Details

analyze1.5s (16.5%)

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%	99.9%	0.1%	8
0%	96.7%	3.3%	9
16.4%	74.9%	8.7%	10
17.6%	71.8%	10.7%	11
26.3%	59.5%	14.2%	12
30.7%	45.7%	23.5%	13
31.7%	43.5%	24.7%	14

Compiler

Compiled 33 to 25 computations (24.2% saved)

sample2.4s (26.4%)

Results

1.4s	8256×	body	128	valid
847.0ms	5050×	body	128	invalid

Compiler

Compiled 98 to 74 computations (24.5% saved)

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-neg_binary64`
464×	`div-sub_binary64`
380×	`associate-l_binary64`
365×	`associate-r_binary64`
276×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	43
1	59	43
2	163	37
3	607	35
4	2744	33
5	4748	33
6	4938	33

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

8.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.5b	(-.f64 (-.f64 (+.f64 3 (/.f64 2 (.f64 r r))) (/.f64 (.f64 (.f64 1/8 (-.f64 3 (.f64 2 v))) (.f64 (.f64 (*.f64 w w) r) r)) (-.f64 1 v))) 9/2)
▶	8.9b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))

Status

Error

Program

13.5b

(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))) 9/2)

▶

8.9b

(-.f64 (/.f64 2 (*.f64 r r)) (fma.f64 r (*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))

Compiler

Compiled 171 to 121 computations (29.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
✓	0.7b	(/.f64 2 (*.f64 r r))
✓	2.4b	(fma.f64 r (.f64 (.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
✓	10.2b	(.f64 r (.f64 w w))

series104.0ms (1.2%)

Counts

4 → 108

Calls

4 calls:

53.0ms	(fma.f64 r (.f64 (.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
39.0ms	(.f64 (.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
9.0ms	(.f64 r (.f64 w w))
2.0ms	(/.f64 2 (*.f64 r r))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-cbrt-cube_binary64`
35×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
25×	`associate-r_binary64`

Counts

4 → 105

Calls

4 calls:

10.0ms	(.f64 (.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
5.0ms	(.f64 r (.f64 w w))
3.0ms	(/.f64 2 (*.f64 r r))
0.0ms	(fma.f64 r (.f64 (.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

simplify151.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-def_binary64`
703×	`times-frac_binary64`
347×	`associate-l_binary64`
306×	`associate-r_binary64`
172×	`*-commutative_binary64`

Counts

213 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	5076
1	712	4298
2	2670	4167
3	4781	4167
4	4974	4167
5	4962	4167

prune275.0ms (3.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	184	12	196
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	186	12	198

Error

1.6b

Counts

198 → 12

Alt Table

Status	Error	Program
	9.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 2 (.f64 r r))) (cbrt.f64 (/.f64 2 (.f64 r r)))) (cbrt.f64 (/.f64 2 (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	33.4b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 (.f64 (sqrt.f64 r) w) (*.f64 (sqrt.f64 r) w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
▶	2.7b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	9.0b	(-.f64 (.f64 (sqrt.f64 (/.f64 2 (.f64 r r))) (sqrt.f64 (/.f64 2 (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	26.3b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 2 2) 2) (.f64 (.f64 (.f64 r r) (.f64 r r)) (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	9.2b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 (.f64 r (.f64 w w)) (/.f64 (.f64 (cbrt.f64 (fma.f64 v -1/4 3/8)) (cbrt.f64 (fma.f64 v -1/4 3/8))) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))) (/.f64 (cbrt.f64 (fma.f64 v -1/4 3/8)) (cbrt.f64 (-.f64 1 v)))) 3/2))
	32.3b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (-.f64 (.f64 3/8 (/.f64 (pow.f64 r 2) (-.f64 1 v))) (.f64 1/4 (/.f64 (*.f64 v (pow.f64 r 2)) (-.f64 1 v)))) (pow.f64 w 2)))
	23.1b	(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
	8.9b	(-.f64 (/.f64 (/.f64 2 r) r) (fma.f64 r (.f64 (.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	9.1b	(-.f64 (/.f64 (sqrt.f64 2) (/.f64 (.f64 r r) (sqrt.f64 2))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	21.2b	(-.f64 (/.f64 2 (.f64 r r)) (cbrt.f64 (.f64 (.f64 (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
	8.9b	(-.f64 (/.f64 2 (.f64 r r)) (+.f64 (.f64 (.f64 (.f64 w w) r) (*.f64 (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)) r)) 3/2))

