Details

analyze998.0ms (8.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 31 to 21 computations (32.3% saved)

sample60.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	172×	body	128	valid
11.0ms	43×	body	1024	valid
6.0ms	21×	body	1024	nan
5.0ms	24×	body	512	valid
3.0ms	42×	body	128	nan
3.0ms	14×	body	512	nan
2.0ms	14×	body	256	valid
1.0ms	8×	body	256	nan
1.0ms	3×	body	2048	valid

Compiler

Compiled 64 to 44 computations (31.3% saved)

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

706×	`div-sub_binary64`
508×	`distribute-neg-in_binary64`
500×	`distribute-rgt-in_binary64`
420×	`distribute-lft-in_binary64`
403×	`cancel-sign-sub-inv_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	46	41
2	95	41
3	184	41
4	355	41
5	714	41
6	1619	41
7	3620	41
8	4716	41
9	5192	41

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

43.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	43.9b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))

Compiler

Compiled 60 to 40 computations (33.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
13.7b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.3b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite266.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

43.8b

Rules

17×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
12×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`

Counts

4 → 80

Calls

4 calls:

19.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
17.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
14.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
5.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 3285 to 1868 computations (43.1% saved)

series978.0ms (7.9%)

Error

8.1b

Counts

4 → 61

Calls

4 calls:

411.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
321.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
158.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
9.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 10862 to 8841 computations (18.6% saved)

simplify126.0ms (1%)

Algorithm

1×	egg-herbie

Rules

407×	`times-frac_binary64`
345×	`associate-/l*_binary64`
322×	`associate-/r*_binary64`
318×	`associate-l_binary64`
303×	`associate-r_binary64`

Counts

141 → 104

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	404	7450
1	1190	6801
2	4977	6801

prune119.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Error

8.1b

Counts

105 → 8

Alt Table

Status	Error	Program
	37.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	46.5b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (/.f64 (.f64 l l) (.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (+.f64 (/.f64 t (.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 t (.f64 (sqrt.f64 2) x)))) (/.f64 (.f64 l l) (.f64 t (.f64 (sqrt.f64 2) (.f64 x x))))))) (+.f64 (.f64 2 (+.f64 (/.f64 t (.f64 2 (.f64 (sqrt.f64 2) (.f64 x x)))) (/.f64 (.f64 l l) (.f64 t (.f64 2 (.f64 (sqrt.f64 2) (.f64 x x))))))) (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (.f64 x x) (pow.f64 (.f64 t (sqrt.f64 2)) 3)))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))
	38.4b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (.f64 l l) (.f64 t (*.f64 (sqrt.f64 2) x))))))
	63.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1)))))
	37.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))))))
	43.9b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 (.f64 t t) (-.f64 x 1)) (.f64 (/.f64 (*.f64 t t) (-.f64 x 1)) x)))))
▶	34.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (*.f64 x x))))))))

Compiler

Compiled 4245 to 2751 computations (35.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.1b	(/.f64 (*.f64 t t) x)
12.8b	(/.f64 (.f64 l l) (.f64 x x))
19.5b	(/.f64 (.f64 t t) (.f64 x x))
28.1b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))

rewrite172.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

8.1b

Rules

33×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`associate-*r/_binary64`
16×	`frac-add_binary64`
10×	`sqrt-div_binary64` `div-exp_binary64` `cbrt-undiv_binary64`
9×	`prod-exp_binary64` `cbrt-unprod_binary64`

Counts

4 → 86

Calls

4 calls:

20.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
6.0ms	(/.f64 (.f64 t t) (.f64 x x))
6.0ms	(/.f64 (.f64 l l) (.f64 x x))
4.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 5734 to 1640 computations (71.4% saved)

series521.0ms (4.2%)

Error

0.7b

Counts

4 → 42

Calls

4 calls:

385.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
27.0ms	(/.f64 (.f64 l l) (.f64 x x))
26.0ms	(/.f64 (.f64 t t) (.f64 x x))
21.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 8465 to 6603 computations (22% saved)

simplify113.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-l_binary64`
441×	`times-frac_binary64`
246×	`distribute-rgt-in_binary64`
245×	`associate-/l*_binary64`
237×	`associate-/r*_binary64`

