Details

analyze157.0ms (4.2%)

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
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.2s (32%)

Results

1.1s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify46.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
320×	`+-commutative_binary64`
277×	`sub-neg_binary64`
265×	`associate-l_binary64`
250×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	198	37
3	696	37
4	2292	33
5	4251	33

Stop Event

1×	node limit

Counts

1 → 2

prune21.0ms (0.6%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)

▶

0.0b

(fma.f64 4 (-.f64 (fma.f64 b (*.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))

Compiler

Compiled 166 to 105 computations (36.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 b (+.f64 a 3))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))
✓	0.1b	(fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a))

series72.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

29.0ms	(pow.f64 (hypot.f64 a b) 4)
29.0ms	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))
9.0ms	(fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a))
4.0ms	(*.f64 b (+.f64 a 3))

rewrite79.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

302×	`log1p-udef_binary64`
173×	`add-sqr-sqrt_binary64`
171×	`log1p-expm1-u_binary64`
171×	`expm1-log1p-u_binary64`
169×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	61
1	361	61
2	4675	61

Stop Event

1×	node limit

Counts

4 → 90

Calls

4 calls:

72.0ms	(*.f64 b (+.f64 a 3))
72.0ms	(pow.f64 (hypot.f64 a b) 4)
72.0ms	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))
72.0ms	(fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a))

simplify51.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
555×	`fma-neg_binary64`
538×	`cancel-sign-sub-inv_binary64`
493×	`associate-+l+_binary64`
313×	`associate--l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	1701
1	214	1603
2	703	1439
3	3481	1423

Stop Event

1×	node limit

Counts

186 → 138

prune168.0ms (4.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	135	5	140

Error

0.0b

Counts

140 → 5

Alt Table

Status	Error	Program
	0.0b	(+.f64 (+.f64 (.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) -1) (pow.f64 (hypot.f64 a b) 4))
▶	0.0b	(+.f64 (+.f64 (.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) -1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
✓	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))
	0.5b	(pow.f64 (cbrt.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))) 3)

Compiler

Compiled 4030 to 2496 computations (38.1% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 b (+.f64 a 3))
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(+.f64 (.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4))
	0.1b	(fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a))

series28.0ms (0.8%)

Counts

1 → 24

Calls

1 calls:

28.0ms

(+.f64 (*.f64 4 (-.f64 (fma.f64 b (*.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4))

rewrite55.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

291×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
166×	`log1p-expm1-u_binary64`
166×	`expm1-log1p-u_binary64`
163×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	30
1	346	30
2	4671	30

Stop Event

1×	node limit

Counts

1 → 37

Calls

1 calls:

53.0ms

(+.f64 (*.f64 4 (-.f64 (fma.f64 b (*.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4))

simplify34.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

601×	`associate-l_binary64`
520×	`fma-def_binary64`
384×	`cancel-sign-sub-inv_binary64`
362×	`associate-+l+_binary64`
314×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	801
1	149	763
2	512	604
3	2520	590

Stop Event

1×	node limit

Counts

61 → 61

prune232.0ms (6.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	148	6	154

Error

Counts

154 → 6

Alt Table

Status	Error	Program
	0.4b	(+.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (pow.f64 (hypot.f64 a b) 4))) 3) -1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	0.0b	(+.f64 (+.f64 (.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) -1) (pow.f64 (hypot.f64 a b) 4))
✓	0.0b	(+.f64 (+.f64 (.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) -1)
	14.6b	(+.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (pow.f64 (hypot.f64 a b) 4)) 3)) -1)
✓	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))

Compiler

Compiled 4772 to 2985 computations (37.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3))
	0.0b	(*.f64 b (+.f64 a 3))
	0.0b	(pow.f64 (hypot.f64 a b) 4)
	0.1b	(fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a))

series13.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(-.f64 (fma.f64 b (*.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))

rewrite54.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

958×	`prod-diff_binary64`
198×	`log1p-udef_binary64`
114×	`add-sqr-sqrt_binary64`
111×	`log1p-expm1-u_binary64`
111×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	229	20
2	3149	20

Stop Event

1×	node limit

Counts

1 → 84

Calls

1 calls:

