Details

analyze89.0ms (2.3%)

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)

sample1.1s (28.9%)

Results

1.0s	8256×	body	128	valid
7.0ms	64×	body	128	invalid

Compiler

Compiled 67 to 49 computations (26.9% saved)

simplify122.0ms (3.1%)

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

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)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series33.0ms (0.8%)

Counts

4 → 80

Calls

4 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite46.0ms (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:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
8.0ms	(*.f64 m (-.f64 1 m))
7.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify136.0ms (3.5%)

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	4650
1	502	4087
2	2059	4004
3	4566	3999
4	5030	3999

prune328.0ms (8.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

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

Error

Counts

297 → 5

Alt Table

Status	Error	Program
	9.7b	(.f64 (fma.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (sqrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)) -1) (-.f64 1 m))
	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (cbrt.f64 (.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))) (cbrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	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)))
▶	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

Compiler

Compiled 7307 to 4642 computations (36.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	0.0b	(+.f64 (/.f64 m v) m)
✓	7.2b	(/.f64 (pow.f64 m 3) v)
✓	11.7b	(/.f64 (pow.f64 m 2) v)

series46.0ms (1.2%)

Counts

4 → 27

Calls

4 calls:

17.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
12.0ms	(/.f64 (pow.f64 m 3) v)
11.0ms	(/.f64 (pow.f64 m 2) v)
6.0ms	(+.f64 (/.f64 m v) m)

rewrite51.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`*-un-lft-identity_binary64`
69×	`times-frac_binary64`
65×	`add-sqr-sqrt_binary64`
63×	`add-cube-cbrt_binary64`
27×	`add-log-exp_binary64`

Counts

4 → 200

Calls

4 calls:

24.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
5.0ms	(+.f64 (/.f64 m v) m)
4.0ms	(/.f64 (pow.f64 m 3) v)
3.0ms	(/.f64 (pow.f64 m 2) v)

simplify156.0ms (4%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
450×	`unswap-sqr_binary64`
227×	`distribute-rgt-in_binary64`
224×	`associate-l_binary64`
223×	`associate-r_binary64`

Counts

227 → 267

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	326	6089
1	815	4598
2	3507	4321
3	4480	4319
4	5001	4319

prune417.0ms (10.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	266	1	267
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	267	5	272

Error

Counts

272 → 5

Alt Table

Status	Error	Program
	9.7b	(.f64 (fma.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (sqrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)) -1) (-.f64 1 m))
▶	0.1b	(-.f64 (+.f64 (.f64 (pow.f64 m 3) (/.f64 1 v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
	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)))
✓	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

Compiler

Compiled 9463 to 5193 computations (45.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 (pow.f64 m 3) (/.f64 1 v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
	0.0b	(+.f64 (/.f64 m v) m)
✓	7.3b	(*.f64 (pow.f64 m 3) (/.f64 1 v))
	11.7b	(/.f64 (pow.f64 m 2) v)

series29.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(-.f64 (+.f64 (.f64 (pow.f64 m 3) (/.f64 1 v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
13.0ms	(*.f64 (pow.f64 m 3) (/.f64 1 v))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
25×	`add-exp-log_binary64`
23×	`add-log-exp_binary64`
20×	`add-cube-cbrt_binary64`

Counts

2 → 112

Calls

2 calls:

16.0ms	(-.f64 (+.f64 (.f64 (pow.f64 m 3) (/.f64 1 v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
8.0ms	(*.f64 (pow.f64 m 3) (/.f64 1 v))

simplify134.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

607×	`fma-neg_binary64`
344×	`times-frac_binary64`
284×	`associate-l_binary64`
248×	`associate-r_binary64`
227×	`distribute-rgt-in_binary64`

Counts

160 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	4815
1	740	4301
2	3162	4112
3	4758	4110
4	4956	4110

prune348.0ms (8.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	281	5	286

Error

Counts

286 → 5

Alt Table

Status	Error	Program
	9.7b	(.f64 (fma.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (sqrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)) -1) (-.f64 1 m))
✓	0.1b	(-.f64 (+.f64 (.f64 (pow.f64 m 3) (/.f64 1 v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
▶	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)))
✓	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

Compiler

Compiled 10659 to 6164 computations (42.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series33.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

14.0ms	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m))
12.0ms	(+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m)))
6.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

rewrite9.0ms (0.2%)

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:

4.0ms	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m))
2.0ms	(+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m)))
0.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

simplify82.0ms (2.1%)

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 → 114

Iterations

Useful iterations: 3 (0.0ms)

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

prune137.0ms (3.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	136	5	141

Error

Counts

141 → 5

Alt Table

Status	Error	Program
	9.7b	(.f64 (fma.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (sqrt.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)) -1) (-.f64 1 m))
✓	0.1b	(-.f64 (+.f64 (.f64 (pow.f64 m 3) (/.f64 1 v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	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)))
✓	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

Compiler

Compiled 3384 to 1751 computations (48.3% saved)

regimes431.0ms (11%)

Accuracy

Total 0.1b remaining (81.8%)

Threshold costs 0.1b (81.8%)

Counts

150 → 1

Compiler

Compiled 9410 to 6544 computations (30.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	19	22
2	20	22
3	19	22

end90.0ms (2.3%)

Compiler: Compiled 143 to 98 computations (31.5% saved)

Details

analyze89.0ms (2.3%)

sample1.1s (28.9%)

simplify122.0ms (3.1%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series33.0ms (0.8%)

rewrite46.0ms (1.2%)

simplify136.0ms (3.5%)

prune328.0ms (8.3%)

localize12.0ms (0.3%)

series46.0ms (1.2%)

rewrite51.0ms (1.3%)

simplify156.0ms (4%)

prune417.0ms (10.6%)

localize13.0ms (0.3%)

series29.0ms (0.7%)

rewrite36.0ms (0.9%)

simplify134.0ms (3.4%)

prune348.0ms (8.8%)

localize8.0ms (0.2%)

series33.0ms (0.8%)

rewrite9.0ms (0.2%)

simplify82.0ms (2.1%)

prune137.0ms (3.5%)

regimes431.0ms (11%)

simplify2.0ms (0%)

end90.0ms (2.3%)

Profiling