Details

analyze70.0ms (1.8%)

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)

sample1.1s (29%)

Results

983.0ms	8256×	body	128	valid
7.0ms	68×	body	128	invalid

Compiler

Compiled 67 to 49 computations (26.9% saved)

simplify121.0ms (3.2%)

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
	0.4b	(*.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 (0.2%)

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

series37.0ms (1%)

Counts

4 → 80

Calls

4 calls:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
12.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
10.0ms	(/.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:

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

simplify137.0ms (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 → 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 (8.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	290	5	295
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	292	5	297

Error

Counts

297 → 5

Alt Table

Status	Error	Program
	9.5b	(.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 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) 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)))
	0.2b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
	0.9b	(.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))))

Compiler

Compiled 7332 to 4655 computations (36.5% saved)

localize11.0ms (0.3%)

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)
✓	9.5b	(/.f64 (pow.f64 m 3) v)

series57.0ms (1.5%)

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)

rewrite51.0ms (1.3%)

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:

21.0ms	(+.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))
5.0ms	(*.f64 (/.f64 m v) m)
4.0ms	(/.f64 (pow.f64 m 3) v)

simplify139.0ms (3.6%)

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

prune360.0ms (9.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	257	4	261

Error

Counts

261 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 m (fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)) (/.f64 (pow.f64 m 3) 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)))
	0.2b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
	0.9b	(.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))))

Compiler

Compiled 8429 to 3737 computations (55.7% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 m (fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)) (/.f64 (pow.f64 m 3) v))
✓	0.0b	(fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)
	9.5b	(/.f64 (pow.f64 m 3) v)

series25.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(+.f64 (+.f64 m (fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)) (/.f64 (pow.f64 m 3) v))
10.0ms	(fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
7×	`add-log-exp_binary64`
4×	`distribute-lft-out_binary64`
4×	`fma-def_binary64`
3×	`sum-log_binary64`

Counts

2 → 33

Calls

2 calls:

12.0ms	(+.f64 (+.f64 m (fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)) (/.f64 (pow.f64 m 3) v))
0.0ms	(fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)

simplify91.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-neg_binary64`
384×	`distribute-rgt-in_binary64`
358×	`distribute-lft-in_binary64`
307×	`times-frac_binary64`
276×	`fma-def_binary64`

Counts

81 → 76

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	90	1921
1	258	1772
2	771	1522
3	3390	1522
4	4745	1516
5	5206	1516

prune154.0ms (4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	144	4	148

Error

Counts

148 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 m (fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)) (/.f64 (pow.f64 m 3) 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)))
	0.2b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
	0.9b	(.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))))

Compiler

Compiled 3876 to 2337 computations (39.7% 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))

series37.0ms (1%)

Counts

3 → 72

Calls

3 calls:

15.0ms	(+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m)))
14.0ms	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (neg.f64 m))
7.0ms	(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))
3.0ms	(+.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)

simplify83.0ms (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 → 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

prune129.0ms (3.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	136	4	140

Error

Counts

140 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 m (fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)) (/.f64 (pow.f64 m 3) v))
	0.0b	(+.f64 -1 (+.f64 m (/.f64 (+.f64 m (.f64 (.f64 m m) (-.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)))
	0.9b	(.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))))

Compiler

Compiled 3377 to 1743 computations (48.4% saved)

regimes696.0ms (18.2%)

Accuracy

Total 0.1b remaining (79.7%)

Threshold costs 0.1b (79.7%)

Counts

225 → 1

Compiler

Compiled 12816 to 8984 computations (29.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	26	29
2	32	29
3	36	29
4	39	29
5	40	29
6	38	29

end83.0ms (2.2%)

Compiler: Compiled 146 to 96 computations (34.2% saved)

Details

analyze70.0ms (1.8%)

sample1.1s (29%)

simplify121.0ms (3.2%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series37.0ms (1%)

rewrite46.0ms (1.2%)

simplify137.0ms (3.6%)

prune328.0ms (8.6%)

localize11.0ms (0.3%)

series57.0ms (1.5%)

rewrite51.0ms (1.3%)

simplify139.0ms (3.6%)

prune360.0ms (9.4%)

localize11.0ms (0.3%)

series25.0ms (0.6%)

rewrite14.0ms (0.4%)

simplify91.0ms (2.4%)

prune154.0ms (4%)

localize8.0ms (0.2%)

series37.0ms (1%)

rewrite9.0ms (0.2%)

simplify83.0ms (2.2%)

prune129.0ms (3.4%)

regimes696.0ms (18.2%)

simplify3.0ms (0.1%)

end83.0ms (2.2%)

Profiling