Details

analyze180.0ms (5.4%)

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%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.2s (36.4%)

Results

1.2s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 68 to 44 computations (35.3% saved)

preprocess37.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

473×	`fma-neg_binary64`
434×	`associate-+l+_binary64`
393×	`associate-l_binary64`
373×	`associate-+r+_binary64`
313×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	84
1	111	80
2	348	72
3	1374	72
4	4082	64
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify30.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
312×	`+-commutative_binary64`
277×	`fma-neg_binary64`
232×	`associate-+l+_binary64`
211×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	193	36
3	742	36
4	2867	32
5	4882	32

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

0.0b

Counts

3 → 2

Alt Table

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

Status

Error

Program

▶

0.0b

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

Compiler

Compiled 172 to 109 computations (36.6% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series27.0ms (0.8%)

Counts

4 → 84

Calls

21 calls:

3.0ms	(*.f64 b (fma.f64 a -3 1))	b	inf
2.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))	b	inf
2.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))	b	-inf
2.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))	b	0
1.0ms	(.f64 b (.f64 b (fma.f64 a -3 1)))	a	-inf

rewrite56.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

830×	`log1p-expm1-u_binary64`
830×	`expm1-log1p-u_binary64`
328×	`prod-diff_binary64`
95×	`add-sqr-sqrt_binary64`
87×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	195	43
2	2243	43

Stop Event

1×	node limit

Counts

4 → 80

simplify41.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

571×	`cancel-sign-sub-inv_binary64`
533×	`fma-neg_binary64`
446×	`fma-def_binary64`
373×	`associate-l_binary64`
266×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	1149
1	86	1002
2	240	838
3	695	834
4	2639	834

Stop Event

1×	node limit

Counts

164 → 107

prune105.0ms (3.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	107	2	109

Error

0.0b

Counts

109 → 2

Alt Table

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

Status

Error

Program

✓

0.0b

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

Compiler

Compiled 2862 to 1627 computations (43.2% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))
✓	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series40.0ms (1.2%)

Counts

4 → 84

Calls

21 calls:

5.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))	a	-inf
5.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))	b	inf
4.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))	b	-inf
3.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))	b	0
2.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)	a	0

rewrite37.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

192×	`log1p-expm1-u_binary64`
192×	`expm1-log1p-u_binary64`
189×	`add-sqr-sqrt_binary64`
185×	`add-cbrt-cube_binary64`
180×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	60
1	412	55

Stop Event

1×	node limit

Counts

4 → 101

simplify46.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-def_binary64`
382×	`cancel-sign-sub-inv_binary64`
312×	`fma-neg_binary64`
258×	`unswap-sqr_binary64`
232×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	1383
1	127	1250
2	385	1160
3	1271	1126
4	3157	1122

Stop Event

1×	node limit

Counts

185 → 136

prune165.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	135	3	138

Error

Counts

138 → 3

Alt Table

Status	Error	Program
	15.2b	(-.f64 (+.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2)) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
▶	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 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 1 (.f64 3 a)))))) 1)

Compiler

Compiled 5090 to 2987 computations (41.3% saved)

localize21.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))
	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
	0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	3.0b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series11.0ms (0.3%)

Counts

1 → 0

Calls

6 calls:

3.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	b	0
2.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	a	0
2.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	b	inf
2.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	a	-inf
2.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	b	-inf

rewrite29.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

528×	`log1p-expm1-u_binary64`
528×	`expm1-log1p-u_binary64`
399×	`unpow-prod-down_binary64`
296×	`log-prod_binary64`
161×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	144	7
2	1607	7

Stop Event

1×	node limit

Counts

1 → 18

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

18 → 18

prune174.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	119	3	122

Error

Counts

122 → 3

Alt Table

Status	Error	Program
▶	15.2b	(-.f64 (+.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2)) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 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 1 (.f64 3 a)))))) 1)

Compiler

Compiled 5235 to 3739 computations (28.6% saved)

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (pow.f64 (hypot.f64 b a) 2) 2)
	0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	18.1b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2))
✓	28.8b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4))

series94.0ms (2.8%)

Counts

3 → 40

Calls

18 calls:

9.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2))	b	0
8.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4))	b	0
8.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4))	a	0
8.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2))	a	0
5.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4))	b	-inf

rewrite41.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

729×	`log1p-expm1-u_binary64`
729×	`expm1-log1p-u_binary64`
153×	`log1p-udef_binary64`
93×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	223	25
2	2305	25

Stop Event

1×	node limit

Counts

3 → 75

simplify42.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

542×	`associate-r_binary64`
515×	`associate-l_binary64`
459×	`fma-neg_binary64`
428×	`distribute-rgt-neg-in_binary64`
377×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	946
1	301	930
2	936	888
3	4008	888

Stop Event

1×	node limit

Counts

115 → 115

prune179.0ms (5.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	141	3	144

Error

Counts

144 → 3

Alt Table

Status	Error	Program
✓	15.2b	(-.f64 (+.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2)) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 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 1 (.f64 3 a)))))) 1)

Compiler

Compiled 6378 to 4180 computations (34.5% saved)

regimes582.0ms (17.4%)

Accuracy

Total 0.0b remaining (42.8%)

Threshold costs 0.0b (42.8%)

Counts

89 → 1

Compiler

Compiled 14190 to 10156 computations (28.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	52
1	35	52
2	36	52

Stop Event

1×

saturated

end119.0ms (3.6%)

Stop Event

1×

done

Compiler

Compiled 191 to 138 computations (27.7% saved)

Details

analyze180.0ms (5.4%)

sample1.2s (36.4%)

preprocess37.0ms (1.1%)

simplify30.0ms (0.9%)

prune5.0ms (0.1%)

localize15.0ms (0.4%)

series27.0ms (0.8%)

rewrite56.0ms (1.7%)

simplify41.0ms (1.2%)

prune105.0ms (3.2%)

localize15.0ms (0.4%)

series40.0ms (1.2%)

rewrite37.0ms (1.1%)

simplify46.0ms (1.4%)

prune165.0ms (4.9%)

localize21.0ms (0.6%)

series11.0ms (0.3%)

rewrite29.0ms (0.9%)

simplify6.0ms (0.2%)

prune174.0ms (5.2%)

localize22.0ms (0.6%)

series94.0ms (2.8%)

rewrite41.0ms (1.2%)

simplify42.0ms (1.3%)

prune179.0ms (5.4%)

regimes582.0ms (17.4%)

simplify2.0ms (0.1%)

end119.0ms (3.6%)

Profiling