Details

analyze63.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample1.2s (38.3%)

Results

889.0ms	8256×	body	128	valid
7.0ms	63×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify118.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 m) v)
✓	0.1b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
✓	0.1b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

series26.0ms (0.8%)

Counts

3 → 64

Calls

3 calls:

11.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
7.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
7.0ms	(/.f64 (-.f64 1 m) v)

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`

Counts

3 → 76

Calls

3 calls:

5.0ms	(/.f64 (-.f64 1 m) v)
3.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
0.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

simplify94.0ms (3%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
332×	`distribute-rgt-neg-out_binary64`
308×	`associate-l_binary64`
305×	`div-sub_binary64`
264×	`exp-prod_binary64`

Counts

140 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2018
1	285	1760
2	745	1726
3	2553	1726
4	4478	1726
5	4976	1726

prune111.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	8	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Error

0.0b

Counts

129 → 8

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)) (neg.f64 m))
	4.6b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	0.8b	(.f64 (.f64 m (*.f64 (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))) (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))
	0.6b	(.f64 (sqrt.f64 m) (.f64 (sqrt.f64 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))
▶	0.1b	(+.f64 (.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m) (*.f64 -1 m))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))) (cbrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	0.3b	(*.f64 m (fma.f64 m (/.f64 (/.f64 (-.f64 1 m) (sqrt.f64 v)) (sqrt.f64 v)) -1))
	19.7b	(*.f64 m (cbrt.f64 (pow.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) 3)))

Compiler

Compiled 2294 to 1397 computations (39.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m) (*.f64 -1 m))
	0.0b	(/.f64 (-.f64 1 m) v)
✓	0.2b	(.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m)
✓	0.2b	(*.f64 m (/.f64 (-.f64 1 m) v))

series41.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

15.0ms	(.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m)
15.0ms	(+.f64 (.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m) (*.f64 -1 m))
11.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
25×	`associate-r_binary64`
24×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 82

Calls

3 calls:

8.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
8.0ms	(+.f64 (.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m) (*.f64 -1 m))
7.0ms	(.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m)

simplify60.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

504×	`associate-*l/_binary64`
374×	`fma-def_binary64`
362×	`associate-/l*_binary64`
275×	`distribute-rgt-in_binary64`
246×	`distribute-lft-in_binary64`

Counts

154 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	2143
1	391	2007
2	1293	1980
3	5156	1980

prune185.0ms (5.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	194	7	201

Error

0.0b

Counts

201 → 7

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)) (neg.f64 m))
	4.6b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
▶	0.1b	(fma.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m (.f64 -1 m))
	0.9b	(+.f64 (.f64 (.f64 m (.f64 (/.f64 (-.f64 1 m) v) (.f64 (cbrt.f64 m) (cbrt.f64 m)))) (cbrt.f64 m)) (*.f64 -1 m))
	0.8b	(+.f64 (.f64 (.f64 (.f64 m (.f64 (cbrt.f64 (/.f64 (-.f64 1 m) v)) (cbrt.f64 (/.f64 (-.f64 1 m) v)))) (cbrt.f64 (/.f64 (-.f64 1 m) v))) m) (*.f64 -1 m))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))) (cbrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	0.3b	(*.f64 m (fma.f64 m (/.f64 (/.f64 (-.f64 1 m) (sqrt.f64 v)) (sqrt.f64 v)) -1))

Compiler

Compiled 4026 to 2433 computations (39.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 1 m) v)
✓	0.1b	(fma.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m (.f64 -1 m))
	0.2b	(*.f64 m (/.f64 (-.f64 1 m) v))

series12.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(fma.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) m (*.f64 -1 m))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) m (*.f64 -1 m))

simplify72.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-neg_binary64`
409×	`associate-l_binary64`
382×	`cancel-sign-sub-inv_binary64`
364×	`associate-r_binary64`
359×	`exp-prod_binary64`

