Details

Time bar (total: 5.4s)

analyze310.0ms (5.8%)

Algorithm
1×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)

sample1.3s (23.6%)

Infinites
52.3% of outputs are infinite.
Results
1.2s8256×body128valid
Compiler

Compiled 98 to 74 computations (24.5% saved)

simplify43.0ms (0.8%)

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)

IterNodesCost
02343
15943
216337
360735
4274433
5474833
6493833

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
9.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶9.3b
(-.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 107 to 73 computations (31.8% saved)

localize15.0ms (0.3%)

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)))
✓0.6b
(/.f64 2 (*.f64 r r))
✓3.1b
(fma.f64 r (*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
✓8.1b
(*.f64 r (*.f64 w w))

series195.0ms (3.6%)

Counts
4 → 108
Calls

4 calls:

132.0ms
(*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
50.0ms
(fma.f64 r (*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)
10.0ms
(*.f64 r (*.f64 w w))
2.0ms
(/.f64 2 (*.f64 r r))

rewrite25.0ms (0.5%)

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)

simplify147.0ms (2.7%)

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)

IterNodesCost
02665076
17124298
226704167
347814167
449744167
549624167

prune263.0ms (4.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1879196
Fresh000
Picked101
Done000
Total1889197
Error
0.7b
Counts
197 → 9
Alt Table
StatusErrorProgram
27.3b
(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
16.5b
(-.f64 (/.f64 2 (*.f64 r r)) (fma.f64 (*.f64 (*.f64 w w) (*.f64 r r)) 1/4 3/2))
9.4b
(-.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))
9.4b
(-.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))
17.9b
(-.f64 (cbrt.f64 (/.f64 8 (pow.f64 r 6))) (fma.f64 r (*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
9.5b
(-.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))))
16.5b
(-.f64 (/.f64 2 (*.f64 r r)) (+.f64 3/2 (*.f64 3/8 (*.f64 (pow.f64 w 2) (pow.f64 r 2)))))
▶3.3b
(-.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))
7.4b
(-.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 6630 to 3825 computations (42.3% saved)

localize13.0ms (0.2%)

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)
0.6b
(/.f64 2 (*.f64 r r))
✓3.1b
(fma.f64 r (*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2)

series97.0ms (1.8%)

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)
38.0ms
(*.f64 (*.f64 (*.f64 r w) w) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
8.0ms
(*.f64 (*.f64 r w) w)

rewrite21.0ms (0.4%)

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:

9.0ms
(*.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)

simplify185.0ms (3.4%)

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)

IterNodesCost
02274716
16603983
229253947
346793943
449703943

prune400.0ms (7.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1922194
Fresh088
Picked011
Done000
Total19211203
Error
0.7b
Counts
203 → 11
Alt Table
StatusErrorProgram
3.5b
(-.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))
9.4b
(-.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))
27.3b
(-.f64 (/.f64 2 (*.f64 r r)) 3/2)
16.5b
(-.f64 (/.f64 2 (*.f64 r r)) (fma.f64 (*.f64 (*.f64 w w) (*.f64 r r)) 1/4 3/2))
▶3.3b
(-.f64 (/.f64 2 (*.f64 r r)) (fma.f64 r (*.f64 w (*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2))
9.4b
(-.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))
17.9b
(-.f64 (cbrt.f64 (/.f64 8 (pow.f64 r 6))) (fma.f64 r (*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
9.5b
(-.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))))
16.5b
(-.f64 (/.f64 2 (*.f64 r r)) (+.f64 3/2 (*.f64 3/8 (*.f64 (pow.f64 w 2) (pow.f64 r 2)))))
✓3.3b
(-.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))
7.4b
(-.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 6683 to 3871 computations (42.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
✓0.1b
(*.f64 w (*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))))
0.6b
(/.f64 2 (*.f64 r r))
✓3.1b
(fma.f64 r (*.f64 w (*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2)

series117.0ms (2.2%)

Counts
3 → 108
Calls

3 calls:

50.0ms
(fma.f64 r (*.f64 w (*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2)
41.0ms
(*.f64 w (*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))))
25.0ms
(*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))

rewrite27.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
33×add-cbrt-cube_binary64
33×add-exp-log_binary64
25×associate-*r*_binary64
23×*-un-lft-identity_binary64
23×add-sqr-sqrt_binary64
Counts
3 → 84
Calls

3 calls:

11.0ms
(*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))
8.0ms
(*.f64 w (*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))))
0.0ms
(fma.f64 r (*.f64 w (*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2)

simplify164.0ms (3%)

