Details

analyze988.0ms (7.4%)

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)

sample57.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	169×	body	128	valid
8.0ms	41×	body	512	valid
7.0ms	28×	body	1024	valid
6.0ms	24×	body	1024	nan
4.0ms	65×	body	128	nan
2.0ms	13×	body	512	nan
2.0ms	15×	body	256	valid
1.0ms	3×	body	2048	valid
1.0ms	5×	body	256	nan

Compiler

Compiled 64 to 44 computations (31.3% saved)

simplify80.0ms (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

43.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	43.2b	(/.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)

localize17.0ms (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))))
0.5b	(*.f64 (sqrt.f64 2) t)
14.2b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
20.4b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite261.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

43.1b

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:

21.0ms	(/.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))))
15.0ms	(-.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)

series854.0ms (6.4%)

Error

5.4b

Counts

4 → 62

Calls

4 calls:

375.0ms	(/.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))))
225.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
154.0ms	(-.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 9966 to 8151 computations (18.2% saved)

simplify141.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

652×	`times-frac_binary64`
461×	`associate-/l*_binary64`
456×	`associate-/r*_binary64`
228×	`associate-*r/_binary64`
210×	`associate-*l/_binary64`

Counts

142 → 105

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	502	8414
1	1449	7939
2	5109	7939

prune149.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	97	8	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	8	106

Error

5.4b

Counts

106 → 8

Alt Table

Status	Error	Program
	49.2b	(/.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 (.f64 l l) (.f64 t (.f64 (sqrt.f64 2) (.f64 x x)))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 6) (.f64 (pow.f64 t 5) (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 x 3))))) (+.f64 (.f64 6 (/.f64 (.f64 l l) (.f64 t (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 x 3))))) (+.f64 (.f64 4 (/.f64 t (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 x 3)))) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 3)))) (+.f64 (/.f64 (.f64 l l) (.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 3)))) (.f64 3 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (pow.f64 (sqrt.f64 2) 5) (pow.f64 x 3)))))))))))))) (+.f64 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3)))) (+.f64 (.f64 4 (/.f64 (.f64 l l) (.f64 t (.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))))) (+.f64 (.f64 2 (/.f64 (.f64 l l) (.f64 t (.f64 (.f64 x x) (.f64 2 (sqrt.f64 2)))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (.f64 (.f64 x x) (.f64 2 (sqrt.f64 2))) (pow.f64 t 3)))) (+.f64 (.f64 2 (/.f64 t (.f64 (.f64 x x) (.f64 2 (sqrt.f64 2))))) (.f64 4 (/.f64 t (.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3)))))))))))
	37.1b	(/.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))))))))
	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)))))
▶	32.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))))
	38.7b	(/.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))))))
	43.3b	(cbrt.f64 (pow.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l)))) 3))
	39.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	37.5b	(neg.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))))

Compiler

Compiled 5139 to 3402 computations (33.8% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

13.2b	(/.f64 (*.f64 l l) (pow.f64 x 3))
19.8b	(/.f64 (.f64 t t) (.f64 x x))
20.1b	(/.f64 (*.f64 t t) (pow.f64 x 3))
26.7b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x)))))))))

rewrite358.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

5.4b

Rules

42×	`add-exp-log_binary64` `associate-*r/_binary64`
38×	`frac-add_binary64`
26×	`add-cbrt-cube_binary64`
25×	`times-frac_binary64` `associate-/r*_binary64`
18×	`add-sqr-sqrt_binary64`

Counts

4 → 134

Calls

4 calls:

32.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x)))))))))
7.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
6.0ms	(/.f64 (.f64 t t) (.f64 x x))
6.0ms	(/.f64 (*.f64 l l) (pow.f64 x 3))

Compiler

Compiled 11919 to 4675 computations (60.8% saved)

series852.0ms (6.4%)

Error

0.2b

Counts

4 → 43

Calls

4 calls:

663.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x)))))))))
32.0ms	(/.f64 (*.f64 l l) (pow.f64 x 3))
31.0ms	(/.f64 (.f64 t t) (.f64 x x))
31.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))

Compiler

Compiled 14364 to 11417 computations (20.5% saved)

simplify205.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

743×	`times-frac_binary64`
443×	`distribute-rgt-in_binary64`
245×	`*-commutative_binary64`
132×	`+-commutative_binary64`
111×	`associate-r_binary64`

Counts

177 → 131

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	685	13069
1	2206	11764
2	5041	11764

prune192.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	125	6	131
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	129	10	139

