Details

analyze212.0ms (3.1%)

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 25 to 18 computations (28% saved)

sample35.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 42 to 31 computations (26.2% saved)

simplify143.0ms (2.1%)

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

prune3.0ms (0%)

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

0.0b

Counts

3 → 2

Alt Table

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

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))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.0b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

rewrite49.0ms (0.7%)

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:

16.0ms	(.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))

series86.0ms (1.2%)

Counts

4 → 80

Calls

4 calls:

41.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
21.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
17.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(*.f64 m (-.f64 1 m))

simplify247.0ms (3.6%)

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 → 509

Iterations

Useful iterations: 3 (0.0ms)

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

prune582.0ms (8.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	504	5	509
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	505	6	511

Error

Counts

511 → 6

Alt Table

Status	Error	Program
	30.3b	(exp.f64 (log.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	27.9b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	0.8b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (-.f64 1 m)))
▶	0.1b	(+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m)))
	27.4b	(.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))))

Compiler

Compiled 7319 to 4656 computations (36.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`associate-r_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 56

Calls

3 calls:

8.0ms	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m))
4.0ms	(+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m)))
1.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

series137.0ms (2%)

Counts

3 → 72

Calls

3 calls:

53.0ms	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m))
53.0ms	(+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m)))
31.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

simplify149.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

693×	`unsub-neg_binary64`
614×	`fma-neg_binary64`
365×	`distribute-rgt-in_binary64`
343×	`distribute-lft-in_binary64`
343×	`fma-def_binary64`

Counts

128 → 222

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	2483
1	290	2171
2	951	2030
3	3433	1866
4	5047	1866

prune244.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	278	1	279
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	280	5	285

Error

Counts

285 → 5

Alt Table

Status	Error	Program
	30.3b	(exp.f64 (log.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
▶	0.8b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (-.f64 1 m)))
✓	0.1b	(+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m)))
	27.9b	(/.f64 (-.f64 (+.f64 (pow.f64 m 3) m) (*.f64 2 (pow.f64 m 2))) v)

Compiler

Compiled 3416 to 1785 computations (47.7% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
	0.3b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
✓	0.3b	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
✓	0.3b	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))

rewrite60.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`cbrt-prod_binary64`
43×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
14×	`swap-sqr_binary64`
14×	`cbrt-div_binary64`

Counts

2 → 85

Calls

2 calls:

37.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
12.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

series207.0ms (3%)

Counts

2 → 48

Calls

2 calls:

128.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
78.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

simplify334.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

298×	`fma-def_binary64`
277×	`fma-neg_binary64`
258×	`associate-r_binary64`
244×	`times-frac_binary64`
208×	`associate-/l*_binary64`

Counts

133 → 255

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	389	7590
1	1184	7170
2	4675	6566
3	4980	6566

prune987.0ms (14.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	504	0	504
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	504	5	509

Error

Counts

509 → 5

Alt Table

Status	Error	Program
	30.3b	(exp.f64 (log.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
✓	0.8b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (-.f64 1 m)))
✓	0.1b	(+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m)))
▶	27.9b	(/.f64 (-.f64 (+.f64 (pow.f64 m 3) m) (*.f64 2 (pow.f64 m 2))) v)

Compiler

Compiled 21037 to 15016 computations (28.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 m 2))
✓	0.0b	(+.f64 (pow.f64 m 3) m)
✓	0.1b	(/.f64 (-.f64 (+.f64 (pow.f64 m 3) m) (*.f64 2 (pow.f64 m 2))) v)
✓	0.1b	(-.f64 (+.f64 (pow.f64 m 3) m) (*.f64 2 (pow.f64 m 2)))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
12×	`fma-def_binary64`
11×	`add-exp-log_binary64`

Counts

4 → 117

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (+.f64 (pow.f64 m 3) m) (*.f64 2 (pow.f64 m 2))) v)
13.0ms	(-.f64 (+.f64 (pow.f64 m 3) m) (*.f64 2 (pow.f64 m 2)))
9.0ms	(+.f64 (pow.f64 m 3) m)
7.0ms	(*.f64 2 (pow.f64 m 2))

series137.0ms (2%)

Counts

4 → 25

Calls

4 calls:

88.0ms	(/.f64 (-.f64 (+.f64 (pow.f64 m 3) m) (*.f64 2 (pow.f64 m 2))) v)
19.0ms	(+.f64 (pow.f64 m 3) m)
18.0ms	(*.f64 2 (pow.f64 m 2))
12.0ms	(-.f64 (+.f64 (pow.f64 m 3) m) (*.f64 2 (pow.f64 m 2)))

simplify174.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary64`
610×	`fma-def_binary64`
301×	`distribute-rgt-in_binary64`
288×	`distribute-lft-in_binary64`
193×	`cancel-sign-sub-inv_binary64`

Counts

142 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	2623
1	397	2050
2	1166	1873
3	4403	1873
4	4908	1873

prune280.0ms (4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	252	5	257

Error

Counts

257 → 5

Alt Table

Status	Error	Program
	30.3b	(exp.f64 (log.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
✓	0.8b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (-.f64 1 m)))
✓	0.1b	(+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m)))
✓	27.9b	(/.f64 (-.f64 (+.f64 (pow.f64 m 3) m) (*.f64 2 (pow.f64 m 2))) v)

Compiler

Compiled 4039 to 2694 computations (33.3% saved)

regimes1.0s (14.9%)

Accuracy

Total 0.1b remaining (78.5%)

Threshold costs 0.1b (78.5%)

Compiler

Compiled 9081 to 6276 computations (30.9% saved)

simplify7.0ms (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	19
1	18	19
2	22	19
3	24	19
4	25	19
5	23	19

end1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample1.7s (24.3%)

Algorithm

1×

intervals

Results

689.0ms	8000×	body	128	valid
316.0ms	8076×	pre	128	true
7.0ms	76×	body	128	invalid

Compiler

Compiled 148 to 107 computations (27.7% saved)

Details

analyze212.0ms (3.1%)

sample35.0ms (0.5%)

simplify143.0ms (2.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite49.0ms (0.7%)

series86.0ms (1.2%)

simplify247.0ms (3.6%)

prune582.0ms (8.4%)

localize16.0ms (0.2%)

rewrite19.0ms (0.3%)

series137.0ms (2%)

simplify149.0ms (2.2%)

prune244.0ms (3.5%)

localize22.0ms (0.3%)

rewrite60.0ms (0.9%)

series207.0ms (3%)

simplify334.0ms (4.8%)

prune987.0ms (14.3%)

localize15.0ms (0.2%)

rewrite55.0ms (0.8%)

series137.0ms (2%)

simplify174.0ms (2.5%)

prune280.0ms (4%)

regimes1.0s (14.9%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample1.7s (24.3%)

Profiling