Counts

128 → 89

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	438	6426
1	1334	5749
2	5192	5749

prune106.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Error

0.7b

Counts

97 → 10

Alt Table

Status	Error	Program
	43.7b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (*.f64 x x))))))) 3)))
	37.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	46.5b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (/.f64 (.f64 l l) (.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (+.f64 (/.f64 t (.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 t (.f64 (sqrt.f64 2) x)))) (/.f64 (.f64 l l) (.f64 t (.f64 (sqrt.f64 2) (.f64 x x))))))) (+.f64 (.f64 2 (+.f64 (/.f64 t (.f64 2 (.f64 (sqrt.f64 2) (.f64 x x)))) (/.f64 (.f64 l l) (.f64 t (.f64 2 (.f64 (sqrt.f64 2) (.f64 x x))))))) (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (.f64 x x) (pow.f64 (.f64 t (sqrt.f64 2)) 3)))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))
▶	34.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))))))))
	55.7b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 x))))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 2 (.f64 (/.f64 (.f64 t t) (.f64 (.f64 x x) l)) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (.f64 x x)) (/.f64 2 x)))))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (.f64 x x)) (/.f64 2 x)))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 x l))) (/.f64 (.f64 t t) l))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 x)))))))
	37.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 x)))))
	43.9b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 (.f64 t t) (-.f64 x 1)) (.f64 (/.f64 (*.f64 t t) (-.f64 x 1)) x)))))

Compiler

Compiled 4639 to 2237 computations (51.8% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

19.5b	(/.f64 (.f64 t t) (.f64 x x))
19.5b	(/.f64 (.f64 t t) (.f64 x x))
28.9b	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
28.9b	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))

rewrite219.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

40×	`associate-*r/_binary64`
32×	`frac-add_binary64`
28×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`cbrt-div_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`

Counts

4 → 84

Calls

4 calls:

18.0ms	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
17.0ms	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
6.0ms	(/.f64 (.f64 t t) (.f64 x x))
6.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 10779 to 2784 computations (74.2% saved)

series826.0ms (6.7%)

Error

0.7b

Counts

4 → 47

Calls

4 calls:

362.0ms	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
319.0ms	(cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))
32.0ms	(/.f64 (.f64 t t) (.f64 x x))
32.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 14785 to 10277 computations (30.5% saved)

simplify307.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

403×	`associate-r_binary64`
399×	`associate-l_binary64`
244×	`times-frac_binary64` `distribute-rgt-in_binary64`
238×	`distribute-lft-in_binary64`
162×	`associate-/l*_binary64`

Counts

131 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	9570
1	1129	8853
2	4837	8734
3	4996	8734
4	5000	8734
5	4991	8734

