Details

analyze1.2s (7%)

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)

sample84.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	163×	body	128	valid
16.0ms	44×	body	1024	valid
10.0ms	30×	body	1024	nan
7.0ms	27×	body	512	valid
7.0ms	48×	body	128	nan
4.0ms	15×	body	512	nan
3.0ms	19×	body	256	valid
2.0ms	14×	body	256	nan
1.0ms	3×	body	2048	valid

Compiler

Compiled 64 to 44 computations (31.3% saved)

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-def_binary64`
506×	`fma-neg_binary64`
500×	`distribute-rgt-in_binary64`
420×	`distribute-lft-in_binary64`
403×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	48	39
2	103	39
3	222	39
4	455	39
5	975	39
6	2136	39
7	4390	39
8	4971	39

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

46.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	46.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))

Compiler

Compiled 114 to 72 computations (36.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
✓	0.5b	(*.f64 (sqrt.f64 2) t)
✓	14.9b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	21.3b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

rewrite74.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-cube-cbrt_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
17×	`pow1_binary64`

Counts

4 → 170

Calls

4 calls:

19.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
19.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
12.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
12.0ms	(*.f64 (sqrt.f64 2) t)

series1.9s (11.6%)

Counts

4 → 120

Calls

4 calls:

1.5s	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
311.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
134.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
11.0ms	(*.f64 (sqrt.f64 2) t)

simplify351.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

390×	`fma-def_binary64`
343×	`associate-+r+_binary64`
286×	`associate-r_binary64`
230×	`associate-*r/_binary64`
215×	`associate-/l*_binary64`

Counts

290 → 443

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1668	34039
1	5061	34039

prune893.0ms (5.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	434	9	443
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	435	9	444

Error

6.6b

Counts

444 → 9

Alt Table

Status	Error	Program
	41.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
▶	35.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	39.5b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))
	37.9b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	41.4b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
	46.4b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	46.2b	(pow.f64 (cbrt.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))) 3)
	49.7b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (.f64 t t) (-.f64 x 1)))))))

Compiler

Compiled 45322 to 32790 computations (27.7% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.6b	(/.f64 (.f64 l l) (.f64 x x))
✓	18.6b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	19.7b	(/.f64 (.f64 t t) (.f64 x x))
✓	29.6b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))

rewrite64.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
27×	`add-cube-cbrt_binary64`
24×	`add-cbrt-cube_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`

Counts

4 → 173

Calls

4 calls:

18.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
13.0ms	(/.f64 (.f64 l l) (.f64 x x))
13.0ms	(/.f64 (.f64 t t) (.f64 x x))
10.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))

series758.0ms (4.5%)

Counts

4 → 104

Calls

4 calls:

597.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))
60.0ms	(/.f64 (.f64 l l) (.f64 x x))
56.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
43.0ms	(/.f64 (.f64 t t) (.f64 x x))

simplify228.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-def_binary64`
662×	`associate-/r*_binary64`
435×	`associate-/l*_binary64`
221×	`*-commutative_binary64`
141×	`+-commutative_binary64`

Counts

277 → 442

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	675	15344
1	2007	12958
2	5167	12958

prune631.0ms (3.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	434	8	442
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	436	15	451

Error

0.5b

Counts

451 → 15

Alt Table

Status	Error	Program
	41.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	53.9b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (/.f64 (.f64 t t) l) (.f64 2 (/.f64 (.f64 t t) (.f64 l x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 l (.f64 x x)))) (.f64 2 (/.f64 (.f64 t t) (.f64 l (pow.f64 x 3)))))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))))))
✓	35.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	46.4b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	39.5b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 (.f64 l l) (.f64 t (*.f64 x (sqrt.f64 2)))))))
	46.2b	(pow.f64 (cbrt.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))) 3)
	38.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 (/.f64 (.f64 l l) (.f64 (.f64 x x) t)) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (fma.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (+.f64 (/.f64 (.f64 l l) (.f64 (pow.f64 x 3) t)) (/.f64 (.f64 l l) (.f64 x t))))))))
	41.4b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
	53.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))
	53.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
▶	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4) (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)))
	37.9b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))) (cbrt.f64 (sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))))))) 2))

Compiler

Compiled 28772 to 16916 computations (41.2% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	19.7b	(/.f64 (.f64 t t) (.f64 x x))
	19.7b	(/.f64 (.f64 t t) (.f64 x x))
	30.3b	(pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))) 1/4)
✓	30.3b	(pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))) 1/4)

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cube-cbrt_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-exp-log_binary64`
3×	`pow-to-exp_binary64`
3×	`sqr-pow_binary64`

Counts

1 → 37

Calls

1 calls:

11.0ms

(pow.f64 (fma.f64 (/.f64 (*.f64 t t) (*.f64 x x)) 4 (fma.f64 (/.f64 (*.f64 t t) x) 4 (fma.f64 (/.f64 (*.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (*.f64 l l) (*.f64 x x)) (*.f64 2 (+.f64 (/.f64 (*.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))) 1/4)

series1.1s (6.7%)

Counts

1 → 36

Calls

1 calls:

1.1s

(pow.f64 (fma.f64 (/.f64 (*.f64 t t) (*.f64 x x)) 4 (fma.f64 (/.f64 (*.f64 t t) x) 4 (fma.f64 (/.f64 (*.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (*.f64 l l) (*.f64 x x)) (*.f64 2 (+.f64 (/.f64 (*.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))) 1/4)

simplify338.0ms (2%)

