Details

analyze1.0s (5.6%)

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)

sample137.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms	163×	body	128	valid
12.0ms	35×	body	1024	valid
9.0ms	35×	body	512	valid
9.0ms	25×	body	1024	nan
5.0ms	57×	body	128	nan
4.0ms	22×	body	256	valid
3.0ms	13×	body	512	nan
3.0ms	15×	body	256	nan
0.0ms	1×	body	2048	valid

Compiler

Compiled 64 to 44 computations (31.3% saved)

simplify54.0ms (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

44.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	44.1b	(/.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)

localize17.0ms (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))))
✓	0.4b	(*.f64 (sqrt.f64 2) t)
✓	16.3b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	20.7b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

series1.8s (9.7%)

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))))
300.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
75.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
3.0ms	(*.f64 (sqrt.f64 2) t)

rewrite40.0ms (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:

12.0ms	(/.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))))
10.0ms	(-.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)

simplify408.0ms (2.2%)

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 → 258

Iterations

Useful iterations: 0 (0.0ms)

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

prune898.0ms (4.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	250	8	258
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	251	8	259

Error

6.1b

Counts

259 → 8

Alt Table

Status	Error	Program
	44.9b	(/.f64 (.f64 (sqrt.f64 2) t) (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	63.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (sqrt.f64 (+.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) -1)) l)))
	41.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	63.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1)) l))
	37.5b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	41.1b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x)) (/.f64 (.f64 l l) (.f64 t (*.f64 (sqrt.f64 2) x))))))
	37.2b	(/.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)))
▶	33.4b	(/.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))))))))))

Compiler

Compiled 42223 to 31130 computations (26.3% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	15.8b	(/.f64 (*.f64 l l) (pow.f64 x 3))
✓	18.1b	(/.f64 (.f64 t t) (.f64 x x))
✓	20.5b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	28.1b	(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)))))))))

series703.0ms (3.7%)

Counts

4 → 104

Calls

4 calls:

596.0ms	(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)))))))))
37.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
37.0ms	(/.f64 (*.f64 l l) (pow.f64 x 3))
32.0ms	(/.f64 (.f64 t t) (.f64 x x))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

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

simplify195.0ms (1%)

Algorithm

1×	egg-herbie

Rules

742×	`associate-/r*_binary64`
672×	`fma-def_binary64`
516×	`associate-/l*_binary64`
217×	`*-commutative_binary64`
137×	`+-commutative_binary64`

Counts

232 → 206

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	694	14697
1	2004	12426
2	5495	12426

prune504.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	201	5	206
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	204	10	214

Error

0.4b

Counts

214 → 10

Alt Table

Status	Error	Program
	53.2b	(/.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))))))))
	44.9b	(/.f64 (.f64 (sqrt.f64 2) t) (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
▶	33.5b	(/.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))))))))))))
	41.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	55.1b	(/.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)))))))))
	37.5b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	54.3b	(/.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)))))))
	41.1b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x)) (/.f64 (.f64 l l) (.f64 t (*.f64 (sqrt.f64 2) x))))))
	37.2b	(/.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)))
	33.6b	(/.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))))))))))))

Compiler

Compiled 26107 to 15764 computations (39.6% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	15.8b	(/.f64 (*.f64 l l) (pow.f64 x 3))
	18.1b	(/.f64 (.f64 t t) (.f64 x x))
	20.5b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	28.1b	(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)))))))))

series591.0ms (3.1%)

Counts

1 → 32

Calls

1 calls:

591.0ms

(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)))))))))

rewrite6.0ms (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:

4.0ms

(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)))))))))

simplify158.0ms (0.8%)

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 → 78

Iterations

Useful iterations: 1 (0.0ms)

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

prune1.8s (9.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	412	0	412
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	412	10	422

Error

0.4b

Counts

422 → 10

Alt Table

Status	Error	Program
	53.2b	(/.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))))))))
	44.9b	(/.f64 (.f64 (sqrt.f64 2) t) (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
✓	33.5b	(/.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))))))))))))
	41.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	55.1b	(/.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)))))))))
	37.5b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	54.3b	(/.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)))))))
	41.1b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x)) (/.f64 (.f64 l l) (.f64 t (*.f64 (sqrt.f64 2) x))))))
	37.2b	(/.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)))
▶	33.6b	(/.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))))))))))))