prune148.0ms (1.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	95	12	107

Error

0.7b

Counts

107 → 12

Alt Table

Status	Error	Program
▶	37.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	46.5b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (/.f64 (.f64 l l) (.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (+.f64 (/.f64 t (.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 t (.f64 (sqrt.f64 2) x)))) (/.f64 (.f64 l l) (.f64 t (.f64 (sqrt.f64 2) (.f64 x x))))))) (+.f64 (.f64 2 (+.f64 (/.f64 t (.f64 2 (.f64 (sqrt.f64 2) (.f64 x x)))) (/.f64 (.f64 l l) (.f64 t (.f64 2 (.f64 (sqrt.f64 2) (.f64 x x))))))) (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (.f64 x x) (pow.f64 (.f64 t (sqrt.f64 2)) 3)))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))
✓	34.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))))))))
	54.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))) (sqrt.f64 (/.f64 (cbrt.f64 (+.f64 (.f64 (.f64 2 (.f64 l l)) (-.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))) (.f64 x (-.f64 (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) 16)) (.f64 4 (.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))))))) (cbrt.f64 (.f64 x (-.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (*.f64 x x)))))))))))
	59.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (/.f64 (cbrt.f64 (+.f64 (.f64 (.f64 2 (.f64 l l)) (.f64 (+.f64 (pow.f64 t 4) (.f64 (/.f64 (.f64 l l) (.f64 x x)) (-.f64 (/.f64 (.f64 l l) (.f64 x x)) (.f64 t t)))) (-.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 x (+.f64 (.f64 (+.f64 (pow.f64 t 4) (.f64 (/.f64 (.f64 l l) (.f64 x x)) (-.f64 (/.f64 (.f64 l l) (.f64 x x)) (.f64 t t)))) (.f64 4 (-.f64 (/.f64 (pow.f64 t 4) (.f64 x x)) (/.f64 (pow.f64 t 4) (pow.f64 x 4))))) (.f64 (+.f64 (pow.f64 t 6) (pow.f64 (/.f64 (.f64 l l) (.f64 x x)) 3)) (.f64 2 (-.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))))))))) (cbrt.f64 (.f64 x (.f64 (+.f64 (pow.f64 t 4) (.f64 (/.f64 (.f64 l l) (.f64 x x)) (-.f64 (/.f64 (.f64 l l) (.f64 x x)) (.f64 t t)))) (-.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (*.f64 x x))))))))))
	57.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (/.f64 (cbrt.f64 (+.f64 (.f64 (.f64 2 (.f64 l l)) (+.f64 (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) 16)) (.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))) (-.f64 (.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))) 4) (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) 8))))) (.f64 x (+.f64 (pow.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) 3) (pow.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) 3))))) (cbrt.f64 (.f64 x (+.f64 (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) 16)) (.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))) (-.f64 (.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))) 4) (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) 8)))))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (*.f64 x x))))))))))
	55.7b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 x))))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 2 (.f64 (/.f64 (.f64 t t) (.f64 (.f64 x x) l)) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (.f64 x x)) (/.f64 2 x)))))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (.f64 x x)) (/.f64 2 x)))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 x l))) (/.f64 (.f64 t t) l))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 x)))))))
	37.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 x)))))
	43.9b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 (.f64 t t) (-.f64 x 1)) (.f64 (/.f64 (*.f64 t t) (-.f64 x 1)) x)))))

Compiler

Compiled 9677 to 3690 computations (61.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
0.0b	(+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))
0.4b	(*.f64 (sqrt.f64 2) t)
0.4b	(.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))

rewrite159.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
9×	`sqrt-prod_binary64` `associate-r/_binary64` `associate-l*_binary64`
8×	`pow1_binary64`

Counts

4 → 85

Calls

4 calls:

18.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
14.0ms	(.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))
11.0ms	(+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))
5.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 2642 to 2037 computations (22.9% saved)

series164.0ms (1.3%)

Error

0.7b

Counts

4 → 37

Calls

4 calls:

64.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
52.0ms	(.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))
14.0ms	(+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))
11.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 1818 to 1552 computations (14.6% saved)

simplify130.0ms (1%)

Algorithm

1×	egg-herbie

Rules

352×	`associate-/l/_binary64`
323×	`times-frac_binary64`
239×	`associate-/r/_binary64`
193×	`associate-l_binary64`
190×	`associate-/r*_binary64`

Counts

122 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	225	3647
1	609	3107
2	2721	2953
3	4702	2953
4	4989	2953

