Details

analyze100.0ms (4.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	50%	12.6%	6
50%	37.5%	12.6%	7
56.2%	25%	18.8%	8
62.4%	18.7%	18.8%	9
65.6%	12.5%	22%	10
68.7%	9.4%	22%	11
70.2%	6.2%	23.5%	12
71.8%	4.7%	23.5%	13
72.6%	3.1%	24.3%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample15.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify17.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

265×	`fma-def_binary64`
84×	`fma-neg_binary64`
35×	`distribute-rgt-in_binary64`
26×	`unsub-neg_binary64`
25×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 x y))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

series10.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

6.0ms	(.f64 x (-.f64 1 (.f64 x y)))
3.0ms	(-.f64 1 (*.f64 x y))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
5×	`distribute-lft-in_binary64`

Counts

2 → 52

Calls

2 calls:

4.0ms	(.f64 x (-.f64 1 (.f64 x y)))
2.0ms	(-.f64 1 (*.f64 x y))

simplify92.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1016×	`fma-def_binary64`
587×	`unsub-neg_binary64`
328×	`associate-l_binary64`
293×	`unswap-sqr_binary64`
278×	`*-commutative_binary64`

Counts

100 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	1128
1	162	1037
2	490	982
3	1467	953
4	3061	953
5	4899	953
6	4821	953

prune68.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Error

0.0b

Counts

82 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	8.0b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	11.1b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))
	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

Compiler

Compiled 1239 to 576 computations (53.5% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1 1 (neg.f64 (*.f64 y x)))
✓	0.1b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
✓	50.0b	(fma.f64 (neg.f64 y) x (*.f64 y x))

series19.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

8.0ms	(fma.f64 (neg.f64 y) x (*.f64 y x))
6.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
4.0ms	(fma.f64 1 1 (neg.f64 (*.f64 y x)))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

3.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
0.0ms	(fma.f64 (neg.f64 y) x (*.f64 y x))
0.0ms	(fma.f64 1 1 (neg.f64 (*.f64 y x)))

simplify102.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
640×	`distribute-rgt-in_binary64`
588×	`distribute-lft-in_binary64`
390×	`distribute-neg-out_binary64`
241×	`associate-l_binary64`

Counts

112 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	907
1	108	825
2	295	777
3	922	777
4	3226	777
5	4767	777
6	4999	777
7	4815	777

prune68.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	80	5	85

Error

0.0b

Counts

85 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	8.0b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	11.1b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))
▶	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

Compiler

Compiled 1965 to 699 computations (64.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))
✓	0.1b	(.f64 (neg.f64 (.f64 x y)) x)

series18.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(.f64 (neg.f64 (.f64 x y)) x)
7.0ms	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`associate-l_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(.f64 (neg.f64 (.f64 x y)) x)
3.0ms	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

simplify97.0ms (4%)

Algorithm

1×	egg-herbie

Rules

786×	`unsub-neg_binary64`
423×	`times-frac_binary64`
380×	`neg-sub0_binary64`
365×	`neg-mul-1_binary64`
320×	`distribute-lft-neg-out_binary64`

Counts

88 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	933
1	189	909
2	748	899
3	2086	893
4	3687	893
5	4607	893
6	5301	893

prune51.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	70	5	75

Error

0.0b

Counts

75 → 5

Alt Table

Status	Error	Program
▶	0.5b	(+.f64 (.f64 1 x) (.f64 (.f64 (neg.f64 (.f64 x y)) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	11.1b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	8.0b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

Compiler

Compiled 1205 to 474 computations (60.7% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (neg.f64 (.f64 x y)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
✓	0.2b	(.f64 (neg.f64 (.f64 x y)) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)

series551.0ms (22.5%)

Counts

4 → 72

Calls

4 calls:

457.0ms	(.f64 (neg.f64 (.f64 x y)) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
35.0ms	(cbrt.f64 x)
23.0ms	(.f64 (.f64 (neg.f64 (.f64 x y)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))

rewrite25.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 107

Calls

4 calls:

8.0ms	(.f64 (.f64 (neg.f64 (.f64 x y)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
6.0ms	(.f64 (neg.f64 (.f64 x y)) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify113.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
504×	`*-commutative_binary64`
394×	`log-prod_binary64`
389×	`exp-prod_binary64`
372×	`unsub-neg_binary64`

Counts

179 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	2110
1	276	1765
2	1181	1639
3	2854	1619
4	4959	1619
5	5149	1619

prune169.0ms (6.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	195	6	201

Error

Counts

201 → 6

Alt Table

Status	Error	Program
	0.4b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (.f64 x y)) (.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	0.5b	(+.f64 (.f64 1 x) (.f64 (.f64 (neg.f64 (.f64 x y)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x)))))
	8.0b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	11.1b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))
✓	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

Compiler

Compiled 4246 to 1529 computations (64% saved)

regimes352.0ms (14.4%)

Accuracy

Total 0.1b remaining (74.8%)

Threshold costs 0.1b (74.8%)

Counts

116 → 1

Compiler

Compiled 6549 to 4027 computations (38.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	26	28
2	34	28
3	38	28
4	39	28
5	38	28

end1.0ms (0%)

Compiler: Compiled 21 to 12 computations (42.9% saved)

sample520.0ms (21.2%)

Algorithm

1×

intervals

Results

226.0ms	8000×	body	128	valid
3.0ms	98×	body	128	invalid

Compiler

Compiled 150 to 89 computations (40.7% saved)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Details

analyze100.0ms (4.1%)

sample15.0ms (0.6%)

simplify17.0ms (0.7%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series10.0ms (0.4%)

rewrite9.0ms (0.4%)

simplify92.0ms (3.8%)

prune68.0ms (2.8%)

localize10.0ms (0.4%)

series19.0ms (0.8%)

rewrite5.0ms (0.2%)

simplify102.0ms (4.2%)

prune68.0ms (2.8%)

localize6.0ms (0.2%)

series18.0ms (0.7%)

rewrite9.0ms (0.3%)

simplify97.0ms (4%)

prune51.0ms (2.1%)

localize9.0ms (0.4%)

series551.0ms (22.5%)

rewrite25.0ms (1%)

simplify113.0ms (4.6%)

prune169.0ms (6.9%)

regimes352.0ms (14.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample520.0ms (21.2%)

Profiling

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10