Details

Time bar (total: 11.3s)

analyze665.0ms (5.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
25%74.9%0.1%4
37.4%62.4%0.1%5
37.4%62.4%0.1%6
56.2%43.7%0.1%7
65.5%34.3%0.1%8
65.5%34.3%0.1%9
76.5%23.4%0.1%10
81.9%17.9%0.1%11
81.9%17.9%0.1%12
87.8%12.1%0.1%13
90.7%9.2%0.1%14
Compiler

Compiled 33 to 25 computations (24.2% saved)

sample2.4s (20.8%)

Results
2.2s8256×body128valid
Compiler

Compiled 98 to 74 computations (24.5% saved)

simplify84.0ms (0.7%)

Algorithm
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)

IterNodesCost
02343
15943
216337
360735
4274433
5474833
6493833

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
5.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.1b
(-.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)
5.5b
(-.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)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
0.3b
(/.f64 2 (*.f64 r r))
1.9b
(fma.f64 r (*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
4.7b
(*.f64 r (*.f64 w w))

series358.0ms (3.2%)

Counts
4 → 108
Calls

4 calls:

224.0ms
(*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
112.0ms
(fma.f64 r (*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
16.0ms
(*.f64 r (*.f64 w w))
5.0ms
(/.f64 2 (*.f64 r r))

rewrite37.0ms (0.3%)

Algorithm
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:

17.0ms
(*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
5.0ms
(*.f64 r (*.f64 w w))
5.0ms
(/.f64 2 (*.f64 r r))
1.0ms
(fma.f64 r (*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

simplify287.0ms (2.5%)

Algorithm
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)

IterNodesCost
02665076
17124298
226704167
347814167
449744167
549624167

prune731.0ms (6.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1888196
Fresh101
Picked101
Done000
Total1908198
Error
0.5b
Counts
198 → 8
Alt Table
StatusErrorProgram
5.5b
(-.f64 (/.f64 2 (*.f64 r r)) (fma.f64 r (*.f64 (*.f64 (*.f64 r (*.f64 w w)) (sqrt.f64 (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) (sqrt.f64 (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2))
2.1b
(-.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))
5.6b
(-.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))))
5.5b
(-.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))
5.9b
(-.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))
21.6b
(-.f64 (/.f64 2 (*.f64 r r)) (*.f64 (-.f64 (*.f64 3/8 (/.f64 (pow.f64 w 2) (-.f64 1 v))) (*.f64 1/4 (/.f64 (*.f64 v (pow.f64 w 2)) (-.f64 1 v)))) (pow.f64 r 2)))
25.8b
(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
5.5b
(-.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))
Compiler

Compiled 6626 to 3827 computations (42.2% saved)

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
0.1b
(*.f64 (*.f64 r w) w)
0.3b
(/.f64 2 (*.f64 r r))
1.9b
(fma.f64 r (*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

series223.0ms (2%)

Counts
3 → 96
Calls

3 calls:

135.0ms
(fma.f64 r (*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
73.0ms
(*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
15.0ms
(*.f64 (*.f64 r w) w)

rewrite36.0ms (0.3%)

Algorithm
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:

19.0ms
(*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
9.0ms
(*.f64 (*.f64 r w) w)
1.0ms
(fma.f64 r (*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

simplify293.0ms (2.6%)

Algorithm
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)

IterNodesCost
02274716
16603983
229253947
346793943
449703943

prune629.0ms (5.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1913194
Fresh347
Picked011
Done000
Total1948202
Error
0.5b
Counts
202 → 8
Alt Table
StatusErrorProgram
2.2b
(-.f64 (/.f64 2 (*.f64 r r)) (fma.f64 r (*.f64 (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 w) (cbrt.f64 w))) (cbrt.f64 w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
2.2b
(-.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))))
15.9b
(-.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)))))
5.5b
(-.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))
2.1b
(-.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))
5.9b
(-.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))
25.8b
(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
5.5b
(-.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))
Compiler

Compiled 6535 to 3763 computations (42.4% saved)