Error

0.2b

Counts

139 → 10

Alt Table

Status	Error	Program
	59.1b	(/.f64 (.f64 (sqrt.f64 2) t) (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 2 (.f64 l l)) (.f64 x (+.f64 (.f64 4 (/.f64 (pow.f64 l 4) (pow.f64 x 6))) (.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (-.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)))))))) (.f64 x (+.f64 (.f64 (.f64 4 (.f64 t t)) (+.f64 (.f64 4 (/.f64 (pow.f64 l 4) (pow.f64 x 6))) (.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (-.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))))))) (.f64 x (+.f64 (pow.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) 3) (pow.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) 3))))))) (sqrt.f64 (.f64 x (.f64 x (+.f64 (.f64 4 (/.f64 (pow.f64 l 4) (pow.f64 x 6))) (.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (-.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)))))))))))
✓	32.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))))
	38.7b	(/.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))))))
▶	32.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x)))))))))))
	43.3b	(cbrt.f64 (pow.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l)))) 3))
	37.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) (+.f64 2 (/.f64 4 (pow.f64 x 3)))))))))
	52.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 2 (pow.f64 x 3)))))))
	39.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) (+.f64 2 (/.f64 4 (pow.f64 x 3))))))))
	37.5b	(neg.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))))
	55.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 2 (pow.f64 x 3))))))))

Compiler

Compiled 9779 to 4850 computations (50.4% saved)

localize42.0ms (0.3%)

Local error

Found 4 expressions with local error:

20.1b	(/.f64 (*.f64 t t) (pow.f64 x 3))
20.1b	(/.f64 (*.f64 t t) (pow.f64 x 3))
26.7b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))
26.7b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))

rewrite520.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

108×	`associate-*r/_binary64`
104×	`frac-add_binary64`
36×	`sqrt-div_binary64`
30×	`add-exp-log_binary64`
26×	`flip3-+_binary64` `flip-+_binary64`

Counts

4 → 148

Calls

4 calls:

36.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))
32.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))
7.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
7.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))

Compiler

Compiled 25821 to 9334 computations (63.9% saved)

series1.7s (12.6%)

Error

0.2b

Counts

4 → 58

Calls

4 calls:

704.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))
701.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))
40.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
40.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))

Compiler

Compiled 32323 to 23793 computations (26.4% saved)

simplify379.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

558×	`distribute-rgt-in_binary64`
539×	`distribute-lft-in_binary64`
403×	`times-frac_binary64`
251×	`*-commutative_binary64`
125×	`+-commutative_binary64`

Counts

206 → 152

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	616	26106
1	2140	23332
2	5857	23332

prune374.0ms (2.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	152	10	162

Error

0.2b

Counts

162 → 10

Alt Table

Status	Error	Program
	59.1b	(/.f64 (.f64 (sqrt.f64 2) t) (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 2 (.f64 l l)) (.f64 x (+.f64 (.f64 4 (/.f64 (pow.f64 l 4) (pow.f64 x 6))) (.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (-.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)))))))) (.f64 x (+.f64 (.f64 (.f64 4 (.f64 t t)) (+.f64 (.f64 4 (/.f64 (pow.f64 l 4) (pow.f64 x 6))) (.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (-.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))))))) (.f64 x (+.f64 (pow.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) 3) (pow.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) 3))))))) (sqrt.f64 (.f64 x (.f64 x (+.f64 (.f64 4 (/.f64 (pow.f64 l 4) (pow.f64 x 6))) (.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (-.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)))))))))))
✓	32.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))))
	38.7b	(/.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))))))
✓	32.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x)))))))))))
	43.3b	(cbrt.f64 (pow.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l)))) 3))
▶	37.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) (+.f64 2 (/.f64 4 (pow.f64 x 3)))))))))
	52.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 2 (pow.f64 x 3)))))))
	39.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) (+.f64 2 (/.f64 4 (pow.f64 x 3))))))))
	37.5b	(neg.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))))
	55.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 2 (pow.f64 x 3))))))))

Compiler

Compiled 22586 to 10347 computations (54.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 4 (*.f64 x x))
0.4b	(.f64 t (sqrt.f64 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) (+.f64 2 (/.f64 4 (pow.f64 x 3)))))))
0.5b	(*.f64 (sqrt.f64 2) t)
0.5b	(/.f64 4 (pow.f64 x 3))

rewrite218.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

46×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
37×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`

Counts

4 → 139

Calls

4 calls:

30.0ms	(.f64 t (sqrt.f64 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) (+.f64 2 (/.f64 4 (pow.f64 x 3)))))))
5.0ms	(/.f64 4 (pow.f64 x 3))
5.0ms	(*.f64 (sqrt.f64 2) t)
4.0ms	(/.f64 4 (*.f64 x x))

Compiler

Compiled 4197 to 3128 computations (25.5% saved)

series115.0ms (0.9%)

