Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

sample510.0ms (19.5%)

Results

481.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

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

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

26.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	26.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

series5.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 14

Calls

1 calls:

3.0ms

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

simplify160.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

1032×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
575×	`cube-prod_binary64`
527×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

26 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	211
1	36	205
2	63	205
3	79	205
4	87	205
5	114	205
6	145	205
7	203	205
8	414	205
9	768	205
10	776	205
11	906	205
12	1060	205
13	1223	205
14	1451	205
15	1752	205
16	2100	205
17	2575	205
18	3193	205
19	3389	205
20	3563	205
21	3677	205
22	3724	205
23	3776	205
24	4654	205
25	4739	205
26	4663	205

prune19.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	17	5	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	6	23

Error

0.2b

Counts

23 → 6

Alt Table

Status	Error	Program
	31.1b	(*.f64 (sqrt.f64 2) x)
✓	26.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	31.8b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	26.2b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	35.4b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 x (.f64 2 x))) 3))
	32.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 322 to 243 computations (24.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))
✓	0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	26.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

series15.0ms (0.6%)

Counts

2 → 12

Calls

2 calls:

10.0ms	(sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))
5.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))

rewrite30.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`sqrt-pow1_binary64`
144×	`pow1_binary64`
76×	`pow-prod-down_binary64`
31×	`sqrt-prod_binary64`
28×	`add-sqr-sqrt_binary64`

Counts

2 → 112

Calls

2 calls:

14.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
3.0ms	(sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))

simplify97.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

442×	`associate-*l/_binary64`
417×	`associate-*r/_binary64`
315×	`*-commutative_binary64`
310×	`associate-l_binary64`
252×	`cube-div_binary64`

Counts

124 → 108

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	69	1254
1	106	1164
2	303	1134
3	863	1044
4	1341	1014
5	1815	1014
6	3771	1000
7	4901	1000

prune106.0ms (4.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	176	8	184

Error

0.1b

Counts

184 → 8

Alt Table

Status	Error	Program
	31.9b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 x))) (sqrt.f64 (sqrt.f64 (.f64 2 x)))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
	31.8b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.1b	(*.f64 (sqrt.f64 2) x)
✓	26.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
▶	26.4b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))) (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x)))))
✓	26.2b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	35.4b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 x (.f64 2 x))) 3))
	32.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 3490 to 2658 computations (23.8% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))) (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x)))))
✓	0.5b	(.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
✓	0.6b	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))
	26.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

series733.0ms (28%)

Counts

3 → 36

Calls

3 calls:

375.0ms

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

352.0ms

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

6.0ms

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

rewrite36.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`cbrt-prod_binary64`
24×	`pow1_binary64`
19×	`pow1/3_binary64`
16×	`sqrt-pow1_binary64`

Counts

3 → 90

Calls

3 calls:

19.0ms

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

6.0ms

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

3.0ms

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

simplify154.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-neg_binary64`
456×	`fma-def_binary64`
418×	`exp-prod_binary64`
323×	`prod-exp_binary64`
286×	`*-commutative_binary64`

Counts

126 → 138

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	2530
1	274	2238
2	658	1952
3	1105	1578
4	1965	1114
5	3990	1114
6	3961	1114
7	4977	1114
8	4986	1114

prune221.0ms (8.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	275	1	276
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	275	9	284

Error

0.1b

Counts

284 → 9

Alt Table

Status	Error	Program
	31.9b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 x))) (sqrt.f64 (sqrt.f64 (.f64 2 x)))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
	31.8b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	31.1b	(*.f64 (sqrt.f64 2) x)
✓	26.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	31.8b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (sqrt.f64 (*.f64 (sqrt.f64 2) x)))
✓	26.4b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))) (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x)))))
✓	26.2b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	35.4b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 x (.f64 2 x))) 3))
	32.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 10161 to 7860 computations (22.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

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

rewrite5.0ms (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)

simplify57.0ms (2.2%)

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

prune16.0ms (0.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	2	3	5
Picked	0	1	1
Done	1	2	3
Total	26	8	34

Error

0.1b

Counts

34 → 8

Alt Table

Status	Error	Program
	31.9b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 x))) (sqrt.f64 (sqrt.f64 (.f64 2 x)))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
	31.8b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	31.1b	(*.f64 (sqrt.f64 2) x)
✓	26.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	31.1b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
	31.9b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)))
✓	26.2b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	32.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 316 to 255 computations (19.3% saved)

regimes307.0ms (11.7%)

Accuracy

Total 0.3b remaining (70.1%)

Threshold costs 0.3b (70.1%)

Counts

47 → 2

Compiler

Compiled 3610 to 2812 computations (22.1% saved)

bsearch16.0ms (0.6%)

Steps

Iters	Range		Point
10	-1.106363597886901e-299	1.1618897486583786e-301	-2.45058024836507e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	10	20
1	19	20
2	27	20
3	32	20
4	34	20
5	34	20

end89.0ms (3.4%)

Compiler: Compiled 114 to 88 computations (22.8% saved)

Details

analyze1.0ms (0%)

sample510.0ms (19.5%)

simplify7.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series5.0ms (0.2%)

rewrite3.0ms (0.1%)

simplify160.0ms (6.1%)

prune19.0ms (0.7%)

localize6.0ms (0.2%)

series15.0ms (0.6%)

rewrite30.0ms (1.1%)

simplify97.0ms (3.7%)

prune106.0ms (4.1%)

localize11.0ms (0.4%)

series733.0ms (28%)

rewrite36.0ms (1.4%)

simplify154.0ms (5.9%)

prune221.0ms (8.4%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify57.0ms (2.2%)

prune16.0ms (0.6%)

regimes307.0ms (11.7%)

bsearch16.0ms (0.6%)

simplify3.0ms (0.1%)

end89.0ms (3.4%)

Profiling