Compiler

Compiled 6982 to 4063 computations (41.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
✓	0.2b	(.f64 (.f64 r w) w)
	0.7b	(/.f64 2 (*.f64 r r))
✓	2.4b	(fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

series102.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

53.0ms	(fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
39.0ms	(.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
9.0ms	(.f64 (.f64 r w) w)

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-cbrt-cube_binary64`
29×	`add-exp-log_binary64`
27×	`associate-r_binary64`
23×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`

Counts

3 → 81

Calls

3 calls:

10.0ms	(.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
4.0ms	(.f64 (.f64 r w) w)
0.0ms	(fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

simplify362.0ms (4%)

Algorithm

1×	egg-herbie

Rules

778×	`times-frac_binary64`
486×	`associate-l_binary64`
374×	`associate-r_binary64`
186×	`fma-neg_binary64`
172×	`*-commutative_binary64`

Counts

177 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	4716
1	660	3983
2	2925	3947
3	4679	3943
4	4970	3943

prune425.0ms (4.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	188	6	194
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	191	15	206

Error

1.6b

Counts

206 → 15

Alt Table

Status	Error	Program
	9.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 2 (.f64 r r))) (cbrt.f64 (/.f64 2 (.f64 r r)))) (cbrt.f64 (/.f64 2 (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	33.4b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 (.f64 (sqrt.f64 r) w) (*.f64 (sqrt.f64 r) w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	3.6b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (.f64 (cbrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (cbrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))) (cbrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
	9.2b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 (.f64 r (.f64 w w)) (/.f64 (.f64 (cbrt.f64 (fma.f64 v -1/4 3/8)) (cbrt.f64 (fma.f64 v -1/4 3/8))) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))) (/.f64 (cbrt.f64 (fma.f64 v -1/4 3/8)) (cbrt.f64 (-.f64 1 v)))) 3/2))
	29.1b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (.f64 w w) (.f64 (*.f64 r r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))))
	23.1b	(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
	3.6b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 (.f64 (.f64 r w) w) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))) (/.f64 (fma.f64 v -1/4 3/8) (cbrt.f64 (-.f64 1 v)))) 3/2))
▶	2.8b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 r w) (.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2))
	21.2b	(-.f64 (/.f64 2 (.f64 r r)) (cbrt.f64 (.f64 (.f64 (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
	7.7b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (/.f64 (.f64 (.f64 (.f64 r w) w) (fma.f64 v -1/4 3/8)) (-.f64 1 v)) 3/2))
	9.0b	(-.f64 (.f64 (sqrt.f64 (/.f64 2 (.f64 r r))) (sqrt.f64 (/.f64 2 (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	26.3b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 2 2) 2) (.f64 (.f64 (.f64 r r) (.f64 r r)) (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	2.8b	(-.f64 (/.f64 (/.f64 2 r) r) (fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	9.1b	(-.f64 (/.f64 (sqrt.f64 2) (/.f64 (.f64 r r) (sqrt.f64 2))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	8.9b	(-.f64 (/.f64 2 (.f64 r r)) (+.f64 (.f64 (.f64 (.f64 w w) r) (*.f64 (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)) r)) 3/2))

Compiler

Compiled 7185 to 4205 computations (41.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
✓	0.2b	(.f64 (.f64 r w) (*.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))))
	0.7b	(/.f64 2 (*.f64 r r))
✓	2.4b	(fma.f64 r (.f64 (.f64 r w) (*.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2)

series148.0ms (1.6%)

