Details

analyze176.0ms (3.5%)

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)

sample1.3s (26.2%)

Alt Table

Status	Error	Program
▶	0.3b	(-.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)

Results

1.2s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 157 to 97 computations (38.2% saved)

localize13.0ms (0.3%)

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))
✓	0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	2.1b	(.f64 (.f64 b b) (+.f64 3 a))

series54.0ms (1.1%)

Counts

4 → 84

Calls

4 calls:

28.0ms	(+.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)))))
13.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
9.0ms	(.f64 (.f64 b b) (+.f64 3 a))
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite85.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

777×	`prod-diff_binary64`
200×	`log1p-expm1-u_binary64`
200×	`expm1-log1p-u_binary64`
198×	`add-sqr-sqrt_binary64`
192×	`add-log-exp_binary64`

Counts

4 → 85

Calls

4 calls:

82.0ms	(+.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)))))
82.0ms	(.f64 (.f64 a a) (-.f64 1 a))
82.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
82.0ms	(.f64 (.f64 b b) (+.f64 3 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	67
1	419	63
2	4655	63
3	6113	63
0	0	0
1	0	0

prune190.0ms (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	166	4	170

Error

Counts

170 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.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)
	36.4b	(-.f64 (+.f64 (/.f64 (.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) (pow.f64 b 4))) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b)))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.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 3 a))))) 1)
	16.2b	(-.f64 (fma.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 2)) 2) (.f64 4 (fma.f64 (.f64 b b) (+.f64 3 a) (.f64 (.f64 a a) (-.f64 1 a))))) 1)

Compiler

Compiled 6095 to 3688 computations (39.5% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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 3 a)))))
✓	0.1b	(.f64 (.f64 a a) (-.f64 1 a))
✓	2.1b	(.f64 (.f64 b b) (+.f64 3 a))
✓	4.5b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series54.0ms (1.1%)

Counts

4 → 60

Calls

4 calls:

30.0ms	(+.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 3 a)))))
11.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
10.0ms	(.f64 (.f64 b b) (+.f64 3 a))
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite77.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

446×	`log1p-udef_binary64`
252×	`log1p-expm1-u_binary64`
252×	`expm1-log1p-u_binary64`
237×	`add-log-exp_binary64`
236×	`add-exp-log_binary64`

Counts

4 → 74

Calls

4 calls:

74.0ms	(+.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 3 a)))))
74.0ms	(.f64 (.f64 a a) (-.f64 1 a))
74.0ms	(.f64 (.f64 b b) (+.f64 3 a))
74.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	72
1	523	70
2	4679	70
3	5478	70
0	0	0
1	0	0

prune197.0ms (4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	135	3	138

Error

Counts

138 → 3

Alt Table

Status	Error	Program
✓	0.3b	(-.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 (pow.f64 a 4) (+.f64 (.f64 2 (pow.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) 3)) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
	16.2b	(-.f64 (fma.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 2)) 2) (.f64 4 (fma.f64 (.f64 b b) (+.f64 3 a) (.f64 (.f64 a a) (-.f64 1 a))))) 1)

Compiler

Compiled 5198 to 3609 computations (30.6% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 a b) 2)
✓	0.3b	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3)
✓	2.1b	(.f64 (.f64 b b) (+.f64 3 a))
✓	31.5b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series1.1s (22.8%)

Counts

4 → 96

Calls

4 calls:

561.0ms	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3)
555.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
7.0ms	(pow.f64 (*.f64 a b) 2)

rewrite91.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

537×	`log-prod_binary64`
207×	`fma-def_binary64`
204×	`prod-diff_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`

Counts

4 → 150

Calls

4 calls:

88.0ms	(pow.f64 (*.f64 a b) 2)
88.0ms	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3)
88.0ms	(.f64 (.f64 b b) (+.f64 3 a))
88.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	247	31
2	2689	31
3	4990	31
4	4898	31
0	0	0
1	0	0

prune323.0ms (6.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	246	3	249

Error

Counts

249 → 3

Alt Table

Status	Error	Program
✓	0.3b	(-.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 (pow.f64 a 4) (+.f64 (.f64 2 (pow.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) 3)) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	16.2b	(-.f64 (fma.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 2)) 2) (.f64 4 (fma.f64 (.f64 b b) (+.f64 3 a) (.f64 (.f64 a a) (-.f64 1 a))))) 1)

Compiler

Compiled 10715 to 7113 computations (33.6% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (pow.f64 (hypot.f64 b a) 2) 4)
✓	0.5b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 2)) 2)
✓	10.8b	(cbrt.f64 (pow.f64 (hypot.f64 b a) 2))
✓	26.6b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4))

series175.0ms (3.5%)

Counts

4 → 96

Calls

4 calls:

59.0ms	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 2)) 2)
51.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4))
40.0ms	(cbrt.f64 (pow.f64 (hypot.f64 b a) 2))
25.0ms	(pow.f64 (pow.f64 (hypot.f64 b a) 2) 4)

rewrite49.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

726×	`log1p-expm1-u_binary64`
726×	`expm1-log1p-u_binary64`
153×	`expm1-udef_binary64`
153×	`log1p-udef_binary64`
94×	`add-sqr-sqrt_binary64`

Counts

4 → 91

Calls

4 calls:

47.0ms	(pow.f64 (pow.f64 (hypot.f64 b a) 2) 4)
47.0ms	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 2)) 2)
47.0ms	(cbrt.f64 (pow.f64 (hypot.f64 b a) 2))
47.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	221	30
2	1938	30
3	4897	30
0	0	0
1	0	0

prune229.0ms (4.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	187	3	190

Error

Counts

190 → 3

Alt Table

Status	Error	Program
✓	0.3b	(-.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 (pow.f64 a 4) (+.f64 (.f64 2 (pow.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) 3)) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
✓	16.2b	(-.f64 (fma.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 4)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 2)) 2) (.f64 4 (fma.f64 (.f64 b b) (+.f64 3 a) (.f64 (.f64 a a) (-.f64 1 a))))) 1)

Compiler

Compiled 8452 to 5593 computations (33.8% saved)

regimes639.0ms (12.9%)

Accuracy

Total 0.0b remaining (36.5%)

Threshold costs 0.0b (36.5%)

Counts

108 → 1

Compiler

Compiled 19443 to 13880 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	57
1	43	57
2	47	57
3	49	57
4	50	57
5	48	57

end117.0ms (2.4%)

Compiler: Compiled 188 to 135 computations (28.2% saved)

Details

analyze176.0ms (3.5%)

sample1.3s (26.2%)

localize13.0ms (0.3%)

series54.0ms (1.1%)

rewrite85.0ms (1.7%)

prune190.0ms (3.8%)

localize22.0ms (0.4%)

series54.0ms (1.1%)

rewrite77.0ms (1.5%)

prune197.0ms (4%)

localize21.0ms (0.4%)

series1.1s (22.8%)

rewrite91.0ms (1.8%)

prune323.0ms (6.5%)

localize18.0ms (0.4%)

series175.0ms (3.5%)

rewrite49.0ms (1%)

prune229.0ms (4.6%)

regimes639.0ms (12.9%)

simplify3.0ms (0.1%)

end117.0ms (2.4%)

Profiling