x y)) y)) (+.f64 (+.f64 x y) 1))
	32.6b	(/.f64 (/.f64 y x) (+.f64 (+.f64 x y) 1))

Compiler

Compiled 8531 to 3672 computations (57% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x y))
✓	0.1b	(/.f64 (*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y) (+.f64 (+.f64 x y) 1))
✓	0.1b	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
✓	8.2b	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y)

series138.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

77.0ms	(/.f64 (*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y) (+.f64 (+.f64 x y) 1))
24.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
21.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y)
16.0ms	(/.f64 x (+.f64 x y))

rewrite119.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

272×	`times-frac_binary64`
272×	`*-un-lft-identity_binary64`
135×	`add-sqr-sqrt_binary64`
126×	`add-cube-cbrt_binary64`
78×	`associate-l_binary64`

Counts

4 → 284

Calls

4 calls:

24.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y)
23.0ms	(/.f64 (*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y) (+.f64 (+.f64 x y) 1))
18.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
10.0ms	(/.f64 x (+.f64 x y))

simplify615.0ms (8%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-def_binary64`
363×	`times-frac_binary64`
346×	`associate-/r*_binary64`
342×	`associate-/l*_binary64`
286×	`associate-*l/_binary64`

Counts

380 → 414

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	562	10408
1	1608	9658
2	4751	9625
3	5279	9625

prune750.0ms (9.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	407	7	414
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	413	9	422

Error

Counts

422 → 9

Alt Table

Status	Error	Program
	7.7b	(/.f64 (/.f64 x (*.f64 (+.f64 x y) (+.f64 x y))) (/.f64 (+.f64 (+.f64 x y) 1) y))
	0.5b	(/.f64 1 (/.f64 (+.f64 (+.f64 x y) 1) (*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y)))
	13.3b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 y (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))) 3)) (+.f64 (+.f64 x y) 1))
	0.7b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y)) (*.f64 (/.f64 (cbrt.f64 x) (+.f64 x y)) y)) (+.f64 (+.f64 x y) 1))
▶	0.1b	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))) (+.f64 (+.f64 x y) 1))
	0.2b	(/.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 (+.f64 (+.f64 x y) 1) y))
	12.5b	(/.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) 1) (.f64 (/.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) (+.f64 x y)) y)) (+.f64 (+.f64 x y) 1))
	0.2b	(.f64 (.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y) (/.f64 1 (+.f64 (+.f64 x y) 1)))
	7.6b	(/.f64 (.f64 (/.f64 x 1) (.f64 (/.f64 (/.f64 1 (+.f64 x y)) (+.f64 x y)) y)) (+.f64 (+.f64 x y) 1))

Compiler

Compiled 13608 to 4775 computations (64.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series428.0ms (5.5%)

Counts

3 → 72

Calls

3 calls:

291.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))) (+.f64 (+.f64 x y) 1))
105.0ms	(/.f64 y (+.f64 x y))
32.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))

rewrite95.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
45×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
35×	`add-cbrt-cube_binary64`
35×	`add-exp-log_binary64`

Counts

3 → 135

Calls

3 calls:

38.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
28.0ms	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))) (+.f64 (+.f64 x y) 1))
9.0ms	(/.f64 y (+.f64 x y))

simplify240.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-def_binary64`
367×	`times-frac_binary64`
345×	`associate-/l*_binary64`
311×	`associate-/r*_binary64`
236×	`associate-*r/_binary64`

Counts

207 → 227

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	437	6186
1	1332	5629
2	4719	5583
3	5365	5583

prune651.0ms (8.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	280	8	288

Error

Counts

288 → 8

Alt Table

Status	Error	Program
	0.5b	(/.f64 1 (/.f64 (+.f64 (+.f64 x y) 1) (*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y)))
	13.3b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 y (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))) 3)) (+.f64 (+.f64 x y) 1))
	0.7b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y)) (*.f64 (/.f64 (cbrt.f64 x) (+.f64 x y)) y)) (+.f64 (+.f64 x y) 1))
✓	0.1b	(/.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))) (+.f64 (+.f64 x y) 1))
	4.8b	(/.f64 (.f64 x (/.f64 y (+.f64 x y))) (.f64 (+.f64 (+.f64 x y) 1) (+.f64 x y)))
	0.2b	(/.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 (+.f64 (+.f64 x y) 1) y))
	0.2b	(.f64 (.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) y) (/.f64 1 (+.f64 (+.f64 x y) 1)))
	0.2b	(/.f64 (.f64 (.f64 (/.f64 x (+.f64 x y)) y) (/.f64 1 (+.f64 x y))) (+.f64 (+.f64 x y) 1))

Compiler

Compiled 8793 to 3414 computations (61.2% saved)

regimes928.0ms (12%)

Accuracy

Total 0.1b remaining (78.9%)

Threshold costs 0.1b (78.9%)

Counts

153 → 1

Compiler

Compiled 10909 to 5812 computations (46.7% saved)

simplify5.0ms (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

end12.0ms (0.2%)

Remove: (sort x y)
Compiler: Compiled 57 to 27 computations (52.6% saved)

sample1.2s (15.3%)

Algorithm

1×

intervals

Results

615.0ms

8000×

body

128

valid

Compiler

Compiled 209 to 105 computations (49.8% saved)

Details

analyze371.0ms (4.8%)

sample50.0ms (0.7%)

simplify171.0ms (2.2%)

prune6.0ms (0.1%)

localize14.0ms (0.2%)

series150.0ms (1.9%)

rewrite120.0ms (1.6%)

simplify187.0ms (2.4%)

prune391.0ms (5.1%)

localize21.0ms (0.3%)

series165.0ms (2.1%)

rewrite93.0ms (1.2%)

simplify243.0ms (3.2%)

prune547.0ms (7.1%)

localize18.0ms (0.2%)

series138.0ms (1.8%)

rewrite119.0ms (1.5%)

simplify615.0ms (8%)

prune750.0ms (9.7%)

localize9.0ms (0.1%)

series428.0ms (5.5%)

rewrite95.0ms (1.2%)

simplify240.0ms (3.1%)

prune651.0ms (8.4%)

regimes928.0ms (12%)

simplify5.0ms (0.1%)

end12.0ms (0.2%)

sample1.2s (15.3%)

Profiling