Details

analyze22.0ms (1.3%)

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)

sample14.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% saved)

simplify17.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9
3	11	9

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

26.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.5b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

25.5b

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

rewrite9.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

12.7b

Rules

7×	`pow1_binary64`
3×	`sqrt-pow1_binary64`
3×	`pow-prod-down_binary64`
1×	`*-un-lft-identity_binary64`
1×	`sqrt-prod_binary64`

Counts

1 → 12

Calls

1 calls:

3.0ms

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

Compiler

Compiled 115 to 85 computations (26.1% saved)

series16.0ms (0.9%)

Error

0.3b

Counts

1 → 3

Calls

1 calls:

13.0ms

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

Compiler

Compiled 45 to 37 computations (17.8% saved)

simplify160.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

15 → 9

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	129
1	34	123
2	61	123
3	77	123
4	85	123
5	106	123
6	127	123
7	185	123
8	396	123
9	700	123
10	702	123
11	832	123
12	986	123
13	1154	123
14	1383	123
15	1684	123
16	2032	123
17	2507	123
18	3125	123
19	3321	123
20	3495	123
21	3609	123
22	3656	123
23	3708	123
24	4586	123
25	4865	123

prune8.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	6	3	9
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	6	4	10

Error

13.9b

Counts

10 → 4

Alt Table

Status	Error	Program
▶	27.2b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))))
	40.2b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 x (.f64 2 x))) 3))
	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	26.5b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 163 to 124 computations (23.9% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))
25.5b	(sqrt.f64 (.f64 x (.f64 2 x)))
25.5b	(sqrt.f64 (.f64 x (.f64 2 x)))
25.5b	(sqrt.f64 (.f64 x (.f64 2 x)))

rewrite80.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

13.9b

Rules

22×	`pow1_binary64`
9×	`sqrt-pow1_binary64`
9×	`pow-prod-down_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

4 → 48

Calls

4 calls:

40.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
3.0ms	(cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))
3.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
3.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))

Compiler

Compiled 1177 to 886 computations (24.7% saved)

series57.0ms (3.3%)

Error

13.9b

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))
7.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
6.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
6.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))

Compiler

Compiled 784 to 619 computations (21% saved)

simplify125.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

620×	`times-frac_binary64`
507×	`div-sub_binary64`
455×	`associate-l_binary64`
428×	`unswap-sqr_binary64`
419×	`sub-neg_binary64`

Counts

60 → 24

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	49	627
1	83	609
2	158	602
3	355	588
4	783	547
5	1838	547
6	3762	547
7	4233	547
8	4724	547
9	4984	547
10	4835	547

prune17.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	23	5	28

Error

13.9b

Counts

28 → 5

Alt Table

Status	Error	Program
▶	27.4b	(.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) 2)) (cbrt.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (cbrt.f64 (sqrt.f64 (.f64 x (*.f64 2 x)))))
	40.2b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 x (.f64 2 x))) 3))
✓	27.2b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))))
	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	26.5b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 558 to 428 computations (23.3% saved)

localize15.0ms (0.9%)

Local error

Found 4 expressions with local error:

25.5b	(sqrt.f64 (.f64 x (.f64 2 x)))
25.5b	(sqrt.f64 (.f64 x (.f64 2 x)))
25.5b	(sqrt.f64 (.f64 x (.f64 2 x)))
25.5b	(sqrt.f64 (.f64 x (.f64 2 x)))

rewrite78.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

13.9b

Rules

28×	`pow1_binary64`
12×	`sqrt-pow1_binary64`
12×	`pow-prod-down_binary64`
4×	`*-un-lft-identity_binary64`
4×	`sqrt-prod_binary64`

Counts

4 → 48

Calls

4 calls:

3.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
3.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
3.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
3.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))

Compiler

Compiled 1617 to 1254 computations (22.4% saved)

series39.0ms (2.2%)

Error

13.9b

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
9.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
7.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
7.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))

Compiler

Compiled 1105 to 881 computations (20.3% saved)

simplify207.0ms (11.9%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

60 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	516
1	32	492
2	57	492
3	78	492
4	85	492
5	106	492
6	127	492
7	185	492
8	396	492
9	700	492
10	702	492
11	832	492
12	986	492
13	1154	492
14	1383	492
15	1684	492
16	2032	492
17	2507	492
18	3125	492
19	3321	492
20	3495	492
21	3609	492
22	3656	492
23	3708	492
24	4586	492
25	4865	492

prune17.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	20	5	25

Error

13.9b

Counts

25 → 5

Alt Table

Status	Error	Program
✓	27.4b	(.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) 2)) (cbrt.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (cbrt.f64 (sqrt.f64 (.f64 x (*.f64 2 x)))))
	40.2b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 x (.f64 2 x))) 3))
✓	27.2b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))))
▶	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	26.5b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 532 to 418 computations (21.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.5b	(*.f64 (sqrt.f64 2) x)

rewrite14.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

13.8b

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)

series6.0ms (0.3%)

Error

13.9b

Counts

1 → 3

Calls

1 calls:

5.0ms

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

Compiler

Compiled 42 to 35 computations (16.7% saved)

simplify92.0ms (5.3%)

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

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	6	2	8
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	6	7	13

Error

13.9b

Counts

13 → 7

Alt Table

Status	Error	Program
	27.4b	(.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) 2)) (cbrt.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (cbrt.f64 (sqrt.f64 (.f64 x (*.f64 2 x)))))
	33.1b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2)))))
	40.2b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 x (.f64 2 x))) 3))
	33.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 x (cbrt.f64 (sqrt.f64 2)))))
	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	27.2b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))))
	26.5b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 167 to 140 computations (16.2% saved)

regimes194.0ms (11.1%)

Accuracy

Total -14.5b remaining (-3722.2%)

Threshold costs -14.5b (-3722.2%)

Compiler

Compiled 2433 to 1919 computations (21.1% saved)

bsearch15.0ms (0.8%)

Steps

Iters	Range		Point
9	-5.228913216994612e-303	2.5081203618704234e-308	4.08820333917376e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	34
1	28	34
2	41	34
3	48	34
4	52	34
5	53	34
6	53	34

end1.0ms (0%)

Compiler: Compiled 22 to 18 computations (18.2% saved)

sample512.0ms (29.3%)

Algorithm

1×

intervals

Results

245.0ms

8000×

body

128

valid

Compiler

Compiled 140 to 113 computations (19.3% saved)

Details

analyze22.0ms (1.3%)

sample14.0ms (0.8%)

simplify17.0ms (1%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite9.0ms (0.5%)

series16.0ms (0.9%)

simplify160.0ms (9.2%)

prune8.0ms (0.5%)

localize9.0ms (0.5%)

rewrite80.0ms (4.6%)

series57.0ms (3.3%)

simplify125.0ms (7.2%)

prune17.0ms (1%)

localize15.0ms (0.9%)

rewrite78.0ms (4.5%)

series39.0ms (2.2%)

simplify207.0ms (11.9%)

prune17.0ms (1%)

localize4.0ms (0.2%)

rewrite14.0ms (0.8%)

series6.0ms (0.3%)

simplify92.0ms (5.3%)

prune8.0ms (0.5%)

regimes194.0ms (11.1%)

bsearch15.0ms (0.8%)

simplify5.0ms (0.3%)

end1.0ms (0%)

sample512.0ms (29.3%)

Profiling