Details

analyze1.4s (12.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	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)

sample2.5s (22.4%)

Results

1.5s	8256×	body	128	valid
905.0ms	5038×	body	128	invalid

Compiler

Compiled 98 to 74 computations (24.5% saved)

simplify48.0ms (0.4%)

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%)

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

7.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.0b	(-.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)
▶	7.7b	(-.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

13.0b

(-.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)

▶

7.7b

(-.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)

localize16.0ms (0.1%)

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)))
✓	0.5b	(/.f64 2 (*.f64 r r))
✓	1.4b	(fma.f64 r (.f64 (.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
✓	11.2b	(.f64 r (.f64 w w))

series108.0ms (1%)

Counts

4 → 108

Calls

4 calls:

52.0ms	(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)))
8.0ms	(/.f64 2 (*.f64 r r))
8.0ms	(.f64 r (.f64 w w))

rewrite26.0ms (0.2%)

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:

11.0ms	(.f64 (.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
4.0ms	(.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)

simplify161.0ms (1.4%)

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

prune303.0ms (2.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	185	11	196
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	187	11	198

Error

0.5b

Counts

198 → 11

Alt Table

Status	Error	Program
	7.9b	(-.f64 (.f64 (/.f64 (sqrt.f64 2) r) (/.f64 (sqrt.f64 2) r)) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	12.2b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (/.f64 (.f64 (-.f64 (.f64 3/8 (pow.f64 w 2)) (.f64 1/4 (*.f64 v (pow.f64 w 2)))) r) (-.f64 1 v)) 3/2))
▶	1.7b	(-.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))
	32.0b	(-.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)))
	7.7b	(-.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))
	7.9b	(-.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))
	20.6b	(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
	8.0b	(-.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))
	8.0b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (sqrt.f64 (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 r (.f64 w (.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))))) 3/2))
	13.2b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (/.f64 (.f64 w (.f64 w (.f64 r (fma.f64 v -1/4 3/8)))) (-.f64 1 v)) 3/2))

Compiler

Compiled 6814 to 3959 computations (41.9% saved)

localize16.0ms (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)
	0.5b	(/.f64 2 (*.f64 r r))
✓	1.4b	(fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

series100.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

51.0ms	(fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
40.0ms	(.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
9.0ms	(.f64 (.f64 r w) w)

rewrite22.0ms (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)

simplify129.0ms (1.2%)

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

prune332.0ms (3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	192	13	205

Error

0.5b

Counts

205 → 13

Alt Table

Status	Error	Program
	7.9b	(-.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))
	21.7b	(-.f64 (/.f64 2 (.f64 r r)) (-.f64 (fma.f64 3/8 (/.f64 (.f64 (.f64 w w) (.f64 r r)) (-.f64 1 v)) 3/2) (.f64 1/4 (/.f64 (.f64 (.f64 (.f64 w w) (*.f64 r r)) v) (-.f64 1 v)))))
	7.9b	(-.f64 (.f64 (/.f64 (sqrt.f64 2) r) (/.f64 (sqrt.f64 2) r)) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	12.2b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (/.f64 (.f64 (-.f64 (.f64 3/8 (pow.f64 w 2)) (.f64 1/4 (*.f64 v (pow.f64 w 2)))) r) (-.f64 1 v)) 3/2))
	6.2b	(-.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))
	7.7b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (.f64 r (.f64 w (.f64 w (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))))) 3/2))
	3.6b	(-.f64 (/.f64 2 (.f64 r r)) (expm1.f64 (log1p.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
✓	1.7b	(-.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))
	7.7b	(-.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))
	20.6b	(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
	8.0b	(-.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))
▶	2.0b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
	13.2b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (/.f64 (.f64 w (.f64 w (.f64 r (fma.f64 v -1/4 3/8)))) (-.f64 1 v)) 3/2))

Compiler

Compiled 6867 to 3995 computations (41.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 r w) w)
	0.5b	(/.f64 2 (*.f64 r r))
✓	0.8b	(.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (sqrt.f64 (fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)))
	1.4b	(fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

series53.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

53.0ms

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

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
16×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 53

Calls

1 calls:

5.0ms

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

simplify234.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

615×	`associate-l_binary64`
553×	`fma-neg_binary64`
510×	`associate-r_binary64`
411×	`fma-def_binary64`
204×	`associate-/l*_binary64`

