Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample2.9s (68.3%)

Results

1.8s	4183×	body	1024	valid
534.0ms	2033×	body	512	valid
182.0ms	368×	body	2048	valid
180.0ms	1009×	body	256	valid
67.0ms	663×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify55.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
579×	`fma-def_binary64`
510×	`associate-/l*_binary64`
467×	`div-sub_binary64`
425×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	33	13
3	57	13
4	112	13
5	224	13
6	514	13
7	1303	13
8	3047	12
9	4469	12
10	4859	12

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

58.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	58.2b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 35 to 25 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.7b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series2.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

2.0ms

(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

1 → 31

Calls

1 calls:

4.0ms

(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify78.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
326×	`unsub-neg_binary64`
325×	`distribute-rgt-in_binary64`
287×	`associate-/r*_binary64`
265×	`associate-l_binary64`

Counts

39 → 49

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	86	629
1	175	535
2	491	470
3	1944	470
4	3994	468
5	4786	468
6	4810	468

prune28.0ms (0.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	2	50

Error

Counts

50 → 2

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) 2)
	58.2b	(/.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 2)

Status

Error

Program

▶

0.6b

(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) 2)

58.2b

(/.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 2)

Compiler

Compiled 1008 to 395 computations (60.8% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
✓	0.0b	(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
✓	0.1b	(*.f64 1/3 (pow.f64 x 3))

series11.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

4.0ms	(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
4.0ms	(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
3.0ms	(*.f64 1/3 (pow.f64 x 3))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
8×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 53

Calls

3 calls:

5.0ms	(*.f64 1/3 (pow.f64 x 3))
0.0ms	(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
0.0ms	(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

702×	`associate-+l+_binary64`
576×	`associate-l_binary64`
541×	`associate-r_binary64`
232×	`distribute-lft-in_binary64`
232×	`distribute-rgt-in_binary64`

Counts

77 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1289
1	177	1161
2	509	1148
3	2789	1148
4	5095	1148

prune73.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	86	2	88

Error

Counts

88 → 2

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) 2)
▶	58.2b	(/.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 2)

Status

Error

Program

✓

0.6b

(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) 2)

▶

58.2b

(/.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 2)

Compiler

Compiled 2236 to 1789 computations (20% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	0.0b	(pow.f64 (exp.f64 x) -2)
✓	0.0b	(pow.f64 (exp.f64 x) 2)
✓	6.6b	(-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2))

series162.0ms (3.9%)

Counts

4 → 40

Calls

4 calls:

79.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
69.0ms	(pow.f64 (exp.f64 x) -2)
10.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2))
3.0ms	(pow.f64 (exp.f64 x) 2)

rewrite86.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`add-sqr-sqrt_binary64`
115×	`*-un-lft-identity_binary64`
106×	`unpow-prod-down_binary64`
84×	`difference-of-squares_binary64`
80×	`times-frac_binary64`

Counts

4 → 262

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
8.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2))
2.0ms	(pow.f64 (exp.f64 x) -2)
2.0ms	(pow.f64 (exp.f64 x) 2)

simplify300.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

624×	`fma-neg_binary64`
328×	`times-frac_binary64`
254×	`distribute-rgt-in_binary64`
204×	`exp-prod_binary64`
195×	`cancel-sign-sub-inv_binary64`

Counts

302 → 336

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	407	11244
1	757	8660
2	2095	6676
3	3810	6670
4	4888	6670
5	4863	6670

prune258.0ms (6.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	336	2	338

Error

Counts

338 → 2

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) 2)
✓	58.2b	(/.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 2)

Status

Error

Program

✓

0.6b

(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) 2)

✓

58.2b

(/.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 2)

Compiler

Compiled 11060 to 5638 computations (49% saved)

regimes97.0ms (2.3%)

Accuracy

Total -0.1b remaining (-982.3%)

Threshold costs -0.1b (-982.3%)

Counts

35 → 1

Compiler

Compiled 1946 to 1373 computations (29.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	7	9
2	7	9

end64.0ms (1.5%)

Compiler: Compiled 54 to 42 computations (22.2% saved)

Details

analyze5.0ms (0.1%)

sample2.9s (68.3%)

simplify55.0ms (1.3%)

prune2.0ms (0.1%)

localize6.0ms (0.1%)

series2.0ms (0.1%)

rewrite6.0ms (0.2%)

simplify78.0ms (1.9%)

prune28.0ms (0.7%)

localize12.0ms (0.3%)

series11.0ms (0.3%)

rewrite9.0ms (0.2%)

simplify56.0ms (1.3%)

prune73.0ms (1.8%)

localize11.0ms (0.3%)

series162.0ms (3.9%)

rewrite86.0ms (2.1%)

simplify300.0ms (7.2%)

prune258.0ms (6.2%)

regimes97.0ms (2.3%)

simplify2.0ms (0%)

end64.0ms (1.5%)

Profiling