Counts

3 → 96

Calls

3 calls:

92.0ms

(fma.f64 r (*.f64 (*.f64 r w) (*.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2)

41.0ms

(*.f64 (*.f64 r w) (*.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))))

15.0ms

(*.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-cbrt-cube_binary64`
29×	`add-exp-log_binary64`
28×	`add-sqr-sqrt_binary64`
25×	`associate-r_binary64`
23×	`*-un-lft-identity_binary64`

Counts

3 → 84

Calls

3 calls:

9.0ms

(*.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))

9.0ms

(*.f64 (*.f64 r w) (*.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))))

0.0ms

(fma.f64 r (*.f64 (*.f64 r w) (*.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2)

simplify126.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

592×	`times-frac_binary64`
347×	`associate-l_binary64`
340×	`associate-r_binary64`
273×	`fma-neg_binary64`
252×	`distribute-rgt-out_binary64`

Counts

180 → 175

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	5086
1	723	4262
2	2712	4136
3	4838	4134
4	4975	4134

prune345.0ms (3.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	206	13	219

Error

0.0b

Counts

219 → 13

Alt Table

Status	Error	Program
	33.4b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 (.f64 (sqrt.f64 r) w) (*.f64 (sqrt.f64 r) w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	8.0b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (/.f64 (.f64 (.f64 r w) (.f64 w (fma.f64 v -1/4 3/8))) (-.f64 1 v)) 3/2))
	9.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 2 (.f64 r r))) (cbrt.f64 (/.f64 2 (.f64 r r)))) (cbrt.f64 (/.f64 2 (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	15.2b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 r w) (cbrt.f64 (.f64 (.f64 (.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) (.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) (.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))))) 3/2))
	9.0b	(-.f64 (.f64 (sqrt.f64 (/.f64 2 (.f64 r r))) (sqrt.f64 (/.f64 2 (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	26.3b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 2 2) 2) (.f64 (.f64 (.f64 r r) (.f64 r r)) (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	14.7b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (sqrt.f64 (fma.f64 (.f64 w (.f64 r r)) (.f64 (/.f64 w (-.f64 1 v)) (fma.f64 v -1/4 3/8)) 3/2)) (sqrt.f64 (fma.f64 (.f64 w (.f64 r r)) (.f64 (/.f64 w (-.f64 1 v)) (fma.f64 v -1/4 3/8)) 3/2))))
▶	2.8b	(-.f64 (/.f64 (/.f64 2 r) r) (fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	29.1b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (.f64 w w) (.f64 (*.f64 r r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))))
	3.6b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 (.f64 (.f64 r w) w) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))) (/.f64 (fma.f64 v -1/4 3/8) (cbrt.f64 (-.f64 1 v)))) 3/2))
	9.1b	(-.f64 (/.f64 (sqrt.f64 2) (/.f64 (.f64 r r) (sqrt.f64 2))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	21.2b	(-.f64 (/.f64 2 (.f64 r r)) (cbrt.f64 (.f64 (.f64 (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
	8.9b	(-.f64 (/.f64 2 (.f64 r r)) (+.f64 (.f64 (.f64 (.f64 w w) r) (*.f64 (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)) r)) 3/2))

Compiler

Compiled 7271 to 4412 computations (39.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
	0.2b	(.f64 (.f64 r w) w)
✓	0.2b	(/.f64 (/.f64 2 r) r)
	2.4b	(fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(/.f64 (/.f64 2 r) r)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 72

Calls

1 calls:

4.0ms

(/.f64 (/.f64 2 r) r)

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

508×	`associate-/r/_binary64`
476×	`*-commutative_binary64`
393×	`associate-*r/_binary64`
346×	`distribute-rgt-in_binary64`
345×	`fma-neg_binary64`

Counts

84 → 113

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	141	1388
1	293	1287
2	541	1206
3	1200	1182
4	2176	1177
5	3375	1127
6	4799	1097
7	4968	1097
8	4852	1097

prune443.0ms (4.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	275	3	278
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	278	13	291