Counts

89 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	3474
1	291	3052
2	984	2732
3	4271	2656
4	5202	2656

prune680.0ms (6.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	256	2	258
Fresh	3	8	11
Picked	0	1	1
Done	1	0	1
Total	260	11	271

Error

0.5b

Counts

271 → 11

Alt Table

Status	Error	Program
	2.9b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 w (.f64 w r)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))) 5) (cbrt.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)))))
	20.6b	(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
	7.9b	(-.f64 (.f64 (/.f64 (sqrt.f64 2) r) (/.f64 (sqrt.f64 2) r)) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	6.2b	(-.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))
	7.7b	(-.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))
	7.9b	(-.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))
	8.0b	(-.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))
▶	2.3b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (sqrt.f64 (.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))))))
✓	2.0b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
	3.6b	(-.f64 (/.f64 2 (.f64 r r)) (expm1.f64 (log1p.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
	13.2b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (/.f64 (.f64 w (.f64 w (.f64 r (fma.f64 v -1/4 3/8)))) (-.f64 1 v)) 3/2))

Compiler

Compiled 13218 to 7622 computations (42.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (sqrt.f64 (.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)))))
✓	0.8b	(cbrt.f64 (fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
✓	0.8b	(.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)))
	1.4b	(fma.f64 r (.f64 (.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

series1.1s (9.9%)

Counts

3 → 108

Calls

3 calls:

802.0ms

(*.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)))

240.0ms

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

59.0ms

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

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
23×	`pow1_binary64`
19×	`cbrt-prod_binary64`
19×	`pow1/3_binary64`
16×	`add-cube-cbrt_binary64`

Counts

3 → 90

Calls

3 calls:

12.0ms

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

4.0ms

(*.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)))

1.0ms

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

simplify341.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-def_binary64`
348×	`*-commutative_binary64`
199×	`+-commutative_binary64`
176×	`cancel-sign-sub-inv_binary64`
156×	`associate-r_binary64`

Counts

198 → 278

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	949	26976
1	3295	25496
2	5007	25496

prune2.0s (17.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	608	0	608
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	608	11	619

Error

0.5b

Counts

619 → 11

Alt Table

Status	Error	Program
	2.9b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 w (.f64 w r)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))) 5) (cbrt.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)))))
	20.6b	(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
	7.9b	(-.f64 (.f64 (/.f64 (sqrt.f64 2) r) (/.f64 (sqrt.f64 2) r)) (fma.f64 r (.f64 (.f64 r (.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
	6.2b	(-.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))
	7.7b	(-.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))
	7.9b	(-.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))
	8.0b	(-.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))
✓	2.3b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (sqrt.f64 (.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))))))
✓	2.0b	(-.f64 (/.f64 2 (.f64 r r)) (.f64 (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)) (sqrt.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
	3.6b	(-.f64 (/.f64 2 (.f64 r r)) (expm1.f64 (log1p.f64 (fma.f64 r (.f64 (.f64 (.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))))
	13.2b	(-.f64 (/.f64 2 (.f64 r r)) (fma.f64 r (/.f64 (.f64 w (.f64 w (.f64 r (fma.f64 v -1/4 3/8)))) (-.f64 1 v)) 3/2))

Compiler

Compiled 85725 to 55015 computations (35.8% saved)

regimes1.3s (11.2%)

Accuracy

Total 0.8b remaining (34.7%)

Threshold costs 0.8b (34.7%)

Counts

143 → 1

Compiler

Compiled 32652 to 22148 computations (32.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	33
1	28	33
2	35	33
3	39	33
4	41	33
5	40	33

end267.0ms (2.4%)

Compiler: Compiled 450 to 308 computations (31.6% saved)

Details

analyze1.4s (12.4%)

sample2.5s (22.4%)

simplify48.0ms (0.4%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series108.0ms (1%)

rewrite26.0ms (0.2%)

simplify161.0ms (1.4%)

prune303.0ms (2.7%)

localize16.0ms (0.1%)

series100.0ms (0.9%)

rewrite22.0ms (0.2%)

simplify129.0ms (1.2%)

prune332.0ms (3%)

localize16.0ms (0.1%)

series53.0ms (0.5%)

rewrite13.0ms (0.1%)

simplify234.0ms (2.1%)

prune680.0ms (6.1%)

localize22.0ms (0.2%)

series1.1s (9.9%)

rewrite30.0ms (0.3%)

simplify341.0ms (3.1%)

prune2.0s (17.9%)

regimes1.3s (11.2%)

simplify3.0ms (0%)

end267.0ms (2.4%)

Profiling