Details

analyze199.0ms (7.8%)

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 8 computations (20% saved)

sample20.0ms (0.8%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify308.0ms (12.1%)

Algorithm

1×	egg-herbie

Rules

906×	`distribute-rgt-out_binary64`
671×	`count-2_binary64`
636×	`sqr-pow_binary64`
453×	`associate-l_binary64`
434×	`unswap-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	23	9
3	43	9
4	92	9
5	229	9
6	713	9
7	1190	9
8	1725	9
9	2294	9
10	2928	9
11	3273	9
12	3505	9
13	3979	9
14	4427	9
15	4996	9
16	4737	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

26.5b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

25.5b

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

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

26.5b

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 2 (*.f64 x x)))

Compiler

Compiled 115 to 71 computations (38.3% saved)

series9.0ms (0.3%)

Error

0.3b

Counts

1 → 3

Calls

1 calls:

6.0ms

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

Compiler

Compiled 45 to 37 computations (17.8% saved)

simplify130.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

437×	`sqr-pow_binary64`
362×	`unswap-sqr_binary64`
342×	`distribute-rgt-neg-in_binary64`
338×	`cube-prod_binary64`
306×	`distribute-lft-neg-in_binary64`

Counts

15 → 6

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	126
1	33	120
2	61	120
3	78	120
4	85	120
5	106	120
6	127	120
7	185	120
8	397	120
9	706	120
10	713	120
11	881	120
12	1141	120
13	1511	120
14	2329	120
15	2870	120
16	4500	120
17	4834	120
18	4767	120

prune6.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	4	2	6
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	4	3	7

Error

0.3b

Counts

7 → 3

Alt Table

Status	Error	Program
	40.2b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 x x))) 3))
✓	26.5b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	0.5b	(*.f64 (sqrt.f64 2) (fabs.f64 x))

Compiler

Compiled 66 to 51 computations (22.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite20.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
6×	`associate-l_binary64`
6×	`sqrt-prod_binary64`
6×	`unswap-sqr_binary64`

Counts

1 → 31

Calls

1 calls:

6.0ms

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

Compiler

Compiled 274 to 186 computations (32.1% saved)

series48.0ms (1.9%)

Error

0.3b

Counts

1 → 3

Calls

1 calls:

48.0ms

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

Compiler

Compiled 42 to 35 computations (16.7% saved)

simplify83.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

443×	`log-div_binary64`
342×	`cube-div_binary64`
309×	`*-commutative_binary64`
302×	`log-prod_binary64`
300×	`unswap-sqr_binary64`

Counts

34 → 18

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	410
1	87	398
2	221	398
3	334	398
4	449	398
5	536	398
6	678	398
7	1928	398
8	2963	398
9	4896	398
10	4929	398

prune13.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	13	5	18
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	14	7	21

Error

0.0b

Counts

21 → 7

Alt Table

Status	Error	Program
	0.7b	(.f64 (sqrt.f64 (.f64 (fabs.f64 x) (sqrt.f64 2))) (sqrt.f64 (*.f64 (fabs.f64 x) (sqrt.f64 2))))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (fabs.f64 x) (sqrt.f64 2))) (cbrt.f64 (.f64 (fabs.f64 x) (sqrt.f64 2)))) (cbrt.f64 (*.f64 (fabs.f64 x) (sqrt.f64 2))))
✓	26.5b	(sqrt.f64 (.f64 2 (.f64 x x)))
	1.3b	(.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (fabs.f64 (cbrt.f64 x)))
▶	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
✓	0.5b	(*.f64 (sqrt.f64 2) (fabs.f64 x))

Compiler

Compiled 298 to 230 computations (22.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite131.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

39×	`add-sqr-sqrt_binary64`
32×	`sqrt-prod_binary64`
16×	`associate-l_binary64`
10×	`associate-r_binary64`
10×	`*-un-lft-identity_binary64`

Counts

2 → 66

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))
6.0ms	(*.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 812 to 660 computations (18.7% saved)

series14.0ms (0.6%)

Error

0.0b

Counts

2 → 6

Calls

2 calls:

