Details

analyze26.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample29.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	86×	body	1024	valid
5.0ms	124×	body	128	valid
4.0ms	34×	body	512	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`distribute-rgt-in_binary64`
9×	`neg-mul-1_binary64`
8×	`associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	27	17
4	34	17
5	50	17
6	72	17
7	81	17
8	93	17
9	95	17
10	89	17
11	75	17

prune3.0ms (0%)

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

21.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	21.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 36 to 30 computations (16.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 1 (sqrt.f64 x))
2.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite347.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

21.1b

Rules

127×	`add-sqr-sqrt_binary64`
118×	`times-frac_binary64`
117×	`*-un-lft-identity_binary64`
76×	`sqrt-prod_binary64`
56×	`add-cube-cbrt_binary64`

Counts

4 → 189

Calls

4 calls:

37.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 2812 to 2163 computations (23.1% saved)

series39.0ms (0.4%)

Error

21.4b

Counts

4 → 18

Calls

4 calls:

9.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(sqrt.f64 (+.f64 x 1))
5.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 515 to 413 computations (19.8% saved)

simplify200.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

449×	`cancel-sign-sub-inv_binary64`
319×	`distribute-rgt-in_binary64`
271×	`distribute-lft-in_binary64`
256×	`associate-/l/_binary64`
219×	`neg-mul-1_binary64`

Counts

207 → 178

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	164	3319
1	357	3234
2	773	3220
3	2124	3211
4	4313	3142
5	4916	3142
6	4883	3142

prune124.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	167	11	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	168	11	179

Error

21.1b

Counts

179 → 11

Alt Table

Status	Error	Program
	23.6b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	30.3b	(/.f64 (+.f64 (/.f64 1 (pow.f64 x 3/2)) (/.f64 -1 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))))
	23.6b	(exp.f64 (log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	61.2b	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (neg.f64 (sqrt.f64 (+.f64 -1 x))) (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
	32.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) 3)))
▶	21.7b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	22.1b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (cbrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	24.5b	(*.f64 (+.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (-.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x))))))
	29.8b	(-.f64 (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 x))) (/.f64 1 (sqrt.f64 (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	32.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))))
	61.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (-.f64 x 1))))

Compiler

Compiled 1704 to 1327 computations (22.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
0.2b	(/.f64 1 (sqrt.f64 x))
2.8b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite858.0ms (9.5%)

Algorithm

1×	rewrite-expression-head

Error

20.2b

Rules

1332×	`*-un-lft-identity_binary64`
1249×	`times-frac_binary64`
725×	`add-sqr-sqrt_binary64`
429×	`distribute-lft-out_binary64`
304×	`sqrt-prod_binary64`

Counts

4 → 554

Calls

4 calls:

68.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
22.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 10904 to 8671 computations (20.5% saved)

series63.0ms (0.7%)

Error

6.4b

Counts

4 → 24

Calls

4 calls:

15.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
11.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
9.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
7.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 1003 to 806 computations (19.6% saved)

simplify765.0ms (8.5%)

Algorithm

1×	egg-herbie

Rules

355×	`div-sub_binary64`
326×	`times-frac_binary64`
324×	`associate-/l*_binary64`
288×	`distribute-rgt-in_binary64`
272×	`associate-*l/_binary64`

Counts

578 → 535

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	20776
1	616	20605
2	1536	20588
3	4117	20582
4	4724	20582
5	4974	20582
6	4871	20582

prune144.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	532	3	535
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	542	4	546

Error

6.4b

Counts

546 → 4

Alt Table

Status	Error	Program
	23.6b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	6.6b	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	34.6b	(/.f64 (+.f64 (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	21.7b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

Compiler

Compiled 3225 to 2556 computations (20.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (sqrt.f64 x))
0.5b	(/.f64 1 (+.f64 x (*.f64 x x)))
5.9b	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite869.0ms (9.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

1041×	`times-frac_binary64`
965×	`*-un-lft-identity_binary64`
356×	`distribute-lft-out_binary64`
352×	`add-sqr-sqrt_binary64`
352×	`add-cube-cbrt_binary64`

Counts

4 → 530

Calls

4 calls:

50.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 x x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 11642 to 7482 computations (35.7% saved)

series57.0ms (0.6%)

Error

6.4b

Counts

4 → 24

Calls

4 calls:

15.0ms	(/.f64 1 (+.f64 x (*.f64 x x)))
10.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
9.0ms	(/.f64 1 (sqrt.f64 x))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 969 to 747 computations (22.9% saved)

simplify664.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

407×	`associate-/r*_binary64`
356×	`times-frac_binary64`
298×	`associate-/l*_binary64`
274×	`distribute-rgt-in_binary64`
247×	`associate-/l/_binary64`

