Details

analyze1.2s (11.6%)

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)

sample77.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms	174×	body	128	valid
11.0ms	33×	body	1024	valid
9.0ms	26×	body	1024	nan
8.0ms	29×	body	512	valid
6.0ms	47×	body	128	nan
4.0ms	17×	body	512	nan
3.0ms	15×	body	256	valid
2.0ms	5×	body	2048	valid
2.0ms	12×	body	256	nan

Compiler

Compiled 64 to 44 computations (31.3% saved)

simplify78.0ms (0.8%)

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

42.4b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	42.4b	(/.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)

localize18.0ms (0.2%)

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))))
0.5b	(*.f64 (sqrt.f64 2) t)
12.6b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
20.2b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite213.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

42.2b

Rules

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

Counts

4 → 80

Calls

4 calls:

18.0ms	(/.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))))
14.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
12.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
4.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 3285 to 1868 computations (43.1% saved)

series659.0ms (6.4%)

Error

8.0b

Counts

4 → 55

Calls

4 calls:

236.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
235.0ms	(/.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))))
127.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
7.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 9115 to 7369 computations (19.2% saved)

simplify163.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

367×	`associate-/l*_binary64`
242×	`times-frac_binary64`
233×	`associate-r_binary64`
215×	`associate-l_binary64`
199×	`associate-/r*_binary64`

Counts

135 → 112

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	366	6856
1	1031	6179
2	4357	6179
3	5009	6179

prune90.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Error

8.0b

Counts

113 → 8

Alt Table

Status	Error	Program
	63.3b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (/.f64 (.f64 (sqrt.f64 2) t) l)))
	37.4b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (.f64 l l) (.f64 t (*.f64 (sqrt.f64 2) x))))))
	46.6b	(.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (*.f64 t t) (-.f64 x 1))))))
	39.1b	(neg.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))))
▶	32.6b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (+.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) x)) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))))
	46.4b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))))) (/.f64 (.f64 l l) t))) (+.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))) (+.f64 (/.f64 (.f64 (.f64 l l) x) (.f64 t (-.f64 x 1))) (/.f64 (.f64 l l) (*.f64 t (-.f64 x 1))))))))
	38.8b	(/.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))) -1)
	39.8b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))

Compiler

Compiled 4116 to 2589 computations (37.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.3b	(/.f64 (*.f64 t t) x)
10.8b	(/.f64 (.f64 l l) (.f64 x x))
17.3b	(/.f64 (.f64 t t) (.f64 x x))
28.4b	(sqrt.f64 (+.f64 (.f64 2 (+.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) x)) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (*.f64 t t) x)))))

rewrite210.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

8.0b

Rules

33×	`add-cbrt-cube_binary64`
33×	`add-exp-log_binary64`
24×	`associate-*r/_binary64`
22×	`frac-add_binary64`
14×	`sqrt-div_binary64`

Counts

4 → 90

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 (.f64 2 (+.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) x)) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (*.f64 t t) x)))))
8.0ms	(/.f64 (.f64 l l) (.f64 x x))
5.0ms	(/.f64 (.f64 t t) (.f64 x x))
4.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 6046 to 1381 computations (77.2% saved)

series349.0ms (3.4%)

Error

0.6b

Counts

4 → 40

Calls

4 calls:

257.0ms	(sqrt.f64 (+.f64 (.f64 2 (+.f64 (+.f64 (.f64 t t) (/.f64 (.f64 l l) x)) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (*.f64 t t) x)))))
20.0ms	(/.f64 (.f64 l l) (.f64 x x))
19.0ms	(/.f64 (.f64 t t) (.f64 x x))
18.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 6879 to 5277 computations (23.3% saved)

simplify152.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

457×	`times-frac_binary64`
409×	`associate-l_binary64`
292×	`associate-/l*_binary64`
244×	`associate-/r*_binary64`
244×	`distribute-rgt-in_binary64`