Algorithm

1×	egg-herbie

Rules

949×	`fma-def_binary64`
337×	`*-commutative_binary64`
238×	`+-commutative_binary64`
198×	`associate-+r+_binary64`
138×	`associate-*r/_binary64`

Counts

73 → 129

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	928	23582
1	3082	22348
2	5046	22348

prune1.9s (11.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	582	3	585
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	584	16	600

Error

0.5b

Counts

600 → 16

Alt Table

Status	Error	Program
	41.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	53.9b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (/.f64 (.f64 t t) l) (.f64 2 (/.f64 (.f64 t t) (.f64 l x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 l (.f64 x x)))) (.f64 2 (/.f64 (.f64 t t) (.f64 l (pow.f64 x 3)))))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))))))
	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)) 2) (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)))
✓	35.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	46.4b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	39.5b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 (.f64 l l) (.f64 t (*.f64 x (sqrt.f64 2)))))))
	46.2b	(pow.f64 (cbrt.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))) 3)
	38.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 (/.f64 (.f64 l l) (.f64 (.f64 x x) t)) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (fma.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (+.f64 (/.f64 (.f64 l l) (.f64 (pow.f64 x 3) t)) (/.f64 (.f64 l l) (.f64 x t))))))))
	41.4b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
	53.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))
	35.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)) 3) (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)))
	53.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
	37.9b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))))) (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4))) (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)))
▶	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t)))))))))) 2))

Compiler

Compiled 92472 to 59326 computations (35.8% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	13.6b	(/.f64 (.f64 l l) (.f64 x x))
	18.6b	(/.f64 (*.f64 t t) (pow.f64 x 3))
	19.7b	(/.f64 (.f64 t t) (.f64 x x))
	29.6b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune594.0ms (3.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	766	3	769
Fresh	2	12	14
Picked	1	0	1
Done	0	1	1
Total	769	16	785

Error

0.5b

Counts

785 → 16

Alt Table

Status	Error	Program
	41.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)) 2) (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)))
	55.7b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (/.f64 (.f64 t t) l) (.f64 2 (/.f64 (.f64 t t) (.f64 l x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 l (.f64 x x)))) (.f64 2 (/.f64 (.f64 t t) (.f64 l (pow.f64 x 3)))))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x))))))))) 2))
✓	35.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	35.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)) 3) (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)))
	56.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))) 2))
	46.2b	(pow.f64 (cbrt.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))) 3)
	38.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 (/.f64 (.f64 l l) (.f64 (.f64 x x) t)) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (fma.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (+.f64 (/.f64 (.f64 l l) (.f64 (pow.f64 x 3) t)) (/.f64 (.f64 l l) (.f64 x t))))))))
	41.4b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
	53.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))
	53.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
	46.4b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	37.9b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))))) (cbrt.f64 (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4))) (pow.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 1/4)))
	41.8b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 (.f64 l l) (.f64 t (*.f64 x (sqrt.f64 2))))))) 2))

Compiler

Compiled 28867 to 17215 computations (40.4% saved)

regimes3.2s (18.9%)

Accuracy

Total 10.7b remaining (95.6%)

Threshold costs 0b (0%)

Compiler

Compiled 84866 to 46735 computations (44.9% saved)

bsearch336.0ms (2%)

Steps

Iters	Range		Point
4	4.2145235227952613e-13	6.172307242600739e-13	6.10072181429215e-13
6	8.434697565262045e-168	1.320285067614206e-166	8.6523588372652e-168
5	-8.211797583174785e-265	-3.517501962030867e-265	-3.5654619165290006e-265
8	-2.2055866486749815e+49	-5.040410135187974e+45	-1.6243357543600368e+49

Compiler

Compiled 4 to 3 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	203
1	67	203
2	76	203
3	81	203
4	83	203
5	81	203

end2.0ms (0%)

Compiler: Compiled 137 to 89 computations (35% saved)

sample2.9s (17.2%)

Algorithm

1×

intervals

Results

565.0ms	5383×	body	128	valid
428.0ms	1143×	body	1024	valid
298.0ms	801×	body	1024	nan
234.0ms	840×	body	512	valid
161.0ms	1562×	body	128	nan
143.0ms	527×	body	512	nan
110.0ms	576×	body	256	valid
55.0ms	291×	body	256	nan
29.0ms	58×	body	2048	valid

Compiler

Compiled 1122 to 681 computations (39.3% saved)

Details

analyze1.2s (7%)

sample84.0ms (0.5%)

simplify56.0ms (0.3%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite74.0ms (0.4%)

series1.9s (11.6%)

simplify351.0ms (2.1%)

prune893.0ms (5.3%)

localize32.0ms (0.2%)

rewrite64.0ms (0.4%)

series758.0ms (4.5%)

simplify228.0ms (1.4%)

prune631.0ms (3.8%)

localize35.0ms (0.2%)

rewrite16.0ms (0.1%)

series1.1s (6.7%)

simplify338.0ms (2%)

prune1.9s (11.3%)

localize32.0ms (0.2%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify19.0ms (0.1%)

prune594.0ms (3.6%)

regimes3.2s (18.9%)

bsearch336.0ms (2%)

simplify9.0ms (0.1%)

end2.0ms (0%)

sample2.9s (17.2%)

Profiling