Error

0.2b

Counts

4 → 21

Calls

4 calls:

70.0ms	(.f64 t (sqrt.f64 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) (+.f64 2 (/.f64 4 (pow.f64 x 3)))))))
11.0ms	(*.f64 (sqrt.f64 2) t)
10.0ms	(/.f64 4 (pow.f64 x 3))
9.0ms	(/.f64 4 (*.f64 x x))

Compiler

Compiled 1397 to 1142 computations (18.3% saved)

simplify168.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

476×	`unswap-sqr_binary64`
323×	`associate-l_binary64`
287×	`associate-r_binary64`
262×	`cancel-sign-sub-inv_binary64`
193×	`associate-/r*_binary64`

Counts

160 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	2927
1	672	2810
2	3049	2773
3	4812	2773
4	4992	2773
5	4916	2773

prune105.0ms (0.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	115	10	125

Error

0.2b

Counts

125 → 10

Alt Table

Status	Error	Program
	59.1b	(/.f64 (.f64 (sqrt.f64 2) t) (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 2 (.f64 l l)) (.f64 x (+.f64 (.f64 4 (/.f64 (pow.f64 l 4) (pow.f64 x 6))) (.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (-.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)))))))) (.f64 x (+.f64 (.f64 (.f64 4 (.f64 t t)) (+.f64 (.f64 4 (/.f64 (pow.f64 l 4) (pow.f64 x 6))) (.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (-.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))))))) (.f64 x (+.f64 (pow.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) 3) (pow.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) 3))))))) (sqrt.f64 (.f64 x (.f64 x (+.f64 (.f64 4 (/.f64 (pow.f64 l 4) (pow.f64 x 6))) (.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (-.f64 (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))) (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)))))))))))
	32.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3))) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (*.f64 x x))))))))))
	38.7b	(/.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))))))
	32.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x))))))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) (/.f64 (.f64 t t) (.f64 x x)))))))))))
	43.3b	(cbrt.f64 (pow.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l)))) 3))
	37.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) (+.f64 2 (/.f64 4 (pow.f64 x 3)))))))))
	52.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 2 (pow.f64 x 3)))))))
	39.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) (+.f64 2 (/.f64 4 (pow.f64 x 3))))))))
	37.5b	(neg.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1)))))))
	55.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 2 (pow.f64 x 3))))))))

Compiler

Compiled 3172 to 2222 computations (29.9% saved)

regimes3.1s (23.2%)

Accuracy

Total 12.1b remaining (96.1%)

Threshold costs 0b (0%)

Compiler

Compiled 62482 to 37111 computations (40.6% saved)

bsearch152.0ms (1.1%)

Steps

Iters	Range		Point
8	1.6202676681609123e+70	1.3020071034597176e+74	2.1538944959529218e+71
7	-3.590688325586197e-258	-2.132885538060615e-259	-3.5574732430533503e-258

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64` `+-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`
1×	`1-exp_binary64` `cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	125
1	72	125
2	81	125
3	86	125
4	88	125
5	86	125

end2.0ms (0%)

Compiler: Compiled 85 to 62 computations (27.1% saved)

sample2.2s (16.9%)

Algorithm

1×

intervals

Results

363.0ms	5335×	body	128	valid
293.0ms	1119×	body	1024	valid
202.0ms	790×	body	1024	nan
185.0ms	933×	body	512	valid
104.0ms	1614×	body	128	nan
103.0ms	526×	body	512	nan
73.0ms	545×	body	256	valid
31.0ms	253×	body	256	nan
25.0ms	68×	body	2048	valid

Compiler

Compiled 833 to 479 computations (42.5% saved)

Details

analyze988.0ms (7.4%)

sample57.0ms (0.4%)

simplify80.0ms (0.6%)

prune2.0ms (0%)

localize17.0ms (0.1%)

rewrite261.0ms (2%)

series854.0ms (6.4%)

simplify141.0ms (1.1%)

prune149.0ms (1.1%)

localize33.0ms (0.2%)

rewrite358.0ms (2.7%)

series852.0ms (6.4%)

simplify205.0ms (1.5%)

prune192.0ms (1.4%)

localize42.0ms (0.3%)

rewrite520.0ms (3.9%)

series1.7s (12.6%)

simplify379.0ms (2.8%)

prune374.0ms (2.8%)

localize19.0ms (0.1%)

rewrite218.0ms (1.6%)

series115.0ms (0.9%)

simplify168.0ms (1.3%)

prune105.0ms (0.8%)

regimes3.1s (23.2%)

bsearch152.0ms (1.1%)

simplify7.0ms (0.1%)

end2.0ms (0%)

sample2.2s (16.9%)

Profiling