prune83.0ms (0.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	77	12	89

Error

0.7b

Counts

89 → 12

Alt Table

Status	Error	Program
	37.2b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))
	34.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))))))))
	54.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))))) (sqrt.f64 (/.f64 (cbrt.f64 (+.f64 (.f64 (.f64 2 (.f64 l l)) (-.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))))) (.f64 x (-.f64 (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) 16)) (.f64 4 (.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))))))) (cbrt.f64 (.f64 x (-.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (*.f64 x x)))))))))))
	59.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (/.f64 (cbrt.f64 (+.f64 (.f64 (.f64 2 (.f64 l l)) (.f64 (+.f64 (pow.f64 t 4) (.f64 (/.f64 (.f64 l l) (.f64 x x)) (-.f64 (/.f64 (.f64 l l) (.f64 x x)) (.f64 t t)))) (-.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 x (+.f64 (.f64 (+.f64 (pow.f64 t 4) (.f64 (/.f64 (.f64 l l) (.f64 x x)) (-.f64 (/.f64 (.f64 l l) (.f64 x x)) (.f64 t t)))) (.f64 4 (-.f64 (/.f64 (pow.f64 t 4) (.f64 x x)) (/.f64 (pow.f64 t 4) (pow.f64 x 4))))) (.f64 (+.f64 (pow.f64 t 6) (pow.f64 (/.f64 (.f64 l l) (.f64 x x)) 3)) (.f64 2 (-.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))))))))) (cbrt.f64 (.f64 x (.f64 (+.f64 (pow.f64 t 4) (.f64 (/.f64 (.f64 l l) (.f64 x x)) (-.f64 (/.f64 (.f64 l l) (.f64 x x)) (.f64 t t)))) (-.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (*.f64 x x))))))))))
	37.7b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 t (sqrt.f64 2))) (cbrt.f64 (.f64 t (sqrt.f64 2)))) (cbrt.f64 (.f64 t (sqrt.f64 2)))) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	37.3b	(/.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 t (cbrt.f64 (sqrt.f64 2)))) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	57.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (/.f64 (cbrt.f64 (+.f64 (.f64 (.f64 2 (.f64 l l)) (+.f64 (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) 16)) (.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))) (-.f64 (.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))) 4) (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) 8))))) (.f64 x (+.f64 (pow.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) 3) (pow.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) 3))))) (cbrt.f64 (.f64 x (+.f64 (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) 16)) (.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))) (-.f64 (.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))) 4) (.f64 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x))) 8)))))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (*.f64 x x))))))))))
	55.7b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 x))))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 2 (.f64 (/.f64 (.f64 t t) (.f64 (.f64 x x) l)) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (.f64 x x)) (/.f64 2 x)))))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (.f64 x x)) (/.f64 2 x)))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 x l))) (/.f64 (.f64 t t) l))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 x)))))))
	37.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 x)))))

Compiler

Compiled 2332 to 1514 computations (35.1% saved)

regimes4.0s (32.4%)

Accuracy

Total 11.9b remaining (96.1%)

Threshold costs 0b (0%)

Compiler

Compiled 78428 to 41974 computations (46.5% saved)

bsearch342.0ms (2.8%)

Steps

Iters	Range		Point
9	5.747035250080123e-265	2.1245861294815812e-259	2.1011173123428155e-259
7	-2.943109202023788e-241	-3.069690317785188e-243	-2.9041377634221667e-241
4	-5.670696162900394e-150	-2.872195314855817e-150	-2.9474172478993817e-150
8	-2.605137824922211e+93	-1.6613111182418083e+89	-3.064774607274823e+89

Compiler

Compiled 4 to 3 computations (25% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
13×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	295
1	105	295
2	114	295
3	119	295
4	121	295
5	119	295

end4.0ms (0%)

Compiler: Compiled 196 to 130 computations (33.7% saved)

sample2.3s (18.9%)

Algorithm

1×

intervals

Results

390.0ms	5401×	body	128	valid
306.0ms	1092×	body	1024	valid
212.0ms	766×	body	1024	nan
179.0ms	864×	body	512	valid
104.0ms	525×	body	512	nan
102.0ms	1507×	body	128	nan
78.0ms	572×	body	256	valid
33.0ms	253×	body	256	nan
27.0ms	71×	body	2048	valid

Compiler

Compiled 1189 to 572 computations (51.9% saved)

Details

analyze998.0ms (8.1%)

sample60.0ms (0.5%)

simplify72.0ms (0.6%)

prune2.0ms (0%)

localize16.0ms (0.1%)

rewrite266.0ms (2.2%)

series978.0ms (7.9%)

simplify126.0ms (1%)

prune119.0ms (1%)

localize22.0ms (0.2%)

rewrite172.0ms (1.4%)

series521.0ms (4.2%)

simplify113.0ms (0.9%)

prune106.0ms (0.9%)

localize32.0ms (0.3%)

rewrite219.0ms (1.8%)

series826.0ms (6.7%)

simplify307.0ms (2.5%)

prune148.0ms (1.2%)

localize12.0ms (0.1%)

rewrite159.0ms (1.3%)

series164.0ms (1.3%)

simplify130.0ms (1%)

prune83.0ms (0.7%)

regimes4.0s (32.4%)

bsearch342.0ms (2.8%)

simplify11.0ms (0.1%)

end4.0ms (0%)

sample2.3s (18.9%)

Profiling