Counts

554 → 487

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	255	17985
1	582	17628
2	1491	17212
3	4224	17203
4	4606	17189
5	4972	17189
6	4920	17189

prune175.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	480	7	487
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	483	8	491

Error

0.0b

Counts

491 → 8

Alt Table

Status	Error	Program
	6.6b	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) 3))))
	15.0b	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	0.5b	(*.f64 (sqrt.f64 (/.f64 (/.f64 1 (+.f64 1 x)) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x)))))) (sqrt.f64 (/.f64 (/.f64 1 (+.f64 1 x)) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x)))))))
	0.5b	(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (+.f64 1 x)) (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
	21.7b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
▶	0.3b	(/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x)))))
	6.5b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x (.f64 x x)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 x (*.f64 x x)))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	0.9b	(/.f64 1 (*.f64 (+.f64 1 x) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x))))))

Compiler

Compiled 3271 to 2094 computations (36% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.2b	(/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x)))))
0.3b	(/.f64 x (sqrt.f64 (+.f64 1 x)))
0.5b	(/.f64 x (sqrt.f64 x))

rewrite675.0ms (7.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

840×	`*-un-lft-identity_binary64`
825×	`times-frac_binary64`
319×	`distribute-lft-out_binary64`
297×	`add-sqr-sqrt_binary64`
297×	`add-cube-cbrt_binary64`

Counts

4 → 427

Calls

4 calls:

48.0ms	(/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x)))))
6.0ms	(/.f64 x (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (+.f64 x 1))
4.0ms	(/.f64 x (sqrt.f64 x))

Compiler

Compiled 8862 to 5735 computations (35.3% saved)

series59.0ms (0.7%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

14.0ms	(/.f64 1 (+.f64 x 1))
11.0ms	(/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x)))))
10.0ms	(/.f64 x (sqrt.f64 (+.f64 1 x)))
7.0ms	(/.f64 x (sqrt.f64 x))

Compiler

Compiled 895 to 643 computations (28.2% saved)

simplify542.0ms (6%)

Algorithm

1×	egg-herbie

Rules

399×	`cancel-sign-sub-inv_binary64`
325×	`*-commutative_binary64`
292×	`distribute-rgt-in_binary64`
272×	`distribute-lft-in_binary64`
235×	`log-prod_binary64`

Counts

451 → 417

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	320	14116
1	704	13152
2	2019	13144
3	3329	13105
4	4282	13089
5	4863	13089
6	5038	13089

prune253.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	414	3	417
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	418	7	425

Error

Counts

425 → 7

Alt Table

Status	Error	Program
	0.4b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 x 1))) (/.f64 (sqrt.f64 (/.f64 1 (+.f64 x 1))) (+.f64 (sqrt.f64 x) (/.f64 x (sqrt.f64 (+.f64 x 1))))))
	0.3b	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 1 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
	6.6b	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) 3))))
	0.5b	(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (+.f64 1 x)) (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
	0.4b	(/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 x (sqrt.f64 x)) (*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))))
	21.7b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	0.9b	(/.f64 1 (*.f64 (+.f64 1 x) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x))))))

Compiler

Compiled 3821 to 2517 computations (34.1% saved)

regimes2.0s (22.4%)

Accuracy

Total 0.3b remaining (93%)

Threshold costs 0.3b (93%)

Compiler

Compiled 32821 to 25164 computations (23.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	18	24
2	15	24

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample1.0s (11.4%)

Algorithm

1×

intervals

Results

342.0ms	2250×	body	1024	valid
167.0ms	4240×	body	128	valid
116.0ms	999×	body	512	valid
40.0ms	511×	body	256	valid

Compiler

Compiled 203 to 157 computations (22.7% saved)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	27	17
4	34	17
5	50	17
6	72	17
7	81	17
8	93	17
9	95	17
10	89	17
11	75	17

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	27	17
4	34	17
5	50	17
6	72	17
7	81	17
8	93	17
9	95	17
10	89	17
11	75	17

Details

analyze26.0ms (0.3%)

sample29.0ms (0.3%)

simplify19.0ms (0.2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite347.0ms (3.9%)

series39.0ms (0.4%)

simplify200.0ms (2.2%)

prune124.0ms (1.4%)

localize12.0ms (0.1%)

rewrite858.0ms (9.5%)

series63.0ms (0.7%)

simplify765.0ms (8.5%)

prune144.0ms (1.6%)

localize12.0ms (0.1%)

rewrite869.0ms (9.7%)

series57.0ms (0.6%)

simplify664.0ms (7.4%)

prune175.0ms (2%)

localize11.0ms (0.1%)

rewrite675.0ms (7.5%)

series59.0ms (0.7%)

simplify542.0ms (6%)

prune253.0ms (2.8%)

regimes2.0s (22.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.0s (11.4%)

Profiling

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	27	17
4	34	17
5	50	17
6	72	17
7	81	17
8	93	17
9	95	17
10	89	17
11	75	17