Compiler

Compiled 73496 to 39061 computations (46.9% saved)

localize56.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	15.8b	(/.f64 (*.f64 l l) (pow.f64 x 3))
	18.1b	(/.f64 (.f64 t t) (.f64 x x))
	20.5b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	28.9b	(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)))))))))

series1.1s (5.9%)

Counts

1 → 36

Calls

1 calls:

1.1s

(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)))))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(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)))))))))

simplify286.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

970×	`times-frac_binary64`
947×	`fma-def_binary64`
311×	`*-commutative_binary64`
221×	`+-commutative_binary64`
185×	`associate-+r+_binary64`

Counts

49 → 78

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	831	22095
1	2924	22063
2	5050	22063

prune1.7s (9.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	412	0	412
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	412	10	422

Error

0.4b

Counts

422 → 10

Alt Table

Status	Error	Program
	53.2b	(/.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))))))))
	44.9b	(/.f64 (.f64 (sqrt.f64 2) t) (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
✓	33.5b	(/.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))))))))))))
	41.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	55.1b	(/.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)))))))))
	37.5b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	54.3b	(/.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)))))))
	41.1b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x)) (/.f64 (.f64 l l) (.f64 t (*.f64 (sqrt.f64 2) x))))))
	37.2b	(/.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)))
✓	33.6b	(/.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))))))))))))

Compiler

Compiled 102411 to 62573 computations (38.9% saved)

regimes3.9s (20.6%)

Accuracy

Total 10.5b remaining (96%)

Threshold costs 0b (0%)

Counts

198 → 5

Compiler

Compiled 91290 to 53376 computations (41.5% saved)

bsearch478.0ms (2.5%)

Steps

Iters	Range		Point
7	3.7938399598365873e+52	2.714850890151783e+54	1.4755055794994423e+54
8	-2.8336743744740685e-273	-6.582299552891367e-276	-2.8022286549987483e-273
10	-7.533042811144673e-156	-1.1175471694681079e-170	-1.1374664350483335e-170
8	-3.41149787855655e+62	-4.5680835153799696e+58	-1.505980537706646e+59

Compiler

Compiled 4 to 3 computations (25% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
12×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	307
1	96	307
2	106	307
3	112	307
4	117	307
5	119	307
6	117	307

end3.0ms (0%)

Compiler: Compiled 206 to 134 computations (35% saved)

sample2.8s (14.8%)

Algorithm

1×

intervals

Results

530.0ms	5370×	body	128	valid
438.0ms	1149×	body	1024	valid
337.0ms	782×	body	1024	nan
250.0ms	879×	body	512	valid
147.0ms	534×	body	512	nan
144.0ms	1514×	body	128	nan
100.0ms	533×	body	256	valid
49.0ms	268×	body	256	nan
31.0ms	69×	body	2048	valid

Compiler

Compiled 764 to 477 computations (37.6% saved)

Details

analyze1.0s (5.6%)

sample137.0ms (0.7%)

simplify54.0ms (0.3%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series1.8s (9.7%)

rewrite40.0ms (0.2%)

simplify408.0ms (2.2%)

prune898.0ms (4.8%)

localize32.0ms (0.2%)

series703.0ms (3.7%)

rewrite23.0ms (0.1%)

simplify195.0ms (1%)

prune504.0ms (2.7%)

localize35.0ms (0.2%)

series591.0ms (3.1%)

rewrite6.0ms (0%)

simplify158.0ms (0.8%)

prune1.8s (9.8%)

localize56.0ms (0.3%)

series1.1s (5.9%)

rewrite2.0ms (0%)

simplify286.0ms (1.5%)

prune1.7s (9.1%)

regimes3.9s (20.6%)

bsearch478.0ms (2.5%)

simplify11.0ms (0.1%)

end3.0ms (0%)

sample2.8s (14.8%)

Profiling