Details

analyze23.0ms (0.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample22.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	67×	body	1024	valid
3.0ms	129×	body	128	valid
3.0ms	36×	body	512	valid
1.0ms	10×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify16.0ms (0.4%)

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 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

31.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	31.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

2.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

30.9b

Rules

11×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
6×	`cancel-sign-sub-inv_binary64`
4×	`difference-of-squares_binary64`
3×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`

Counts

1 → 24

Calls

1 calls:

9.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 276 to 175 computations (36.6% saved)

series12.0ms (0.3%)

Error

30.7b

Counts

1 → 3

Calls

1 calls:

10.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 96 to 76 computations (20.8% saved)

simplify75.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

814×	`div-sub_binary64`
642×	`associate-l_binary64`
565×	`associate-r_binary64`
536×	`associate-/l*_binary64`
236×	`associate-/r*_binary64`

Counts

27 → 22

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	413
1	127	390
2	289	390
3	1020	388
4	4504	388
5	4905	388
6	5741	388

prune23.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	18	4	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	4	23

Error

0.1b

Counts

23 → 4

Alt Table

Status	Error	Program
	31.5b	(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
	31.5b	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
▶	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	31.5b	(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

Compiler

Compiled 250 to 177 computations (29.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite94.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

48×	`*-un-lft-identity_binary64`
20×	`sqrt-prod_binary64` `distribute-lft-out_binary64`
18×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-exp-log_binary64` `associate-/r*_binary64`

Counts

2 → 59

Calls

2 calls:

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

Compiler

Compiled 867 to 622 computations (28.3% saved)

series14.0ms (0.4%)

Error

0.1b

Counts

2 → 6

Calls

2 calls:

6.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify108.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

701×	`unsub-neg_binary64`
334×	`times-frac_binary64`
317×	`associate-/l*_binary64`
310×	`distribute-rgt-in_binary64`
261×	`associate-+l-_binary64`

Counts

65 → 39

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	59	1059
1	121	978
2	227	978
3	430	978
4	932	978
5	1979	978
6	4287	978
7	4894	978

prune24.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	38	5	43

Error

0.0b

Counts

43 → 5

Alt Table

Status	Error	Program
▶	9.2b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	31.5b	(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	9.4b	(/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)))
	9.3b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (.f64 x (sqrt.f64 x)))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

Compiler

Compiled 417 to 300 computations (28.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)
9.2b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))

rewrite317.0ms (8.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

176×	`*-un-lft-identity_binary64`
90×	`times-frac_binary64`
68×	`sqrt-prod_binary64` `distribute-lft-out_binary64`
57×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
54×	`cbrt-prod_binary64`

Counts

4 → 195

Calls

4 calls:

17.0ms	(pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)
14.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 2725 to 2095 computations (23.1% saved)

series35.0ms (0.9%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)
8.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
7.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 262 to 238 computations (9.2% saved)

simplify235.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

530×	`log-prod_binary64`
387×	`associate-l_binary64`
317×	`associate-r_binary64`
292×	`exp-prod_binary64`
285×	`times-frac_binary64`

Counts

207 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	4235
1	255	3843
2	660	3827
3	2685	3827
4	4501	3827
5	4985	3827
6	4835	3827

prune67.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	161	4	165
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	163	7	170

Error

0.0b

Counts

170 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	9.4b	(cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3))
	9.4b	(/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)))
	9.3b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (.f64 x (sqrt.f64 x)))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	9.4b	(cbrt.f64 (pow.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 3))
	9.1b	(cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3))
▶	0.5b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

Compiler

Compiled 960 to 719 computations (25.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.3b	(pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)
0.3b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2))
0.4b	(cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

rewrite571.0ms (14.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

175×	`*-un-lft-identity_binary64`
153×	`cbrt-prod_binary64`
118×	`add-sqr-sqrt_binary64`
112×	`times-frac_binary64`
84×	`unpow-prod-down_binary64`

Counts

4 → 216

Calls

4 calls:

49.0ms	(*.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
13.0ms	(pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)
12.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2))
10.0ms	(cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

Compiler

Compiled 6793 to 5183 computations (23.7% saved)

series45.0ms (1.2%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)
11.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2))
10.0ms	(cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
7.0ms	(*.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

Compiler

Compiled 501 to 433 computations (13.6% saved)

simplify335.0ms (8.7%)

Algorithm

1×	egg-herbie

Rules

372×	`associate-/l*_binary64`
328×	`associate-l_binary64`
292×	`sqr-pow_binary64`
278×	`distribute-rgt-in_binary64`
255×	`associate-r_binary64`

Counts

228 → 196

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	165	6915
1	302	6665
2	650	6482
3	1779	6025
4	3497	6025
5	4669	6007
6	4975	6007
7	4820	6007

prune163.0ms (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	196	7	203

Error

0.0b

Counts

203 → 7

Alt Table

Status	Error	Program
	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	0.7b	(.f64 (cbrt.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)) (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.5b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	9.4b	(/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)))
	9.3b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (.f64 x (sqrt.f64 x)))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	9.4b	(cbrt.f64 (pow.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 3))
	9.1b	(cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3))

Compiler

Compiled 2607 to 1965 computations (24.6% saved)

regimes748.0ms (19.5%)

Accuracy

Total 0.1b remaining (65.6%)

Threshold costs 0.1b (65.6%)

Compiler

Compiled 8899 to 7148 computations (19.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	12	14
2	11	14

end1.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample841.0ms (21.9%)

Algorithm

1×

intervals

Results

222.0ms	2020×	body	1024	valid
123.0ms	4282×	body	128	valid
71.0ms	930×	body	512	valid
32.0ms	215×	body	2048	valid
28.0ms	553×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 181 to 141 computations (22.1% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

Details

analyze23.0ms (0.6%)

sample22.0ms (0.6%)

simplify16.0ms (0.4%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite39.0ms (1%)

series12.0ms (0.3%)

simplify75.0ms (1.9%)

prune23.0ms (0.6%)

localize6.0ms (0.2%)

rewrite94.0ms (2.5%)

series14.0ms (0.4%)

simplify108.0ms (2.8%)

prune24.0ms (0.6%)

localize9.0ms (0.2%)

rewrite317.0ms (8.2%)

series35.0ms (0.9%)

simplify235.0ms (6.1%)

prune67.0ms (1.7%)

localize12.0ms (0.3%)

rewrite571.0ms (14.9%)

series45.0ms (1.2%)

simplify335.0ms (8.7%)

prune163.0ms (4.2%)

regimes748.0ms (19.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample841.0ms (21.9%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11