Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.7s (35.9%)

Results

684.0ms	2041×	body	1024	valid
512.0ms	4410×	body	128	valid
245.0ms	1035×	body	512	valid
89.0ms	531×	body	256	valid
89.0ms	239×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify52.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-neg_binary64`
665×	`rules-20_binary64`
567×	`rules-21_binary64`
297×	`fma-def_binary64`
293×	`rules-11_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	52	19
2	192	19
3	890	19
4	3490	19
5	6	19

prune2.0ms (0%)

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

30.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	3.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite83.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

858×	`prod-diff_binary64`
839×	`fma-neg_binary64`
168×	`egg-rr`
156×	`expm1-udef_binary64`
156×	`log1p-udef_binary64`

Counts

3 → 168

Calls

3 calls:

78.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
78.0ms	(/.f64 x (+.f64 x 1))
78.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	198	36
2	2703	36
3	5207	36
0	0	0
1	0	0

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

574×	`rules-40_binary64`
574×	`rules-41_binary64`
574×	`rules-42_binary64`
574×	`rules-43_binary64`
366×	`rules-15-rev_binary64`

Counts

204 → 207

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	475
1	485	454
2	2103	454
3	5217	454

prune207.0ms (4.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	203	4	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	204	4	208

Error

0.0b

Counts

208 → 4

Alt Table

Status	Error	Program
	31.1b	(neg.f64 (+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))))
	32.8b	(fma.f64 x x (fma.f64 3 (+.f64 x (pow.f64 x 3)) 1))
▶	30.4b	(+.f64 (fma.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) 2) (neg.f64 (.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))
	30.6b	(pow.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) 2)

Compiler

Compiled 5539 to 4096 computations (26.1% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (+.f64 x 1))
✓	0.3b	(cbrt.f64 (/.f64 x (+.f64 x 1)))
✓	20.5b	(fma.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) 2) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))
✓	34.1b	(fma.f64 (neg.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (*.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)))

series196.0ms (4.2%)

Counts

4 → 48

Calls

4 calls:

156.0ms	(fma.f64 (neg.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (*.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)))
24.0ms	(fma.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) 2) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))
11.0ms	(cbrt.f64 (/.f64 x (+.f64 x 1)))
4.0ms	(cbrt.f64 (+.f64 x 1))

rewrite97.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

531×	`prod-diff_binary64`
160×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`
149×	`add-cbrt-cube_binary64`

Counts

4 → 136

Calls

4 calls:

94.0ms	(cbrt.f64 (+.f64 x 1))
94.0ms	(cbrt.f64 (/.f64 x (+.f64 x 1)))
94.0ms	(fma.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) 2) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))
94.0ms	(fma.f64 (neg.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (*.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	111
1	390	69
2	4470	69
3	5516	69
0	0	0
1	0	0

simplify48.0ms (1%)

Algorithm

1×	egg-herbie

Rules

419×	`rules-7-rev_binary64`
386×	`fma-neg_binary64`
362×	`fma-def_binary64`
288×	`rules-41_binary64`
288×	`rules-43_binary64`

Counts

184 → 213

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	164	1092
1	1220	1056
2	5090	1056

prune923.0ms (19.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	531	0	531
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	531	4	535

Error

0.0b

Counts

535 → 4

Alt Table

Status	Error	Program
	31.1b	(neg.f64 (+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))))
	32.8b	(fma.f64 x x (fma.f64 3 (+.f64 x (pow.f64 x 3)) 1))
✓	30.4b	(+.f64 (fma.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) 2) (neg.f64 (.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))
▶	30.6b	(pow.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) 2)

Compiler

Compiled 36981 to 29639 computations (19.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (+.f64 x 1))
	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	0.0b	(pow.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) 2)
	3.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series16.0ms (0.3%)

Counts

1 → 4

Calls

1 calls:

16.0ms

(pow.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) 2)

rewrite83.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

880×	`prod-diff_binary64`
182×	`log1p-udef_binary64`
137×	`egg-rr`
104×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Counts

1 → 137

Calls

1 calls:

78.0ms

(pow.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	250	19
2	3129	19
3	5025	19
0	0	0
1	0	0

simplify40.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

502×	`rules-15-rev_binary64`
489×	`rules-40_binary64`
489×	`rules-42_binary64`
487×	`rules-41_binary64`
487×	`rules-43_binary64`

Counts

141 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	110	30
2	434	29
3	2074	29
4	4812	29

prune353.0ms (7.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	351	4	355

Error

0.0b

Counts

355 → 4

Alt Table

Status	Error	Program
▶	31.1b	(neg.f64 (+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))))
	32.8b	(fma.f64 x x (fma.f64 3 (+.f64 x (pow.f64 x 3)) 1))
✓	30.4b	(+.f64 (fma.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) 2) (neg.f64 (.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))
✓	30.6b	(pow.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) 2)

Compiler

Compiled 12015 to 9075 computations (24.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
✓	0.5b	(/.f64 1 (*.f64 x x))
✓	0.5b	(/.f64 3 (pow.f64 x 3))
✓	8.5b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))

series13.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
3.0ms	(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
3.0ms	(/.f64 3 (pow.f64 x 3))
2.0ms	(/.f64 1 (*.f64 x x))

rewrite83.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

770×	`prod-diff_binary64`
195×	`log1p-udef_binary64`
160×	`egg-rr`
112×	`add-sqr-sqrt_binary64`
110×	`log1p-expm1-u_binary64`

Counts

4 → 160

Calls

4 calls:

80.0ms	(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
80.0ms	(/.f64 1 (*.f64 x x))
80.0ms	(/.f64 3 (pow.f64 x 3))
80.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	52
1	268	43
2	3362	43
3	5137	43
0	0	0
1	0	0

simplify75.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1053×	`rules-42_binary64`
912×	`fma-neg_binary64`
761×	`rules-43_binary64`
484×	`rules-40_binary64`
484×	`rules-41_binary64`

Counts

196 → 166

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	252
1	103	252
2	396	252
3	1809	252
4	4012	252
5	20	252

prune131.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	166	4	170

Error

0.0b

Counts

170 → 4

Alt Table

Status	Error	Program
	31.4b	(neg.f64 (+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) (fabs.f64 (/.f64 3 (pow.f64 x 3))))))
	32.8b	(fma.f64 x x (fma.f64 3 (+.f64 x (pow.f64 x 3)) 1))
✓	30.4b	(+.f64 (fma.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x 1))) 2) (neg.f64 (.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))
✓	30.6b	(pow.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) 2)

Compiler

Compiled 3748 to 2997 computations (20% saved)

regimes328.0ms (6.9%)

Accuracy

Total 0.0b remaining (20.6%)

Threshold costs 0.0b (20.6%)

Counts

119 → 3

Compiler

Compiled 4640 to 3596 computations (22.5% saved)

bsearch41.0ms (0.9%)

Steps

Iters	Range		Point
9	1005.9052061022303	248282719.22278193	8938.077962000918
9	-183013409.00420362	-1.6471876307302233	-357154.3964769983

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	130
1	41	130
2	40	130

end153.0ms (3.2%)

Compiler: Compiled 285 to 222 computations (22.1% saved)

Details

analyze5.0ms (0.1%)

sample1.7s (35.9%)

simplify52.0ms (1.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series9.0ms (0.2%)

rewrite83.0ms (1.8%)

simplify44.0ms (0.9%)

prune207.0ms (4.4%)

localize17.0ms (0.4%)

series196.0ms (4.2%)

rewrite97.0ms (2.1%)

simplify48.0ms (1%)

prune923.0ms (19.5%)

localize8.0ms (0.2%)

series16.0ms (0.3%)

rewrite83.0ms (1.8%)

simplify40.0ms (0.9%)

prune353.0ms (7.5%)

localize9.0ms (0.2%)

series13.0ms (0.3%)

rewrite83.0ms (1.8%)

simplify75.0ms (1.6%)

prune131.0ms (2.8%)

regimes328.0ms (6.9%)

bsearch41.0ms (0.9%)

simplify3.0ms (0.1%)

end153.0ms (3.2%)

Profiling