Details

analyze1.2s (5.2%)

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)

sample81.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms	44×	body	1024	valid
15.0ms	163×	body	128	valid
10.0ms	30×	body	1024	nan
7.0ms	27×	body	512	valid
4.0ms	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)

simplify57.0ms (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

prune4.0ms (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)))

rewrite42.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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 → 90

Calls

4 calls:

13.0ms	(/.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))))
11.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
9.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
4.0ms	(*.f64 (sqrt.f64 2) t)

series1.9s (8.4%)

Counts

4 → 120

Calls

4 calls:

1.4s	(/.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))))
319.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
137.0ms	(-.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)

simplify513.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

388×	`fma-def_binary64`
343×	`associate-+r+_binary64`
286×	`associate-r_binary64`
228×	`associate-*r/_binary64`
219×	`associate-/l*_binary64`

Counts

210 → 343

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1626	31940
1	5000	31940
2	5024	31940

prune849.0ms (3.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	334	9	343
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	335	9	344

Error

6.6b

Counts

344 → 9

Alt Table

Status	Error	Program
	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)))
	52.8b	(cbrt.f64 (/.f64 (.f64 (.f64 2 (.f64 t t)) (.f64 (sqrt.f64 2) t)) (.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
▶	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))))))))))
	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))
	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)))
	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))))))
	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))))))
	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 42225 to 31128 computations (26.3% saved)

localize29.0ms (0.1%)

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)))))))))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-exp-log_binary64`
33×	`add-cbrt-cube_binary64`
14×	`associate-/r*_binary64`
14×	`times-frac_binary64`
14×	`div-exp_binary64`

Counts

4 → 106

Calls

4 calls:

6.0ms	(/.f64 (.f64 t t) (.f64 x x))
5.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
5.0ms	(/.f64 (.f64 l l) (.f64 x x))
1.0ms	(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)))))))))

series688.0ms (3.1%)

Counts

4 → 104

Calls

4 calls:

541.0ms	(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)))))))))
58.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
45.0ms	(/.f64 (.f64 t t) (.f64 x x))
43.0ms	(/.f64 (.f64 l l) (.f64 x x))

simplify209.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

731×	`associate-/r*_binary64`
671×	`fma-def_binary64`
519×	`associate-/l*_binary64`
217×	`*-commutative_binary64`
137×	`+-commutative_binary64`

Counts

210 → 377

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	680	14444
1	1992	12162
2	5408	12162

prune557.0ms (2.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	370	7	377
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	372	14	386

Error

0.5b

Counts

386 → 14

Alt Table

Status	Error	Program
	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)))
	53.9b	(/.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)))))))))
	52.8b	(cbrt.f64 (/.f64 (.f64 (.f64 2 (.f64 t t)) (.f64 (sqrt.f64 2) t)) (.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
✓	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))))))))))
	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))
	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)))))))
	46.4b	(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))))))
	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))))))))
	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)))
	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)))))))
	35.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.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)))))))))) (sqrt.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))))))))))))
▶	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.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)))))))))) (sqrt.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))))))))))))

Compiler

Compiled 25223 to 15486 computations (38.6% 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))
	29.6b	(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)))))))))
✓	29.6b	(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)))))))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

(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)))))))))

series539.0ms (2.4%)

Counts

1 → 32

Calls

1 calls:

538.0ms

(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)))))))))

simplify192.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-def_binary64`
410×	`associate-/r*_binary64`
315×	`times-frac_binary64`
296×	`associate-l_binary64`
262×	`associate-*r/_binary64`

Counts

47 → 88

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	565	12538
1	1768	10428
2	5437	10428

prune1.9s (8.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	427	1	428
Fresh	0	12	12
Picked	0	1	1
Done	1	0	1
Total	428	14	442

Error

0.5b

Counts

442 → 14

Alt Table

Status	Error	Program
	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)))
	53.9b	(/.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)))))))))
	52.8b	(cbrt.f64 (/.f64 (.f64 (.f64 2 (.f64 t t)) (.f64 (sqrt.f64 2) t)) (.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	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))
	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)))))))
	46.4b	(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))))))
	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))))))))
	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)))
	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)))))))
▶	35.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (.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 (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 (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)))))))))))) (sqrt.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))))))))))))
	35.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.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)))))))))) (sqrt.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))))))))))))
✓	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.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)))))))))) (sqrt.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))))))))))))

Compiler

Compiled 51050 to 30480 computations (40.3% saved)

localize108.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	29.6b	(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)))))))))
	29.6b	(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)))))))))
	29.6b	(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)))))))))
✓	29.6b	(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)))))))))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

2.0ms

(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)))))))))

series1.1s (5.1%)

Counts

1 → 32

Calls

1 calls:

1.1s

(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)))))))))

simplify369.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-def_binary64`
410×	`associate-/r*_binary64`
315×	`times-frac_binary64`
296×	`associate-l_binary64`
262×	`associate-*r/_binary64`

Counts

47 → 88

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	565	12522
1	1770	10398
2	5445	10398

prune4.2s (18.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	528	0	528
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	528	14	542

Error

0.5b

Counts

542 → 14

Alt Table

Status	Error	Program
	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)))
	53.9b	(/.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)))))))))
	52.8b	(cbrt.f64 (/.f64 (.f64 (.f64 2 (.f64 t t)) (.f64 (sqrt.f64 2) t)) (.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	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))
	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)))))))
	46.4b	(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))))))
	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))))))))
	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)))
	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)))))))
✓	35.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (.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 (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 (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)))))))))))) (sqrt.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))))))))))))
	35.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.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)))))))))) (sqrt.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))))))))))))
✓	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.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)))))))))) (sqrt.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))))))))))))

Compiler

Compiled 118848 to 66010 computations (44.5% saved)

regimes3.7s (16.7%)

Accuracy

Total 10.7b remaining (95.5%)

Threshold costs 0b (0%)

Compiler

Compiled 51334 to 29692 computations (42.2% saved)

bsearch638.0ms (2.9%)

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)

simplify18.0ms (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

end4.0ms (0%)

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

sample3.4s (15.1%)

Algorithm

1×

intervals

Results

649.0ms	5383×	body	128	valid
538.0ms	1143×	body	1024	valid
364.0ms	801×	body	1024	nan
292.0ms	840×	body	512	valid
218.0ms	1562×	body	128	nan
172.0ms	527×	body	512	nan
139.0ms	576×	body	256	valid
65.0ms	291×	body	256	nan
32.0ms	58×	body	2048	valid

Compiler

Compiled 1096 to 641 computations (41.5% saved)

Details

analyze1.2s (5.2%)

sample81.0ms (0.4%)

simplify57.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite42.0ms (0.2%)

series1.9s (8.4%)

simplify513.0ms (2.3%)

prune849.0ms (3.8%)

localize29.0ms (0.1%)

rewrite22.0ms (0.1%)

series688.0ms (3.1%)

simplify209.0ms (0.9%)

prune557.0ms (2.5%)

localize35.0ms (0.2%)

rewrite3.0ms (0%)

series539.0ms (2.4%)

simplify192.0ms (0.9%)

prune1.9s (8.5%)

localize108.0ms (0.5%)

rewrite5.0ms (0%)

series1.1s (5.1%)

simplify369.0ms (1.7%)

prune4.2s (18.8%)

regimes3.7s (16.7%)

bsearch638.0ms (2.9%)

simplify18.0ms (0.1%)

end4.0ms (0%)

sample3.4s (15.1%)

Profiling