Counts

130 → 98

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	450	7553
1	1341	6793
2	5128	6793

prune84.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	94	12	106

Error

0.5b

Counts

106 → 12

Alt Table

Status	Error	Program
	46.6b	(.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (*.f64 t t) (-.f64 x 1))))))
	54.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	39.8b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))
▶	32.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))))))
	41.6b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))) 3)))
	53.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	39.1b	(neg.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))))
	39.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 t x)) (/.f64 (.f64 l l) (.f64 t (.f64 x x))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
	46.4b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))))) (/.f64 (.f64 l l) t))) (+.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))) (+.f64 (/.f64 (.f64 (.f64 l l) x) (.f64 t (-.f64 x 1))) (/.f64 (.f64 l l) (*.f64 t (-.f64 x 1))))))))
	38.8b	(/.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))) -1)
	47.9b	(/.f64 (.f64 (sqrt.f64 2) t) (/.f64 (sqrt.f64 (-.f64 (.f64 4 (.f64 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))) (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))) (.f64 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)) (.f64 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)) 16)))) (sqrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)))))))
	63.3b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (/.f64 (.f64 (sqrt.f64 2) t) l)))

Compiler

Compiled 5121 to 2152 computations (58% saved)

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

17.3b	(/.f64 (.f64 t t) (.f64 x x))
17.3b	(/.f64 (.f64 t t) (.f64 x x))
29.3b	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (*.f64 t t) x)))))
29.3b	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (*.f64 t t) x)))))

rewrite168.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

48×	`associate-*r/_binary64`
44×	`frac-add_binary64`
28×	`cbrt-div_binary64`
28×	`add-cbrt-cube_binary64`
28×	`add-exp-log_binary64`

Counts

4 → 92

Calls

4 calls:

18.0ms	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (*.f64 t t) x)))))
16.0ms	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (*.f64 t t) x)))))
6.0ms	(/.f64 (.f64 t t) (.f64 x x))
5.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 11715 to 2319 computations (80.2% saved)

series638.0ms (6.2%)

Error

0.5b

Counts

4 → 48

Calls

4 calls:

287.0ms	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (*.f64 t t) x)))))
252.0ms	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (*.f64 t t) x)))))
24.0ms	(/.f64 (.f64 t t) (.f64 x x))
24.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 13461 to 9050 computations (32.8% saved)

simplify289.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

375×	`associate-l_binary64`
292×	`times-frac_binary64`
280×	`distribute-rgt-in_binary64`
278×	`associate-/l*_binary64`
273×	`distribute-lft-in_binary64`

Counts

140 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	438	14672
1	1419	13588
2	4906	13530
3	4967	13530

prune203.0ms (2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	117	13	130

Error

0.5b

Counts

130 → 13

Alt Table

Status	Error	Program
	46.6b	(.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (*.f64 t t) (-.f64 x 1))))))
	54.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	47.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 4 (.f64 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) x))) (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) x))))) (.f64 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)) (.f64 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)) 16)))) (cbrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))))))
▶	38.8b	(/.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))) -1)
	39.8b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))
✓	32.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))))))
	41.6b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))) 3)))
	53.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	39.1b	(neg.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))))
	39.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 t x)) (/.f64 (.f64 l l) (.f64 t (.f64 x x))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
	46.4b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))))) (/.f64 (.f64 l l) t))) (+.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))) (+.f64 (/.f64 (.f64 (.f64 l l) x) (.f64 t (-.f64 x 1))) (/.f64 (.f64 l l) (*.f64 t (-.f64 x 1))))))))
	47.9b	(/.f64 (.f64 (sqrt.f64 2) t) (/.f64 (sqrt.f64 (-.f64 (.f64 4 (.f64 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))) (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))) (.f64 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)) (.f64 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)) 16)))) (sqrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)))))))
	63.3b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (/.f64 (.f64 (sqrt.f64 2) t) l)))

Compiler

Compiled 11345 to 3903 computations (65.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite177.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

66×	`add-sqr-sqrt_binary64`
63×	`times-frac_binary64`
59×	`*-un-lft-identity_binary64`
56×	`sqrt-prod_binary64`
47×	`add-cube-cbrt_binary64`

Counts

4 → 147

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))
10.0ms	(+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))
9.0ms	(sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))
7.0ms	(/.f64 2 (-.f64 x 1))

Compiler

Compiled 3953 to 3341 computations (15.5% saved)

series85.0ms (0.8%)

