Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
50%	50%	0%	4
93.7%	6.2%	0%	5
96.8%	3.1%	0%	6
98.4%	1.6%	0%	7
99.2%	0.8%	0%	8
99.6%	0.4%	0%	9
99.8%	0.2%	0%	10
99.9%	0.1%	0%	11
99.9%	0%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 37 to 29 computations (21.6% saved)

sample1.3s (46.8%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 110 to 86 computations (21.8% saved)

simplify38.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1108×	`fma-def_binary64`
549×	`times-frac_binary64`
299×	`associate-+l+_binary64`
252×	`associate-/l*_binary64`
243×	`associate-+r+_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	52
1	23	48
2	49	46
3	135	42
4	349	42
5	628	42
6	1060	42
7	2279	38
8	3243	36
9	4446	36
10	4793	36

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1) (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2))

Compiler

Compiled 113 to 87 computations (23% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1) (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2))
✓	0.0b	(fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2)
✓	0.0b	(fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1)
✓	0.1b	(/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t)))

series10.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.f64 (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1) (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2))
3.0ms	(/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t)))
2.0ms	(fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1)
2.0ms	(fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2)

rewrite71.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

673×	`prod-diff_binary64`
133×	`add-sqr-sqrt_binary64`
130×	`log1p-expm1-u_binary64`
130×	`expm1-log1p-u_binary64`
129×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	83
1	275	83
2	3826	83

Stop Event

1×	node limit

Counts

4 → 103

Calls

4 calls:

68.0ms	(/.f64 (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1) (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2))
68.0ms	(fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2)
68.0ms	(fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1)
68.0ms	(/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t)))

simplify31.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

497×	`cancel-sign-sub-inv_binary64`
444×	`fma-neg_binary64`
429×	`associate-l_binary64`
310×	`fma-def_binary64`
230×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	656
1	252	634
2	700	617
3	2154	607

Stop Event

1×	node limit

Counts

151 → 159

prune172.0ms (6.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	194	4	198

Error

Counts

198 → 4

Alt Table

Status	Error	Program
	32.1b	(fma.f64 t t 1/2)
✓	0.0b	(/.f64 (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1) (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2))
▶	0.0b	(pow.f64 (/.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2) (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) -1)
	0.0b	(.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2))))

Compiler

Compiled 5908 to 4602 computations (22.1% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2)
✓	0.0b	(fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)
✓	0.0b	(pow.f64 (/.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2) (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) -1)
✓	0.1b	(/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2)))

series10.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2)))
3.0ms	(pow.f64 (/.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2) (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) -1)
2.0ms	(fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2)
2.0ms	(fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)

rewrite68.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

670×	`prod-diff_binary64`
150×	`add-sqr-sqrt_binary64`
146×	`log1p-expm1-u_binary64`
146×	`expm1-log1p-u_binary64`
145×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	86
1	315	83
2	4158	83

Stop Event

1×	node limit

Counts

4 → 113

Calls

4 calls:

66.0ms	(fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2)
66.0ms	(fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)
66.0ms	(pow.f64 (/.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2) (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) -1)
66.0ms	(/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2)))

simplify34.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

497×	`cancel-sign-sub-inv_binary64`
444×	`fma-neg_binary64`
429×	`associate-l_binary64`
312×	`fma-def_binary64`
226×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	656
1	252	634
2	700	617
3	2158	607

Stop Event

1×	node limit

Counts

161 → 169

prune228.0ms (8.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	207	4	211

Error

Counts

211 → 4

Alt Table

Status	Error	Program
	32.1b	(fma.f64 t t 1/2)
✓	0.0b	(/.f64 (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1) (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2))
✓	0.0b	(pow.f64 (/.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2) (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) -1)
▶	0.0b	(.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2))))

Compiler

Compiled 6635 to 5227 computations (21.2% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2))
✓	0.0b	(*.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2)))
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2))))
	0.1b	(/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2)))

series16.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

7.0ms

(*.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2)))

6.0ms

(/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2))

3.0ms

(*.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (*.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2))))

rewrite65.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

664×	`prod-diff_binary64`
160×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
154×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	97
1	337	94
2	4443	94

Stop Event

1×	node limit

Counts

3 → 67

Calls

3 calls:

63.0ms

(/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2))

63.0ms

(*.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2)))

63.0ms

(*.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (*.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2))))

simplify54.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
334×	`fma-def_binary64`
245×	`times-frac_binary64`
238×	`associate-+l+_binary64`
224×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	797
1	316	767
2	1046	736
3	4370	736

Stop Event

1×	node limit

Counts

103 → 106

prune339.0ms (12%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	220	4	224

Error

Counts

224 → 4

Alt Table

Status	Error	Program
▶	32.1b	(fma.f64 t t 1/2)
✓	0.0b	(/.f64 (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1) (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2))
✓	0.0b	(pow.f64 (/.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2) (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) -1)
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2))))

Compiler

Compiled 9437 to 7482 computations (20.7% saved)

localize2.0ms (0.1%)

prune4.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
✓	32.1b	(fma.f64 t t 1/2)
✓	0.0b	(/.f64 (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 1) (fma.f64 t (/.f64 4 (+.f64 (/.f64 1 t) (+.f64 2 t))) 2))
✓	0.0b	(pow.f64 (/.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2) (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) -1)
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (.f64 (sqrt.f64 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 1)) (/.f64 1 (fma.f64 t (/.f64 4 (+.f64 t (+.f64 (/.f64 1 t) 2))) 2))))

Compiler

Compiled 102 to 79 computations (22.5% saved)

regimes220.0ms (7.8%)

Accuracy

Total 0.0b remaining (68.3%)

Threshold costs 0.0b (68.3%)

Counts

53 → 1

Compiler

Compiled 4636 to 3646 computations (21.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	16	36

Stop Event

1×

saturated

end96.0ms (3.4%)

Compiler: Compiled 154 to 119 computations (22.7% saved)

Details

analyze6.0ms (0.2%)

sample1.3s (46.8%)

simplify38.0ms (1.4%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series10.0ms (0.4%)

rewrite71.0ms (2.5%)

simplify31.0ms (1.1%)

prune172.0ms (6.1%)

localize11.0ms (0.4%)

series10.0ms (0.4%)

rewrite68.0ms (2.4%)

simplify34.0ms (1.2%)

prune228.0ms (8.1%)

localize13.0ms (0.5%)

series16.0ms (0.6%)

rewrite65.0ms (2.3%)

simplify54.0ms (1.9%)

prune339.0ms (12%)

localize2.0ms (0.1%)

prune4.0ms (0.1%)

regimes220.0ms (7.8%)

simplify2.0ms (0.1%)

end96.0ms (3.4%)

Profiling