Details

analyze373.0ms (18.1%)

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 (1%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify133.0ms (6.5%)

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

prune7.0ms (0.3%)

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

30.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.9b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 2 (.f64 x x))
29.8b	(sqrt.f64 (.f64 2 (.f64 x x)))

rewrite50.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

30.8b

Rules

13×	`pow1_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow-prod-down_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64` `sqrt-pow1_binary64` `-un-lft-identity_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `associate-l*_binary64`

Counts

2 → 31

Calls

2 calls:

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

Compiler

Compiled 303 to 186 computations (38.6% saved)

series26.0ms (1.3%)

Error

0.3b

Counts

2 → 6

Calls

2 calls:

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

Compiler

Compiled 93 to 78 computations (16.1% saved)

simplify66.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

759×	`associate-/r/_binary64`
597×	`distribute-rgt-out_binary64`
339×	`*-commutative_binary64`
318×	`times-frac_binary64`
227×	`associate-l_binary64`

Counts

37 → 18

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	351
1	93	309
2	224	298
3	593	298
4	892	298
5	1406	298
6	2628	298
7	4967	298

prune14.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	14	4	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	5	19

Error

0.2b

Counts

19 → 5

Alt Table

Status	Error	Program
	51.0b	(sqrt.f64 (cbrt.f64 (*.f64 8 (pow.f64 x 6))))
	31.7b	(*.f64 (sqrt.f64 2) x)
	42.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 x x))) 3))
✓	30.9b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))

Compiler

Compiled 151 to 115 computations (23.8% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite19.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
4×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`unswap-sqr_binary64`

Counts

1 → 22

Calls

1 calls:

5.0ms

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

Compiler

Compiled 191 to 157 computations (17.8% saved)

series8.0ms (0.4%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

7.0ms

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

Compiler

Compiled 42 to 35 computations (16.7% saved)

simplify66.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

507×	`log-div_binary64`
340×	`log-prod_binary64`
331×	`associate-l_binary64`
288×	`unswap-sqr_binary64`
278×	`associate-*l/_binary64`

Counts

25 → 8

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	223
1	68	211
2	166	211
3	208	211
4	292	211
5	480	211
6	966	211
7	2596	211
8	3940	211
9	4921	211

prune10.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

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

Error

0.2b

Counts

13 → 6

Alt Table

Status	Error	Program
	51.0b	(sqrt.f64 (cbrt.f64 (*.f64 8 (pow.f64 x 6))))
	31.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
▶	31.7b	(*.f64 (sqrt.f64 2) x)
	42.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 x x))) 3))
✓	30.9b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))

Compiler

Compiled 137 to 104 computations (24.1% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite19.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-r_binary64`
2×	`unswap-sqr_binary64`

Counts

1 → 22

Calls

1 calls:

5.0ms

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

Compiler

Compiled 173 to 139 computations (19.7% saved)

series8.0ms (0.4%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

8.0ms

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

Compiler

Compiled 35 to 28 computations (20% saved)

simplify65.0ms (3.1%)

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 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	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

prune17.0ms (0.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	13	8	21

Error

0.1b

Counts

21 → 8

Alt Table

Status	Error	Program
	31.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
✓	31.7b	(*.f64 (sqrt.f64 2) x)
	42.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 x x))) 3))
✓	30.9b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	31.6b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2))))
✓	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
	31.6b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 x (cbrt.f64 (sqrt.f64 2))))
	32.2b	(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))

Compiler

Compiled 253 to 210 computations (17% saved)

localize5.0ms (0.2%)

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))))

rewrite53.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

21×	`sqrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
10×	`associate-r_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

2 → 50

Calls

2 calls:

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

Compiler

Compiled 634 to 567 computations (10.6% saved)

series19.0ms (0.9%)

Error

0.1b

Counts

2 → 6

Calls

2 calls:

10.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 104 to 90 computations (13.5% saved)

simplify79.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

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

Counts

56 → 34

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

prune22.0ms (1.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	2	2	4
Picked	0	1	1
Done	0	3	3
Total	35	7	42

Error

0.1b

Counts

42 → 7

Alt Table

Status	Error	Program
	31.7b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (.f64 (*.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))))
	31.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	31.7b	(*.f64 (sqrt.f64 2) x)
	42.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 x x))) 3))
	30.9b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.6b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2))))
	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))

Compiler

Compiled 333 to 286 computations (14.1% saved)

regimes262.0ms (12.7%)

Accuracy

Total 0.3b remaining (72.9%)

Threshold costs 0.3b (72.9%)

Compiler

Compiled 1966 to 1558 computations (20.8% saved)

bsearch17.0ms (0.8%)

Steps

Iters	Range		Point
9	-6.9717952857711765e-307	4.207346151756919e-305	1.25277216594145e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
5×	`neg-mul-1_binary64` `neg-sub0_binary64` `sub-neg_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `+-commutative_binary64`
1×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	45
1	28	45
2	42	45
3	53	45
4	59	45
5	61	45
6	61	45

end4.0ms (0.2%)

Compiler: Compiled 28 to 25 computations (10.7% saved)

sample681.0ms (33%)

Algorithm

1×

intervals

Results

353.0ms

8000×

body

128

valid

Compiler

Compiled 106 to 88 computations (17% saved)

Details

analyze373.0ms (18.1%)

sample20.0ms (1%)

simplify133.0ms (6.5%)

prune7.0ms (0.3%)

localize5.0ms (0.3%)

rewrite50.0ms (2.4%)

series26.0ms (1.3%)

simplify66.0ms (3.2%)

prune14.0ms (0.7%)

localize4.0ms (0.2%)

rewrite19.0ms (0.9%)

series8.0ms (0.4%)

simplify66.0ms (3.2%)

prune10.0ms (0.5%)

localize3.0ms (0.1%)

rewrite19.0ms (0.9%)

series8.0ms (0.4%)

simplify65.0ms (3.1%)

prune17.0ms (0.8%)

localize5.0ms (0.2%)

rewrite53.0ms (2.6%)

series19.0ms (0.9%)

simplify79.0ms (3.8%)

prune22.0ms (1.1%)

regimes262.0ms (12.7%)

bsearch17.0ms (0.8%)

simplify5.0ms (0.3%)

end4.0ms (0.2%)

sample681.0ms (33%)

Profiling