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 2 (*.f64 r r))
0.5b
(*.f64 (cbrt.f64 w) (cbrt.f64 w))
0.6b
(cbrt.f64 w)
1.9b
(fma.f64 r (*.f64 (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 w) (cbrt.f64 w))) (cbrt.f64 w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

series283.0ms (2.5%)

Counts
3 → 60
Calls

3 calls:

135.0ms
(fma.f64 r (*.f64 (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 w) (cbrt.f64 w))) (cbrt.f64 w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
75.0ms
(*.f64 (cbrt.f64 w) (cbrt.f64 w))
73.0ms
(cbrt.f64 w)

rewrite18.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
19×cbrt-prod_binary64
12×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
10×pow1_binary64
Counts
3 → 65
Calls

3 calls:

10.0ms
(*.f64 (cbrt.f64 w) (cbrt.f64 w))
1.0ms
(cbrt.f64 w)
1.0ms
(fma.f64 r (*.f64 (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 w) (cbrt.f64 w))) (cbrt.f64 w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

simplify588.0ms (5.2%)

Algorithm
egg-herbie
Rules
577×associate-/l*_binary64
520×times-frac_binary64
418×fma-def_binary64
227×unswap-sqr_binary64
202×div-sub_binary64
Counts
125 → 117
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01352514
13362271
212752039
343192024
449502024
549732024

prune613.0ms (5.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1820182
Fresh066
Picked011
Done011
Total1828190
Error
0.5b
Counts
190 → 8
Alt Table
StatusErrorProgram
2.2b
(-.f64 (/.f64 2 (*.f64 r r)) (fma.f64 r (*.f64 (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 w) (cbrt.f64 w))) (cbrt.f64 w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
2.2b
(-.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))))
15.9b
(-.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)))))
5.5b
(-.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))
2.1b
(-.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))
5.9b
(-.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))
25.8b
(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
5.5b
(-.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))
Compiler

Compiled 6633 to 3351 computations (49.5% saved)

localize109.0ms (1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 2 (*.f64 r r))
0.6b
(*.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)))
1.9b
(fma.f64 r (*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
9.4b
(sqrt.f64 (fma.f64 r (*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))

series427.0ms (3.8%)

Counts
2 → 72
Calls

2 calls:

257.0ms
(sqrt.f64 (fma.f64 r (*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
169.0ms
(*.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)))

rewrite30.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
21×sqrt-prod_binary64
18×pow1_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
Counts
2 → 68
Calls

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

simplify295.0ms (2.6%)

Algorithm
egg-herbie
Rules
604×cancel-sign-sub-inv_binary64
299×associate-*r*_binary64
280×fma-neg_binary64
204×fma-def_binary64
202×times-frac_binary64
Counts
140 → 164
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03128197
19537400
239247262
355377262

prune1.7s (14.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New3530353
Fresh055
Picked011
Done022
Total3538361
Error
0.5b
Counts
361 → 8
Alt Table
StatusErrorProgram
2.2b
(-.f64 (/.f64 2 (*.f64 r r)) (fma.f64 r (*.f64 (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 w) (cbrt.f64 w))) (cbrt.f64 w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
2.2b
(-.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))))
15.9b
(-.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)))))
5.5b
(-.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))
2.1b
(-.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))
5.9b
(-.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))
25.8b
(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
5.5b
(-.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))
Compiler

Compiled 23515 to 14559 computations (38.1% saved)

regimes1.2s (10.8%)

Accuracy

Total 0.3b remaining (23.9%)

Threshold costs 0.3b (23.9%)

Counts
93 → 3
Compiler

Compiled 19110 to 13169 computations (31.1% saved)

bsearch74.0ms (0.6%)

Steps
ItersRangePoint
5
2.380603161814143e-119
5.33648258777566e-119
2.4253524215214347e-119
7
-2.269071215292617e-98
-7.526537777856986e-100
-7.614131752839713e-100
Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02757
14257
25057
35457
45657
55457

end203.0ms (1.8%)

Compiler

Compiled 303 to 206 computations (32% saved)

Profiling

Loading profile data...