Error

0.5b

Counts

4 → 38

Calls

4 calls:

22.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))
20.0ms	(sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))
11.0ms	(/.f64 2 (-.f64 x 1))
10.0ms	(+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))

Compiler

Compiled 1772 to 1620 computations (8.6% saved)

simplify190.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

590×	`associate-/r*_binary64`
281×	`associate-/l*_binary64`
270×	`times-frac_binary64`
258×	`associate-*l/_binary64`
232×	`associate-/l/_binary64`

Counts

185 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	6049
1	732	5818
2	2087	5701
3	4826	5701
4	4951	5701

prune122.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	176	11	187

Error

0.5b

Counts

187 → 11

Alt Table

Status	Error	Program
	39.8b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))
✓	32.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))))))
	41.6b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))) 3)))
	53.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	54.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	39.1b	(neg.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))))
	38.7b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))))) -1)
	39.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 t x)) (/.f64 (.f64 l l) (.f64 t (.f64 x x))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
	47.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 4 (.f64 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) x))) (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) x))))) (.f64 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)) (.f64 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)) 16)))) (cbrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x))))))))
	47.9b	(/.f64 (.f64 (sqrt.f64 2) t) (/.f64 (sqrt.f64 (-.f64 (.f64 4 (.f64 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))) (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))) (.f64 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)) (.f64 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)) 16)))) (sqrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (.f64 x x)) (/.f64 (.f64 t t) x)))))))
	63.3b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (/.f64 (.f64 (sqrt.f64 2) t) l)))

Compiler

Compiled 3817 to 2995 computations (21.5% saved)

regimes2.2s (21.4%)

Accuracy

Total 12.4b remaining (96.3%)

Threshold costs 0b (0%)

Compiler

Compiled 42220 to 25996 computations (38.4% saved)

bsearch248.0ms (2.4%)

Steps

Iters	Range	Point
8	4.0772578650128215e+177	9.43899986271408e+180	9.258573850466912e+180
9	-7.844783719352421e+63	-7.884923851290743e+58	-7.737943713271532e+63
11	-2.815116935069647e+168	-1.1492059488477318e+145	-1.344174783853972e+154

Iters

Range

Point

4.0772578650128215e+177

9.43899986271408e+180

9.258573850466912e+180

-7.844783719352421e+63

-7.884923851290743e+58

-7.737943713271532e+63

-2.815116935069647e+168

-1.1492059488477318e+145

-1.344174783853972e+154

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`*-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	150
1	65	150
2	74	150
3	79	150
4	81	150
5	81	150

end2.0ms (0%)

Compiler: Compiled 101 to 64 computations (36.6% saved)

sample2.6s (25.1%)

Algorithm

1×

intervals

Results

504.0ms	5357×	body	128	valid
419.0ms	1157×	body	1024	valid
303.0ms	861×	body	1024	nan
231.0ms	855×	body	512	valid
143.0ms	1543×	body	128	nan
131.0ms	501×	body	512	nan
102.0ms	554×	body	256	valid
46.0ms	258×	body	256	nan
35.0ms	77×	body	2048	valid

Compiler

Compiled 714 to 361 computations (49.4% saved)

Details

analyze1.2s (11.6%)

sample77.0ms (0.7%)

simplify78.0ms (0.8%)

prune2.0ms (0%)

localize18.0ms (0.2%)

rewrite213.0ms (2.1%)

series659.0ms (6.4%)

simplify163.0ms (1.6%)

prune90.0ms (0.9%)

localize24.0ms (0.2%)

rewrite210.0ms (2%)

series349.0ms (3.4%)

simplify152.0ms (1.5%)

prune84.0ms (0.8%)

localize35.0ms (0.3%)

rewrite168.0ms (1.6%)

series638.0ms (6.2%)

simplify289.0ms (2.8%)

prune203.0ms (2%)

localize12.0ms (0.1%)

rewrite177.0ms (1.7%)

series85.0ms (0.8%)

simplify190.0ms (1.8%)

prune122.0ms (1.2%)

regimes2.2s (21.4%)

bsearch248.0ms (2.4%)

simplify8.0ms (0.1%)

end2.0ms (0%)

sample2.6s (25.1%)

Profiling