51.0ms

(-.f64 (fma.f64 b (*.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))

simplify37.0ms (1%)

Algorithm

1×	egg-herbie

Rules

922×	`fma-def_binary64`
910×	`fma-neg_binary64`
307×	`cancel-sign-sub-inv_binary64`
197×	`unswap-sqr_binary64`
195×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	397
1	54	365
2	171	361
3	533	361
4	1654	361
5	4354	361

Stop Event

1×	node limit

Counts

108 → 99

prune301.0ms (8.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	187	6	193

Error

Counts

193 → 6

Alt Table

Status	Error	Program
	0.4b	(+.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (pow.f64 (hypot.f64 a b) 4))) 3) -1)
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
✓	0.0b	(+.f64 (+.f64 (.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) -1) (pow.f64 (hypot.f64 a b) 4))
✓	0.0b	(+.f64 (+.f64 (.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) -1)
	14.6b	(+.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (pow.f64 (hypot.f64 a b) 4)) 3)) -1)
✓	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))

Compiler

Compiled 6952 to 4005 computations (42.4% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
✓	0.1b	(.f64 (.f64 a a) (-.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.5b	(.f64 (.f64 b b) (+.f64 3 a))

series46.0ms (1.2%)

Counts

4 → 84

Calls

4 calls:

24.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
12.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
7.0ms	(.f64 (.f64 b b) (+.f64 3 a))
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite40.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

200×	`log1p-expm1-u_binary64`
200×	`expm1-log1p-u_binary64`
198×	`add-sqr-sqrt_binary64`
196×	`add-cbrt-cube_binary64`
189×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	67
1	420	63

Stop Event

1×	node limit

Counts

4 → 85

Calls

4 calls:

38.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
38.0ms	(.f64 (.f64 a a) (-.f64 1 a))
38.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
38.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify45.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

698×	`associate-l_binary64`
571×	`fma-def_binary64`
392×	`cancel-sign-sub-inv_binary64`
359×	`associate-+l+_binary64`
312×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	1546
1	171	1502
2	585	1319
3	2713	1305

Stop Event

1×	node limit

Counts

169 → 128

prune203.0ms (5.5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	128	6	134

Error

Counts

134 → 6

Alt Table

Status	Error	Program
	0.4b	(+.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (pow.f64 (hypot.f64 a b) 4))) 3) -1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
✓	0.0b	(+.f64 (+.f64 (.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) -1) (pow.f64 (hypot.f64 a b) 4))
✓	0.0b	(+.f64 (+.f64 (.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) -1)
	14.6b	(+.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (pow.f64 (hypot.f64 a b) 4)) 3)) -1)
✓	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))

Compiler

Compiled 4600 to 2819 computations (38.7% saved)

regimes651.0ms (17.5%)

Accuracy

Total 0.0b remaining (53.2%)

Threshold costs 0.0b (53.2%)

Counts

124 → 1

Compiler

Compiled 14438 to 10381 computations (28.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	24	35
2	28	35
3	30	35
4	31	35

Stop Event

1×

saturated

end140.0ms (3.8%)

Compiler: Compiled 216 to 148 computations (31.5% saved)

Details

analyze157.0ms (4.2%)

sample1.2s (32%)

simplify46.0ms (1.2%)

prune21.0ms (0.6%)

localize13.0ms (0.4%)

series72.0ms (1.9%)

rewrite79.0ms (2.1%)

simplify51.0ms (1.4%)

prune168.0ms (4.5%)

localize13.0ms (0.4%)

series28.0ms (0.8%)

rewrite55.0ms (1.5%)

simplify34.0ms (0.9%)

prune232.0ms (6.2%)

localize14.0ms (0.4%)

series13.0ms (0.3%)

rewrite54.0ms (1.4%)

simplify37.0ms (1%)

prune301.0ms (8.1%)

localize15.0ms (0.4%)

series46.0ms (1.2%)

rewrite40.0ms (1.1%)

simplify45.0ms (1.2%)

prune203.0ms (5.5%)

regimes651.0ms (17.5%)

simplify3.0ms (0.1%)

end140.0ms (3.8%)

Profiling