Details

analyze20.0ms (1.2%)

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 10 to 5 computations (50% saved)

sample13.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 20 to 10 computations (50% saved)

simplify10.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	9	9
2	12	9
3	13	9
4	13	9

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.7b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 21 to 12 computations (42.9% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

29.5b

(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite12.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

14.5b

Rules

4×	`pow1_binary64`
2×	`sqrt-div_binary64`
2×	`associate-*r/_binary64`
2×	`sqrt-pow1_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 13

Calls

1 calls:

3.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 153 to 46 computations (69.9% saved)

series7.0ms (0.4%)

Error

0.3b

Counts

1 → 3

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 45 to 37 computations (17.8% saved)

simplify194.0ms (11.4%)

Algorithm

1×	egg-herbie

Rules

594×	`distribute-rgt-neg-in_binary64`
533×	`unsub-neg_binary64`
480×	`distribute-lft-neg-in_binary64`
404×	`neg-sub0_binary64`
401×	`neg-mul-1_binary64`

Counts

16 → 6

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	35	155
1	67	143
2	125	140
3	336	140
4	1155	140
5	2398	138
6	4346	138
7	5007	138

prune6.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	3	3	6
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	3	4	7

Error

16.4b

Counts

7 → 4

Alt Table

Status	Error	Program
	42.7b	(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 3))
✓	30.7b	(sqrt.f64 (*.f64 x (+.f64 x x)))
	54.5b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))) x)
▶	33.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 92 to 66 computations (28.3% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) x)

rewrite17.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

16.3b

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
4×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

4.0ms

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

Compiler

Compiled 191 to 157 computations (17.8% saved)

series7.0ms (0.4%)

Error

16.4b

Counts

1 → 3

Calls

1 calls:

6.0ms

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

Compiler

Compiled 42 to 35 computations (16.7% saved)

simplify61.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

444×	`cube-div_binary64`
431×	`log-div_binary64`
363×	`cube-prod_binary64`
332×	`associate-l_binary64`
303×	`log-prod_binary64`

Counts

25 → 8

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	228
1	65	216
2	157	216
3	212	216
4	291	216
5	477	216
6	962	216
7	2473	216
8	3809	216
9	5056	216

prune8.0ms (0.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	6	2	8
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	7	5	12

Error

16.3b

Counts

12 → 5

Alt Table

Status	Error	Program
▶	33.1b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2)))))
	33.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 x (cbrt.f64 (sqrt.f64 2)))))
	54.5b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))) x)
✓	30.7b	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	33.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 141 to 123 computations (12.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.2b	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2))))

rewrite39.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

16.2b

Rules

21×	`sqrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
10×	`associate-r_binary64`
9×	`*-un-lft-identity_binary64`

Counts

2 → 50

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2))))
5.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 673 to 606 computations (10% saved)

series12.0ms (0.7%)

Error

16.3b

Counts

2 → 6

Calls

2 calls:

6.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
5.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 118 to 104 computations (11.9% saved)

simplify76.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

352×	`log-div_binary64`
351×	`cube-div_binary64`
337×	`*-commutative_binary64`
333×	`unswap-sqr_binary64`
308×	`log-prod_binary64`

Counts

56 → 37

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	730
1	126	567
2	328	567
3	530	567
4	650	567
5	871	567
6	2013	567
7	3071	567
8	4940	567

prune19.0ms (1.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	35	7	42

Error

16.2b

Counts

42 → 7

Alt Table

Status	Error	Program
▶	33.1b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (cbrt.f64 2))))))
✓	33.1b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2)))))
	33.5b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)))))
	33.9b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 2))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2)))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2))))))
	54.5b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))) x)
✓	30.7b	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	33.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 450 to 393 computations (12.7% saved)

localize14.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (cbrt.f64 2))))
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)

rewrite59.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

16.2b

Rules

15×	`sqrt-prod_binary64`
12×	`associate-r_binary64`
12×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`

Counts

4 → 60

Calls

4 calls:

8.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (cbrt.f64 2))))
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)

Compiler

Compiled 1399 to 1334 computations (4.6% saved)

series80.0ms (4.7%)

Error

16.2b

Counts

4 → 3

Calls

4 calls:

79.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (cbrt.f64 2))))
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)

Compiler

Compiled 140 to 133 computations (5% saved)

simplify78.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

544×	`associate-*r/_binary64`
531×	`associate-*l/_binary64`
334×	`associate-/l/_binary64`
300×	`log-div_binary64`
298×	`cube-div_binary64`

Counts

63 → 29

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	70	775
1	149	730
2	463	730
3	611	730
4	770	730
5	1011	730
6	1286	730
7	4041	730
8	5110	730

prune20.0ms (1.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	27	2	29
Fresh	0	3	3
Picked	1	0	1
Done	0	3	3
Total	28	8	36

Error

16.2b

Counts

36 → 8

Alt Table

Status	Error	Program
	54.5b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))) x)
	33.1b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)))) (.f64 (.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) x) (fabs.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 2))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 2)))))))
	33.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	63.3b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)))) (exp.f64 (log.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) x) (sqrt.f64 (sqrt.f64 (cbrt.f64 2))))))))
	33.5b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)))))
	33.1b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2)))))
	33.9b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 2))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2)))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2))))))
	30.7b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 550 to 515 computations (6.4% saved)

regimes388.0ms (22.8%)

Accuracy

Total -14.8b remaining (-4128.1%)

Threshold costs -14.8b (-4128.1%)

Compiler

Compiled 3998 to 3452 computations (13.7% saved)

bsearch12.0ms (0.7%)

Steps

Iters	Range		Point
8	-7.527795013771726e-307	4.357159995258407e-306	2.49609637258684e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`distribute-lft-neg-in_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	45
1	30	45
2	43	45
3	56	45
4	64	45
5	69	45
6	71	45
7	71	45

end1.0ms (0%)

Compiler: Compiled 28 to 23 computations (17.9% saved)

sample529.0ms (31.1%)

Algorithm

1×

intervals

Results

236.0ms

8000×

body

128

valid

Compiler

Compiled 161 to 136 computations (15.5% saved)

Details

analyze20.0ms (1.2%)

sample13.0ms (0.8%)

simplify10.0ms (0.6%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

rewrite12.0ms (0.7%)

series7.0ms (0.4%)

simplify194.0ms (11.4%)

prune6.0ms (0.4%)

localize3.0ms (0.2%)

rewrite17.0ms (1%)

series7.0ms (0.4%)

simplify61.0ms (3.6%)

prune8.0ms (0.5%)

localize5.0ms (0.3%)

rewrite39.0ms (2.3%)

series12.0ms (0.7%)

simplify76.0ms (4.5%)

prune19.0ms (1.1%)

localize14.0ms (0.8%)

rewrite59.0ms (3.5%)

series80.0ms (4.7%)

simplify78.0ms (4.6%)

prune20.0ms (1.1%)

regimes388.0ms (22.8%)

bsearch12.0ms (0.7%)

simplify5.0ms (0.3%)

end1.0ms (0%)

sample529.0ms (31.1%)

Profiling