Details

analyze190.0ms (3.8%)

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 26 to 19 computations (26.9% saved)

sample76.0ms (1.5%)

Algorithm

1×

intervals

Results

58.0ms	256×	body	128	valid
6.0ms	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 43 to 32 computations (25.6% saved)

simplify121.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1247×	`unsub-neg_binary64`
616×	`neg-sub0_binary64`
571×	`neg-mul-1_binary64`
560×	`fma-neg_binary64`
452×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	46	17
3	116	17
4	358	17
5	1331	17
6	3463	17
7	3625	17
8	4293	17
9	4678	17
10	4650	17
11	4895	17
12	4905	17

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series41.0ms (0.8%)

Counts

4 → 80

Calls

4 calls:

15.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
10.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite58.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
57×	`prod-diff_binary64`
54×	`add-cube-cbrt_binary64`
26×	`distribute-lft-in_binary64`

Counts

4 → 188

Calls

4 calls:

21.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
7.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify195.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

359×	`associate-/l/_binary64`
345×	`associate-/r*_binary64`
257×	`associate-/r/_binary64`
250×	`associate-l_binary64`
225×	`exp-prod_binary64`

Counts

268 → 295

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	4962
1	502	4321
2	2059	4004
3	4566	3999
4	5030	3999

prune318.0ms (6.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	291	4	295
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	292	5	297

Error

0.0b

Counts

297 → 5

Alt Table

Status	Error	Program
	0.1b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
	27.2b	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	0.2b	(+.f64 (.f64 1 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 7304 to 4637 computations (36.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
✓	0.0b	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
✓	0.2b	(*.f64 (/.f64 m v) m)
✓	7.2b	(/.f64 (pow.f64 m 3) v)

series57.0ms (1.1%)

Counts

4 → 72

Calls

4 calls:

19.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
14.0ms	(/.f64 (pow.f64 m 3) v)
13.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
11.0ms	(*.f64 (/.f64 m v) m)

rewrite49.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`*-un-lft-identity_binary64`
64×	`add-sqr-sqrt_binary64`
55×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
24×	`prod-diff_binary64`

Counts

4 → 183

Calls

4 calls:

20.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
7.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
4.0ms	(*.f64 (/.f64 m v) m)
4.0ms	(/.f64 (pow.f64 m 3) v)

simplify171.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-neg_binary64`
301×	`cancel-sign-sub-inv_binary64`
264×	`unswap-sqr_binary64`
188×	`log-prod_binary64`
174×	`associate-r_binary64`

Counts

255 → 256

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	270	4662
1	552	4309
2	2340	3942
3	4392	3846
4	5016	3846

prune297.0ms (5.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	256	5	261

Error

Counts

261 → 5

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 1 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
	12.5b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 m (/.f64 m v)) (+.f64 m (/.f64 m v))) (.f64 (fma.f64 2 (.f64 (/.f64 m v) m) 1) (fma.f64 2 (.f64 (/.f64 m v) m) 1))) v) (.f64 (+.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (.f64 (/.f64 m v) m) 1)) (pow.f64 m 3))) (.f64 (+.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) v))
	27.2b	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
▶	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 8529 to 3768 computations (55.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series25.0ms (0.5%)

Counts

3 → 64

Calls

3 calls:

11.0ms	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
8.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
6.0ms	(/.f64 (-.f64 1 m) v)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

3 → 81

Calls

3 calls:

6.0ms	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
5.0ms	(/.f64 (-.f64 1 m) v)
0.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

426×	`fma-neg_binary64`
388×	`associate-l_binary64`
380×	`div-sub_binary64`
323×	`associate-r_binary64`
319×	`distribute-rgt-in_binary64`

Counts

145 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2355
1	323	2151
2	936	2109
3	3601	2109
4	5118	2109

prune134.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	131	5	136

Error

Counts

136 → 5

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (.f64 1 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
	12.5b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 m (/.f64 m v)) (+.f64 m (/.f64 m v))) (.f64 (fma.f64 2 (.f64 (/.f64 m v) m) 1) (fma.f64 2 (.f64 (/.f64 m v) m) 1))) v) (.f64 (+.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (.f64 (/.f64 m v) m) 1)) (pow.f64 m 3))) (.f64 (+.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) v))
	27.2b	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 2639 to 1710 computations (35.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.2b	(.f64 (neg.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.5b	(*.f64 (cbrt.f64 m) (cbrt.f64 m))
✓	0.6b	(cbrt.f64 m)

series150.0ms (3%)

Counts

4 → 60

Calls

4 calls:

55.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
38.0ms	(*.f64 (cbrt.f64 m) (cbrt.f64 m))
34.0ms	(cbrt.f64 m)
23.0ms	(.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
42×	`prod-diff_binary64`
25×	`distribute-lft-in_binary64`

Counts

4 → 160

Calls

4 calls:

13.0ms	(.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
4.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
4.0ms	(*.f64 (cbrt.f64 m) (cbrt.f64 m))
1.0ms	(cbrt.f64 m)

simplify143.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

539×	`fma-def_binary64`
429×	`associate-l_binary64`
354×	`distribute-lft-neg-out_binary64`
353×	`fma-neg_binary64`
351×	`associate-r_binary64`

Counts

220 → 229

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	3239
1	426	2664
2	1834	2607
3	3698	2568
4	4978	2568
5	4952	2568

prune441.0ms (8.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	265	5	270

Error

Counts

270 → 5

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (.f64 1 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
	12.5b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 m (/.f64 m v)) (+.f64 m (/.f64 m v))) (.f64 (fma.f64 2 (.f64 (/.f64 m v) m) 1) (fma.f64 2 (.f64 (/.f64 m v) m) 1))) v) (.f64 (+.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (.f64 (/.f64 m v) m) 1)) (pow.f64 m 3))) (.f64 (+.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) v))
	27.2b	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 10807 to 6150 computations (43.1% saved)

regimes1.3s (25.5%)

Accuracy

Total 0.1b remaining (83.7%)

Threshold costs 0.1b (83.7%)

Counts

301 → 1

Compiler

Compiled 21017 to 14326 computations (31.8% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	34
1	30	34
2	39	34
3	47	34
4	51	34
5	52	34
6	50	34

end1.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

sample1.1s (21.6%)

Algorithm

1×

intervals

Results

442.0ms	8000×	body	128	valid
215.0ms	8059×	pre	128	true
3.0ms	59×	body	128	invalid

Compiler

Compiled 220 to 131 computations (40.5% saved)

Details

analyze190.0ms (3.8%)

sample76.0ms (1.5%)

simplify121.0ms (2.4%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series41.0ms (0.8%)

rewrite58.0ms (1.2%)

simplify195.0ms (3.9%)

prune318.0ms (6.3%)

localize10.0ms (0.2%)

series57.0ms (1.1%)

rewrite49.0ms (1%)

simplify171.0ms (3.4%)

prune297.0ms (5.9%)

localize6.0ms (0.1%)

series25.0ms (0.5%)

rewrite15.0ms (0.3%)

simplify87.0ms (1.7%)

prune134.0ms (2.7%)

localize13.0ms (0.3%)

series150.0ms (3%)

rewrite36.0ms (0.7%)

simplify143.0ms (2.8%)

prune441.0ms (8.8%)

regimes1.3s (25.5%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.1s (21.6%)

Profiling