7.0ms	(*.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2)))
6.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 118 to 103 computations (12.7% saved)

simplify94.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

361×	`cube-div_binary64`
361×	`log-div_binary64`
324×	`associate-l_binary64`
308×	`associate-*l/_binary64`
295×	`sqr-pow_binary64`

Counts

72 → 47

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	76	1124
1	146	925
2	358	925
3	681	925
4	840	925
5	1075	925
6	2279	925
7	3507	925
8	5071	925

prune24.0ms (0.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	48	6	54

Error

Counts

54 → 6

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (fabs.f64 (cbrt.f64 x)))
▶	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (.f64 (*.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))))
	0.7b	(.f64 (sqrt.f64 (.f64 (fabs.f64 x) (sqrt.f64 2))) (sqrt.f64 (*.f64 (fabs.f64 x) (sqrt.f64 2))))
✓	26.5b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))
✓	0.5b	(*.f64 (sqrt.f64 2) (fabs.f64 x))

Compiler

Compiled 498 to 390 computations (21.7% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b

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

0.3b

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

0.4b

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

rewrite189.0ms (7.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

109×	`sqrt-prod_binary64`
103×	`add-sqr-sqrt_binary64`
68×	`mul-fabs_binary64`
68×	`rem-sqrt-square_binary64`
22×	`associate-r_binary64`

Counts

3 → 119

Calls

3 calls:

16.0ms

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

11.0ms

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

6.0ms

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

Compiler

Compiled 1840 to 1610 computations (12.5% saved)

series39.0ms (1.5%)

Error

Counts

3 → 9

Calls

3 calls:

20.0ms

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

11.0ms

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

5.0ms

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

Compiler

Compiled 264 to 241 computations (8.7% saved)

simplify138.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-/l*_binary64`
601×	`log-div_binary64`
511×	`associate-/r/_binary64`
348×	`*-commutative_binary64`
309×	`unswap-sqr_binary64`

Counts

128 → 95

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	116	2642
1	250	1733
2	804	1733
3	1082	1733
4	1445	1733
5	2449	1733
6	4483	1733
7	5301	1733

prune33.0ms (1.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	95	6	101

Error

Counts

101 → 6

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (fabs.f64 (cbrt.f64 x)))
	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (.f64 (*.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))))
	0.7b	(.f64 (sqrt.f64 (.f64 (fabs.f64 x) (sqrt.f64 2))) (sqrt.f64 (*.f64 (fabs.f64 x) (sqrt.f64 2))))
	26.5b	(sqrt.f64 (.f64 2 (.f64 x x)))
	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(*.f64 (sqrt.f64 2) (fabs.f64 x))

Compiler

Compiled 832 to 700 computations (15.9% saved)

regimes110.0ms (4.3%)

Accuracy

Total 0.3b remaining (97.3%)

Threshold costs 0.3b (97.3%)

Compiler

Compiled 1610 to 1262 computations (21.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	15	23
2	15	23

end1.0ms (0%)

Compiler: Compiled 15 to 14 computations (6.7% saved)

sample911.0ms (35.6%)

Algorithm

1×

intervals

Results

509.0ms

8000×

body

128

valid

Compiler

Compiled 94 to 78 computations (17% saved)

Details

analyze199.0ms (7.8%)

sample20.0ms (0.8%)

simplify308.0ms (12.1%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite9.0ms (0.3%)

series9.0ms (0.3%)

simplify130.0ms (5.1%)

prune6.0ms (0.2%)

localize4.0ms (0.1%)

rewrite20.0ms (0.8%)

series48.0ms (1.9%)

simplify83.0ms (3.2%)

prune13.0ms (0.5%)

localize5.0ms (0.2%)

rewrite131.0ms (5.1%)

series14.0ms (0.6%)

simplify94.0ms (3.7%)

prune24.0ms (0.9%)

localize8.0ms (0.3%)

rewrite189.0ms (7.4%)

series39.0ms (1.5%)

simplify138.0ms (5.4%)

prune33.0ms (1.3%)

regimes110.0ms (4.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample911.0ms (35.6%)

Profiling