Details

analyze6.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	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%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample760.0ms (47.5%)

Results

733.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	12	9

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0.1%)

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

31.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.7b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize3.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	30.4b	(sqrt.f64 (.f64 2 (.f64 x x)))

series8.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
2.0ms	(.f64 2 (.f64 x x))

rewrite40.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

466×	`log1p-expm1-u_binary64`
466×	`expm1-log1p-u_binary64`
441×	`unpow-prod-down_binary64`
268×	`log-prod_binary64`
138×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	122	13
2	1367	13

Stop Event

1×	node limit

Counts

2 → 71

Calls

2 calls:

39.0ms	(.f64 2 (.f64 x x))
39.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

simplify47.0ms (3%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
286×	`distribute-rgt-in_binary64`
242×	`unswap-sqr_binary64`
225×	`fma-neg_binary64`
201×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	164
1	20	164
2	43	164
3	83	164
4	203	164
5	607	164
6	959	164
7	1606	164
8	2009	164
9	2876	164
10	3703	164
11	4514	164

Stop Event

1×	node limit

Counts

95 → 75

prune37.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	5	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	6	76

Error

0.1b

Counts

76 → 6

Alt Table

Status	Error	Program
	35.1b	(*.f64 (sqrt.f64 2) x)
✓	31.7b	(sqrt.f64 (.f64 2 (.f64 x x)))
	36.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	31.8b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
	35.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
▶	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 876 to 676 computations (22.8% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (sqrt.f64 2) (neg.f64 x))

rewrite28.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

417×	`log1p-expm1-u_binary64`
417×	`expm1-log1p-u_binary64`
303×	`unpow-prod-down_binary64`
221×	`log-prod_binary64`
124×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	125	6
2	1479	6

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

28.0ms

(*.f64 (sqrt.f64 2) (neg.f64 x))

simplify11.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	96
1	12	96
2	25	96
3	29	96
4	33	96
5	51	96
6	73	96
7	84	96
8	96	96
9	121	96

Stop Event

1×

saturated

Counts

35 → 25

prune15.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	25	6	31

Error

0.1b

Counts

31 → 6

Alt Table

Status	Error	Program
	35.1b	(*.f64 (sqrt.f64 2) x)
✓	31.7b	(sqrt.f64 (.f64 2 (.f64 x x)))
	36.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
▶	31.8b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
	35.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
✓	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 286 to 239 computations (16.4% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 x (sqrt.f64 2)))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
✓	0.4b	(*.f64 x (sqrt.f64 2))
✓	30.5b	(pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/2)

series186.0ms (11.7%)

Counts

4 → 48

Calls

4 calls:

173.0ms	(pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/2)
7.0ms	(*.f64 x (sqrt.f64 2))
3.0ms	(.f64 x (.f64 x (sqrt.f64 2)))
3.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))

rewrite45.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

712×	`log1p-expm1-u_binary64`
712×	`expm1-log1p-u_binary64`
141×	`log1p-udef_binary64`
90×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	207	28
2	2302	28

Stop Event

1×	node limit

Counts

4 → 74

Calls

4 calls:

44.0ms	(.f64 x (.f64 x (sqrt.f64 2)))
44.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
43.0ms	(*.f64 x (sqrt.f64 2))
43.0ms	(pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/2)

simplify35.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-neg_binary64`
353×	`fma-def_binary64`
308×	`exp-sum_binary64`
190×	`exp-prod_binary64`
187×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	468
1	73	444
2	160	360
3	388	348
4	1163	348
5	3774	348

Stop Event

1×	node limit

Counts

122 → 64

prune35.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	64	6	70

Error

0.0b

Counts

70 → 6

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))
	35.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	35.1b	(*.f64 (sqrt.f64 2) x)
✓	31.7b	(sqrt.f64 (.f64 2 (.f64 x x)))
	36.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
✓	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 1012 to 857 computations (15.3% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (pow.f64 2 1/4))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))

series36.0ms (2.2%)

Counts

2 → 24

Calls

2 calls:

27.0ms	(*.f64 x (pow.f64 2 1/4))
9.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))

rewrite35.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

651×	`log1p-expm1-u_binary64`
651×	`expm1-log1p-u_binary64`
133×	`expm1-udef_binary64`
133×	`log1p-udef_binary64`
91×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	209	13
2	2302	13

Stop Event

1×	node limit

Counts

2 → 33

Calls

2 calls:

35.0ms	(*.f64 x (pow.f64 2 1/4))
35.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))

simplify64.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1241×	`fabs-mul_binary64`
405×	`sqr-pow_binary64`
286×	`cube-prod_binary64`
235×	`*-commutative_binary64`
208×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	276
1	19	276
2	37	276
3	81	276
4	218	276
5	723	276
6	1105	276
7	1533	276
8	1793	276
9	1966	276
10	2153	276
11	2427	276
12	2798	276
13	3276	276
14	3863	276
15	4627	276

Stop Event

1×	node limit

Counts

57 → 36

prune20.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	35	7	42

Error

0.0b

Counts

42 → 7

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))
	35.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	35.1b	(*.f64 (sqrt.f64 2) x)
✓	31.7b	(sqrt.f64 (.f64 2 (.f64 x x)))
	36.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	1.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (pow.f64 (cbrt.f64 (.f64 x (pow.f64 2 1/4))) 3)))
✓	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 442 to 395 computations (10.6% saved)

regimes75.0ms (4.7%)

Accuracy

Total 0.4b remaining (92.9%)

Threshold costs 0.4b (92.9%)

Counts

19 → 1

Compiler

Compiled 946 to 784 computations (17.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	16
2	16	16

Stop Event

1×

saturated

end82.0ms (5.1%)

Compiler: Compiled 86 to 74 computations (14% saved)

Details

analyze6.0ms (0.4%)

sample760.0ms (47.5%)

simplify6.0ms (0.4%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series8.0ms (0.5%)

rewrite40.0ms (2.5%)

simplify47.0ms (3%)

prune37.0ms (2.3%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite28.0ms (1.8%)

simplify11.0ms (0.7%)

prune15.0ms (1%)

localize9.0ms (0.5%)

series186.0ms (11.7%)

rewrite45.0ms (2.8%)

simplify35.0ms (2.2%)

prune35.0ms (2.2%)

localize7.0ms (0.4%)

series36.0ms (2.2%)

rewrite35.0ms (2.2%)

simplify64.0ms (4%)

prune20.0ms (1.2%)

regimes75.0ms (4.7%)

simplify2.0ms (0.1%)

end82.0ms (5.1%)

Profiling