Details

analyze5.0ms (0.2%)

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 8 to 7 computations (12.5% saved)

sample1.0s (35.1%)

Results

839.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify139.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	22	9
3	41	9
4	88	9
5	221	9
6	693	9
7	1098	9
8	1100	9
9	1248	9
10	1418	9
11	1600	9
12	1825	9
13	2110	9
14	2529	9
15	3094	9
16	3780	9
17	3998	9
18	4242	9
19	4324	9
20	4357	9
21	4378	9
22	4947	9

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

29.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.3b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.3b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`pow1_binary64`
1×	`*-un-lft-identity_binary64`
1×	`sqrt-prod_binary64`
1×	`sqrt-pow1_binary64`
1×	`add-sqr-sqrt_binary64`

Counts

1 → 12

Calls

1 calls:

2.0ms

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

simplify118.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

928×	`fma-def_binary64`
738×	`fma-neg_binary64`
684×	`fabs-mul_binary64`
536×	`distribute-rgt-neg-out_binary64`
382×	`*-commutative_binary64`

Counts

24 → 22

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	209
1	36	200
2	65	198
3	120	198
4	253	198
5	672	198
6	884	198
7	1277	198
8	1600	198
9	2304	198
10	2972	198
11	3583	198
12	4792	198
13	4923	198
14	4799	198

prune12.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	3	23

Error

0.2b

Counts

23 → 3

Alt Table

Status	Error	Program
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	30.4b	(*.f64 (sqrt.f64 2) x)
✓	29.3b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 254 to 200 computations (21.3% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 2) x)

series100.0ms (3.4%)

Counts

1 → 0

Calls

1 calls:

100.0ms

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

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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 → 24

Calls

1 calls:

4.0ms

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

simplify53.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

444×	`cube-div_binary64`
431×	`log-div_binary64`
332×	`associate-l_binary64`
303×	`log-prod_binary64`
288×	`unswap-sqr_binary64`

Counts

24 → 25

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	226
1	67	214
2	159	214
3	214	214
4	293	214
5	479	214
6	964	214
7	2475	214
8	3811	214
9	4892	214

prune77.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	20	5	25
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	21	7	28

Error

0.1b

Counts

28 → 7

Alt Table

Status	Error	Program
	31.1b	(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
▶	30.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
	31.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)))
✓	29.3b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	30.9b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))

Compiler

Compiled 379 to 313 computations (17.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

series377.0ms (13.1%)

Counts

2 → 24

Calls

2 calls:

242.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)
135.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
16×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`associate-l_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 52

Calls

2 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
4.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)

simplify79.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

501×	`associate-/l/_binary64`
437×	`associate-/r/_binary64`
384×	`*-commutative_binary64`
354×	`fma-def_binary64`
320×	`distribute-rgt-in_binary64`

Counts

76 → 73

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	71	778
1	139	669
2	456	669
3	785	669
4	1500	660
5	2968	660
6	4812	660
7	4839	660

prune49.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Error

0.1b

Counts

80 → 8

Alt Table

Status	Error	Program
	31.1b	(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
✓	30.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
	31.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)))
✓	29.3b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
▶	30.3b	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))
	30.9b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))

Compiler

Compiled 1456 to 1310 computations (10% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x (pow.f64 (sqrt.f64 2) 2/3))
✓	0.3b	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))

series419.0ms (14.5%)

Counts

2 → 24

Calls

2 calls:

416.0ms	(*.f64 x (pow.f64 (sqrt.f64 2) 2/3))
3.0ms	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
11×	`associate-r_binary64`
10×	`prod-exp_binary64`

Counts

2 → 58

Calls

2 calls:

6.0ms	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))
4.0ms	(*.f64 x (pow.f64 (sqrt.f64 2) 2/3))

simplify70.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

695×	`associate-/l/_binary64`
552×	`unswap-sqr_binary64`
348×	`associate-+l+_binary64`
324×	`sqr-pow_binary64`
317×	`*-commutative_binary64`

Counts

82 → 81

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	90	1079
1	179	940
2	531	768
3	778	767
4	1382	767
5	3260	722
6	4808	722

prune50.0ms (1.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	81	8	89

Error

0.1b

Counts

89 → 8

Alt Table

Status	Error	Program
	31.1b	(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
✓	30.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
	31.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)))
✓	29.3b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
✓	30.3b	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))
	30.9b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))

Compiler

Compiled 1309 to 1163 computations (11.2% saved)

regimes142.0ms (4.9%)

Accuracy

Total 0.3b remaining (68%)

Threshold costs 0.3b (68%)

Counts

25 → 2

Compiler

Compiled 994 to 842 computations (15.3% saved)

bsearch20.0ms (0.7%)

Steps

Iters	Range		Point
10	-1.3009389159742584e-299	1.8586031302396505e-299	5.8146655483607e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	25	36
2	33	36
3	38	36
4	40	36
5	40	36

end101.0ms (3.5%)

Compiler: Compiled 135 to 115 computations (14.8% saved)

Details

analyze5.0ms (0.2%)

sample1.0s (35.1%)

simplify139.0ms (4.8%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite2.0ms (0.1%)

simplify118.0ms (4.1%)

prune12.0ms (0.4%)

localize2.0ms (0.1%)

series100.0ms (3.4%)

rewrite4.0ms (0.2%)

simplify53.0ms (1.8%)

prune77.0ms (2.7%)

localize5.0ms (0.2%)

series377.0ms (13.1%)

rewrite16.0ms (0.5%)

simplify79.0ms (2.7%)

prune49.0ms (1.7%)

localize9.0ms (0.3%)

series419.0ms (14.5%)

rewrite13.0ms (0.5%)

simplify70.0ms (2.4%)

prune50.0ms (1.7%)

regimes142.0ms (4.9%)

bsearch20.0ms (0.7%)

simplify3.0ms (0.1%)

end101.0ms (3.5%)

Profiling