Details

analyze24.0ms (0.5%)

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)

sample28.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	76×	body	1024	valid
5.0ms	122×	body	128	valid
4.0ms	40×	body	512	valid
1.0ms	18×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify12.0ms (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

prune7.0ms (0.2%)

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

22.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	22.1b	(-.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))
4.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite325.0ms (6.6%)

Algorithm

1×	rewrite-expression-head

Error

21.5b

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:

38.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 2812 to 2163 computations (23.1% saved)

series44.0ms (0.9%)

Error

21.7b

Counts

4 → 17

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 x 1))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
9.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 491 to 394 computations (19.8% saved)

simplify197.0ms (4%)

Algorithm

1×	egg-herbie

Rules

410×	`cancel-sign-sub-inv_binary64`
319×	`distribute-rgt-in_binary64`
271×	`distribute-lft-in_binary64`
262×	`associate-/r/_binary64`
256×	`associate-/l/_binary64`

Counts

206 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	159	3294
1	343	3209
2	735	3198
3	2001	3192
4	4197	3123
5	4850	3123
6	4870	3123

prune122.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	166	11	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	11	178

Error

21.5b

Counts

178 → 11

Alt Table

Status	Error	Program
	33.0b	(/.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)))))))
▶	22.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	24.1b	(exp.f64 (log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	31.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))))
	22.2b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	27.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	29.1b	(-.f64 (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 x))) (/.f64 1 (sqrt.f64 (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	61.4b	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (neg.f64 (sqrt.f64 (+.f64 -1 x))) (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
	33.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) 3)))
	24.3b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	29.1b	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 -1 (fabs.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))))

Compiler

Compiled 1644 to 1280 computations (22.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
4.1b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite221.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

21.3b

Rules

48×	`add-sqr-sqrt_binary64`
42×	`sqrt-prod_binary64`
38×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`

Counts

4 → 114

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 2057 to 1308 computations (36.4% saved)

series63.0ms (1.3%)

Error

21.4b

Counts

4 → 18

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
9.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 706 to 522 computations (26.1% saved)

simplify108.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

538×	`div-sub_binary64`
529×	`associate-/r*_binary64`
442×	`associate-/l*_binary64`
193×	`*-commutative_binary64`
185×	`distribute-rgt-in_binary64`

Counts

132 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2491
1	400	2159
2	1221	2151
3	3951	2149
4	5325	2149

prune76.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	94	3	97

Error

0.3b

Counts

97 → 3

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	21.9b	(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (+.f64 (.f64 (+.f64 1 x) (sqrt.f64 x)) (.f64 x (sqrt.f64 (+.f64 1 x)))))
	24.3b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 1267 to 825 computations (34.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite323.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

114×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
55×	`sqrt-prod_binary64`
51×	`add-sqr-sqrt_binary64`
42×	`distribute-lft-out_binary64`

Counts

4 → 169

Calls

4 calls:

19.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 3659 to 2523 computations (31% saved)

series51.0ms (1%)

Error

0.1b

Counts

4 → 18

Calls

4 calls:

13.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(sqrt.f64 (+.f64 1 x))
7.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 652 to 496 computations (23.9% saved)

simplify174.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

457×	`associate-/r*_binary64`
446×	`associate-/l*_binary64`
369×	`div-sub_binary64`
347×	`associate-/l/_binary64`
198×	`associate-*l/_binary64`

Counts

187 → 162

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	176	4166
1	414	3556
2	1219	3534
3	3668	3532
4	4549	3522
5	5298	3522

prune167.0ms (3.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	157	8	165

Error

0.0b

Counts

165 → 8

Alt Table

Status	Error	Program
	1.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
▶	0.3b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
	1.0b	(/.f64 1 (+.f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (.f64 x (sqrt.f64 (+.f64 x 1)))))
	27.9b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 x 1/2) (/.f64 1/8 x)))
	0.6b	(/.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (.f64 x (sqrt.f64 (+.f64 x 1)))))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))))
	0.6b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (.f64 (.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (*.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))
	24.3b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 2559 to 1770 computations (30.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite401.0ms (8.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

234×	`times-frac_binary64`
159×	`*-un-lft-identity_binary64`
158×	`add-sqr-sqrt_binary64`
119×	`add-cube-cbrt_binary64`
87×	`sqrt-prod_binary64`

Counts

4 → 253

Calls

4 calls:

13.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 6301 to 4541 computations (27.9% saved)

series65.0ms (1.3%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

14.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
12.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
10.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

Compiler

Compiled 767 to 624 computations (18.6% saved)

simplify332.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

686×	`div-sub_binary64`
311×	`associate-/r*_binary64`
234×	`*-commutative_binary64`
229×	`cancel-sign-sub-inv_binary64`
217×	`associate-/l*_binary64`

Counts

274 → 228

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	246	9476
1	570	9021
2	1434	8901
3	3272	8886
4	4554	8876
5	6026	8876

prune165.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	228	8	236

Error

0.0b

Counts

236 → 8

Alt Table

Status	Error	Program
	0.3b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
	1.0b	(/.f64 1 (+.f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (.f64 x (sqrt.f64 (+.f64 x 1)))))
	27.9b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 x 1/2) (/.f64 1/8 x)))
	4.8b	(/.f64 (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 x (*.f64 x x))))) (sqrt.f64 (+.f64 1 x)))
	0.6b	(/.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (.f64 x (sqrt.f64 (+.f64 x 1)))))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))))
	0.6b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (.f64 (.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (*.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))
	24.3b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 2867 to 2030 computations (29.2% saved)

regimes947.0ms (19.2%)

Accuracy

Total 0.3b remaining (92.8%)

Threshold costs 0.3b (92.8%)

Compiler

Compiled 15033 to 11576 computations (23% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`1-exp_binary64` `*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	17	25
2	16	25

end1.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

sample1.1s (21.3%)

Algorithm

1×

intervals

Results

333.0ms	2211×	body	1024	valid
180.0ms	4333×	body	128	valid
119.0ms	984×	body	512	valid
34.0ms	472×	body	256	valid

Compiler

Compiled 210 to 158 computations (24.8% 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

analyze24.0ms (0.5%)

sample28.0ms (0.6%)

simplify12.0ms (0.2%)

prune7.0ms (0.2%)

localize7.0ms (0.1%)

rewrite325.0ms (6.6%)

series44.0ms (0.9%)

simplify197.0ms (4%)

prune122.0ms (2.5%)

localize7.0ms (0.1%)

rewrite221.0ms (4.5%)

series63.0ms (1.3%)

simplify108.0ms (2.2%)

prune76.0ms (1.5%)

localize9.0ms (0.2%)

rewrite323.0ms (6.5%)

series51.0ms (1%)

simplify174.0ms (3.5%)

prune167.0ms (3.4%)

localize10.0ms (0.2%)

rewrite401.0ms (8.1%)

series65.0ms (1.3%)

simplify332.0ms (6.7%)

prune165.0ms (3.3%)

regimes947.0ms (19.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.1s (21.3%)

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