Algorithm
1×egg-herbie
Rules
727×times-frac_binary64
411×associate-*r*_binary64
399×associate-*l*_binary64
240×fma-neg_binary64
211×*-commutative_binary64
Counts
192 → 177
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02685485
18024667
230594631
348274629
449874629
549654629

prune347.0ms (6.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2051206
Fresh369
Picked011
Done011
Total2089217
Error
0.0b
Counts
217 → 9
Alt Table
StatusErrorProgram
9.4b
(-.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))
✓3.3b
(-.f64 (/.f64 2 (*.f64 r r)) (fma.f64 r (*.f64 w (*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2))
9.4b
(-.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))
17.9b
(-.f64 (cbrt.f64 (/.f64 8 (pow.f64 r 6))) (fma.f64 r (*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
9.5b
(-.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))))
16.5b
(-.f64 (/.f64 2 (*.f64 r r)) (+.f64 3/2 (*.f64 3/8 (*.f64 (pow.f64 w 2) (pow.f64 r 2)))))
✓3.3b
(-.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))
11.1b
(-.f64 (/.f64 2 (*.f64 r r)) (*.f64 w (*.f64 r (*.f64 (/.f64 w (-.f64 1 v)) (*.f64 r (fma.f64 v -1/4 3/8))))))
▶7.4b
(-.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 6933 to 4154 computations (40.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.8b
(*.f64 w (*.f64 w (*.f64 r (fma.f64 v -1/4 3/8))))
✓2.3b
(*.f64 w (*.f64 r (fma.f64 v -1/4 3/8)))
✓3.1b
(/.f64 (*.f64 w (*.f64 w (*.f64 r (fma.f64 v -1/4 3/8)))) (-.f64 1 v))
✓3.1b
(fma.f64 r (/.f64 (*.f64 w (*.f64 w (*.f64 r (fma.f64 v -1/4 3/8)))) (-.f64 1 v)) 3/2)

series182.0ms (3.4%)

Counts
4 → 144
Calls

4 calls:

97.0ms
(fma.f64 r (/.f64 (*.f64 w (*.f64 w (*.f64 r (fma.f64 v -1/4 3/8)))) (-.f64 1 v)) 3/2)
47.0ms
(/.f64 (*.f64 w (*.f64 w (*.f64 r (fma.f64 v -1/4 3/8)))) (-.f64 1 v))
24.0ms
(*.f64 w (*.f64 w (*.f64 r (fma.f64 v -1/4 3/8))))
14.0ms
(*.f64 w (*.f64 r (fma.f64 v -1/4 3/8)))

rewrite25.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
32×add-cbrt-cube_binary64
32×add-exp-log_binary64
18×pow1_binary64
16×distribute-lft-in_binary64
16×distribute-rgt-in_binary64
Counts
4 → 100
Calls

4 calls:

8.0ms
(/.f64 (*.f64 w (*.f64 w (*.f64 r (fma.f64 v -1/4 3/8)))) (-.f64 1 v))
5.0ms
(*.f64 w (*.f64 r (fma.f64 v -1/4 3/8)))
5.0ms
(*.f64 w (*.f64 w (*.f64 r (fma.f64 v -1/4 3/8))))
0.0ms
(fma.f64 r (/.f64 (*.f64 w (*.f64 w (*.f64 r (fma.f64 v -1/4 3/8)))) (-.f64 1 v)) 3/2)

simplify111.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
816×fma-def_binary64
413×distribute-rgt-in_binary64
282×associate-*r*_binary64
248×associate-*l*_binary64
200×cancel-sign-sub-inv_binary64
Counts
244 → 193
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02635944
17045061
224574851
355044851

prune346.0ms (6.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1930193
Fresh066
Picked011
Done022
Total1939202
Error
0.0b
Counts
202 → 9
Alt Table
StatusErrorProgram
9.4b
(-.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))
✓3.3b
(-.f64 (/.f64 2 (*.f64 r r)) (fma.f64 r (*.f64 w (*.f64 (*.f64 w r) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)))) 3/2))
9.4b
(-.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))
17.9b
(-.f64 (cbrt.f64 (/.f64 8 (pow.f64 r 6))) (fma.f64 r (*.f64 (*.f64 r (*.f64 w w)) (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v))) 3/2))
9.5b
(-.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))))
16.5b
(-.f64 (/.f64 2 (*.f64 r r)) (+.f64 3/2 (*.f64 3/8 (*.f64 (pow.f64 w 2) (pow.f64 r 2)))))
✓3.3b
(-.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))
11.1b
(-.f64 (/.f64 2 (*.f64 r r)) (*.f64 w (*.f64 r (*.f64 (/.f64 w (-.f64 1 v)) (*.f64 r (fma.f64 v -1/4 3/8))))))
✓7.4b
(-.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 6096 to 3736 computations (38.7% saved)

regimes820.0ms (15.2%)

Accuracy

Total 0.2b remaining (80.2%)

Threshold costs 0.2b (80.2%)

Counts
49 → 3
Compiler

Compiled 8622 to 5943 computations (31.1% saved)

bsearch18.0ms (0.3%)

Steps
ItersRangePoint
3
132615192575.54477
310437993520361.1
16826817815674.701
3
-4.614222407487272e+211
-9.46233692000858e+188
-6.408408175333973e+191
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03279
15379
26879
38479
410079
511579
612379
712779
812879
912779

end216.0ms (4%)

Compiler

Compiled 370 to 254 computations (31.4% saved)

Profiling

Loading profile data...