Details

analyze166.0ms (6.9%)

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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample20.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 45 to 27 computations (40% saved)

simplify109.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

31.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.7b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 80 to 44 computations (45% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	2.1b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	31.1b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series42.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

19.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
14.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
9.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 64

Calls

3 calls:

6.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
3.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
3.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

simplify92.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-def_binary64`
328×	`times-frac_binary64`
299×	`associate-/l*_binary64`
294×	`fma-neg_binary64`
248×	`associate-/r*_binary64`

Counts

136 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	2837
1	356	2636
2	1254	2600
3	4560	2600
4	5037	2600

prune93.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	6	137

Error

0.6b

Counts

137 → 6

Alt Table

Status	Error	Program
	31.7b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4))) 3))
▶	31.7b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))))
	31.8b	(/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))
	32.5b	1
	34.7b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	31.8b	-1

Compiler

Compiled 4051 to 2127 computations (47.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
	2.1b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	2.5b	(log1p.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y))))
	31.1b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series48.0ms (2%)

Counts

1 → 24

Calls

1 calls:

48.0ms

(log1p.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`expm1-log1p-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(log1p.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))))

simplify56.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

537×	`associate-*l/_binary64`
409×	`fma-neg_binary64`
353×	`associate-/r/_binary64`
228×	`sub-neg_binary64`
193×	`distribute-rgt-neg-in_binary64`

Counts

35 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1145
1	228	1046
2	611	1014
3	2304	1012
4	5321	1012

prune345.0ms (14.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	183	5	188

Error

0.6b

Counts

188 → 5

Alt Table

Status	Error	Program
▶	31.6b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))))
	31.8b	(/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))
	32.5b	1
	34.7b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	31.8b	-1

Compiler

Compiled 5537 to 3171 computations (42.7% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (.f64 y 4) (.f64 x x))
✓	1.5b	(fma.f64 y (.f64 y -4) (.f64 x x))
✓	2.5b	(log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x))))
✓	31.1b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))

series76.0ms (3.1%)

Counts

4 → 96

Calls

4 calls:

41.0ms	(log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x))))
20.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))
7.0ms	(fma.f64 y (.f64 y 4) (.f64 x x))
7.0ms	(fma.f64 y (.f64 y -4) (.f64 x x))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 60

Calls

4 calls:

2.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))
0.0ms	(fma.f64 y (.f64 y -4) (.f64 x x))
0.0ms	(log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x))))
0.0ms	(fma.f64 y (.f64 y 4) (.f64 x x))

simplify156.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-neg_binary64`
282×	`fma-def_binary64`
220×	`times-frac_binary64`
200×	`cancel-sign-sub-inv_binary64`
171×	`associate-/l*_binary64`

Counts

156 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	3634
1	387	3353
2	1056	3301
3	3863	3289
4	4953	3289
5	5000	3289
6	4944	3289

prune98.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	152	5	157

Error

0.6b

Counts

157 → 5

Alt Table

Status	Error	Program
✓	31.6b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))))
	31.8b	(/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))
	32.5b	1
	34.7b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
▶	31.8b	-1

Compiler

Compiled 4267 to 2336 computations (45.3% saved)

localize0.0ms (0%)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

0.6b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	31.6b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))))
	31.8b	(/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))
	32.5b	1
	34.7b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	31.8b	-1

Compiler

Compiled 59 to 38 computations (35.6% saved)

regimes351.0ms (14.5%)

Accuracy

Total 3.9b remaining (90.5%)

Threshold costs 0b (0%)

Counts

18 → 3

Compiler

Compiled 1978 to 1267 computations (35.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	44
1	26	44
2	25	44

end1.0ms (0%)

Compiler: Compiled 32 to 24 computations (25% saved)

sample710.0ms (29.3%)

Algorithm

1×

intervals

Results

436.0ms

8000×

body

128

valid

Compiler

Compiled 115 to 77 computations (33% saved)

Details

analyze166.0ms (6.9%)

sample20.0ms (0.8%)

simplify109.0ms (4.5%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series42.0ms (1.7%)

rewrite16.0ms (0.7%)

simplify92.0ms (3.8%)

prune93.0ms (3.8%)

localize10.0ms (0.4%)

series48.0ms (2%)

rewrite1.0ms (0%)

simplify56.0ms (2.3%)

prune345.0ms (14.2%)

localize12.0ms (0.5%)

series76.0ms (3.1%)

rewrite6.0ms (0.3%)

simplify156.0ms (6.4%)

prune98.0ms (4%)

localize0.0ms (0%)

prune3.0ms (0.1%)

regimes351.0ms (14.5%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample710.0ms (29.3%)

Profiling