Error

0.0b

Counts

291 → 13

Alt Table

Status	Error	Program
	33.4b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 (.f64 (sqrt.f64 r) w) (*.f64 (sqrt.f64 r) w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	8.0b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (/.f64 (.f64 (.f64 r w) (.f64 w (fma.f64 v -1/4 3/8))) (-.f64 1 v)) 3/2))
	9.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 2 (.f64 r r))) (cbrt.f64 (/.f64 2 (.f64 r r)))) (cbrt.f64 (/.f64 2 (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	15.2b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 r w) (cbrt.f64 (.f64 (.f64 (.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) (.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) (.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))))) 3/2))
	26.3b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 2 2) 2) (.f64 (.f64 (.f64 r r) (.f64 r r)) (.f64 r r)))) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	14.7b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (sqrt.f64 (fma.f64 (.f64 w (.f64 r r)) (.f64 (/.f64 w (-.f64 1 v)) (fma.f64 v -1/4 3/8)) 3/2)) (sqrt.f64 (fma.f64 (.f64 w (.f64 r r)) (.f64 (/.f64 w (-.f64 1 v)) (fma.f64 v -1/4 3/8)) 3/2))))
	2.9b	(-.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (.f64 r r))) (fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	2.8b	(-.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 2 r) r)) (sqrt.f64 (/.f64 (/.f64 2 r) r))) (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	23.1b	(-.f64 (/.f64 (/.f64 2 r) r) 3/2)
	29.1b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (.f64 w w) (.f64 (*.f64 r r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))))
	3.6b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 (.f64 (.f64 (.f64 r w) w) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))) (/.f64 (fma.f64 v -1/4 3/8) (cbrt.f64 (-.f64 1 v)))) 3/2))
	21.2b	(-.f64 (/.f64 2 (.f64 r r)) (cbrt.f64 (.f64 (.f64 (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
	8.9b	(-.f64 (/.f64 2 (.f64 r r)) (+.f64 (.f64 (.f64 (.f64 w w) r) (*.f64 (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)) r)) 3/2))

Compiler

Compiled 9329 to 5567 computations (40.3% saved)

regimes1.6s (17.9%)

Accuracy

Total 0.5b remaining (88.6%)

Threshold costs 0.5b (88.6%)

Counts

179 → 3

Compiler

Compiled 35062 to 24412 computations (30.4% saved)

bsearch368.0ms (4.1%)

Steps

Iters	Range		Point
10	1.2171352817644592e+125	3.234075128320804e+139	7.389519611649986e+131
9	-4.452052919406759e+219	-2.547153057922464e+212	-2.5867080588929657e+212

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	171
1	49	171
2	61	171
3	69	171
4	73	171
5	72	171

end373.0ms (4.1%)

Compiler: Compiled 699 to 456 computations (34.8% saved)

Details

analyze1.5s (16.5%)

sample2.4s (26.4%)

simplify42.0ms (0.5%)

prune5.0ms (0.1%)

localize15.0ms (0.2%)

series104.0ms (1.2%)

rewrite25.0ms (0.3%)

simplify151.0ms (1.7%)

prune275.0ms (3.1%)

localize13.0ms (0.1%)

series102.0ms (1.1%)

rewrite21.0ms (0.2%)

simplify362.0ms (4%)

prune425.0ms (4.7%)

localize14.0ms (0.2%)

series148.0ms (1.6%)

rewrite25.0ms (0.3%)

simplify126.0ms (1.4%)

prune345.0ms (3.8%)

localize15.0ms (0.2%)

series2.0ms (0%)

rewrite9.0ms (0.1%)

simplify115.0ms (1.3%)

prune443.0ms (4.9%)

regimes1.6s (17.9%)

bsearch368.0ms (4.1%)

simplify6.0ms (0.1%)

end373.0ms (4.1%)

Profiling