Counts

34 → 29

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	545
1	69	512
2	161	462
3	501	462
4	2648	462
5	4604	462
6	5130	462

prune148.0ms (4.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	149	7	156

Error

0.0b

Counts

156 → 7

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)) (neg.f64 m))
	4.6b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.1b	(fma.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m (.f64 -1 m))
	0.9b	(+.f64 (.f64 (.f64 m (.f64 (/.f64 (-.f64 1 m) v) (.f64 (cbrt.f64 m) (cbrt.f64 m)))) (cbrt.f64 m)) (*.f64 -1 m))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))) (cbrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	0.3b	(*.f64 m (fma.f64 m (/.f64 (/.f64 (-.f64 1 m) (sqrt.f64 v)) (sqrt.f64 v)) -1))
	0.7b	(fma.f64 (.f64 (.f64 m (.f64 (cbrt.f64 (/.f64 (-.f64 1 m) v)) (cbrt.f64 (/.f64 (-.f64 1 m) v)))) (cbrt.f64 (/.f64 (-.f64 1 m) v))) m (.f64 -1 m))

Compiler

Compiled 2962 to 1757 computations (40.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)) (neg.f64 m))
✓	0.0b	(-.f64 m (*.f64 m m))
✓	0.0b	(/.f64 (-.f64 m (*.f64 m m)) v)
✓	0.2b	(.f64 m (/.f64 (-.f64 m (.f64 m m)) v))

series45.0ms (1.4%)

Counts

4 → 84

Calls

4 calls:

17.0ms	(.f64 m (/.f64 (-.f64 m (.f64 m m)) v))
14.0ms	(+.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)) (neg.f64 m))
12.0ms	(/.f64 (-.f64 m (*.f64 m m)) v)
2.0ms	(-.f64 m (*.f64 m m))

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

4 → 119

Calls

4 calls:

8.0ms	(.f64 m (/.f64 (-.f64 m (.f64 m m)) v))
6.0ms	(+.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)) (neg.f64 m))
4.0ms	(/.f64 (-.f64 m (*.f64 m m)) v)
3.0ms	(-.f64 m (*.f64 m m))

simplify104.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

750×	`fma-def_binary64`
390×	`div-sub_binary64`
275×	`times-frac_binary64`
249×	`fma-neg_binary64`
241×	`distribute-lft-neg-out_binary64`

Counts

203 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	190	2907
1	444	2777
2	1653	2745
3	4259	2742
4	5152	2742

prune163.0ms (5.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	189	7	196

Error

Counts

196 → 7

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)) (neg.f64 m))
	4.6b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	0.7b	(fma.f64 (.f64 (.f64 m (.f64 (cbrt.f64 (/.f64 (-.f64 1 m) v)) (cbrt.f64 (/.f64 (-.f64 1 m) v)))) (cbrt.f64 (/.f64 (-.f64 1 m) v))) m (.f64 -1 m))
	2.5b	(+.f64 (*.f64 (fma.f64 m m (pow.f64 m 3/2)) (/.f64 (-.f64 (sqrt.f64 m) m) v)) (neg.f64 m))
✓	0.1b	(fma.f64 (.f64 m (/.f64 (-.f64 1 m) v)) m (.f64 -1 m))
	0.9b	(+.f64 (.f64 (.f64 m (.f64 (/.f64 (-.f64 1 m) v) (.f64 (cbrt.f64 m) (cbrt.f64 m)))) (cbrt.f64 m)) (*.f64 -1 m))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))) (cbrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))

Compiler

Compiled 3656 to 953 computations (73.9% saved)

regimes489.0ms (15.6%)

Accuracy

Total 0.2b remaining (89.5%)

Threshold costs 0.2b (89.5%)

Counts

170 → 1

Compiler

Compiled 9692 to 6071 computations (37.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	16	16
2	21	16
3	23	16
4	24	16
5	23	16

end102.0ms (3.3%)

Compiler: Compiled 175 to 112 computations (36% saved)

Details

analyze63.0ms (2%)

sample1.2s (38.3%)

simplify118.0ms (3.8%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series26.0ms (0.8%)

rewrite11.0ms (0.4%)

simplify94.0ms (3%)

prune111.0ms (3.5%)

localize7.0ms (0.2%)

series41.0ms (1.3%)

rewrite27.0ms (0.9%)

simplify60.0ms (1.9%)

prune185.0ms (5.9%)

localize7.0ms (0.2%)

series12.0ms (0.4%)

rewrite1.0ms (0%)

simplify72.0ms (2.3%)

prune148.0ms (4.7%)

localize7.0ms (0.2%)

series45.0ms (1.4%)

rewrite28.0ms (0.9%)

simplify104.0ms (3.3%)

prune163.0ms (5.2%)

regimes489.0ms (15.6%)

simplify3.0ms (0.1%)

end102.0ms (3.3%)

Profiling