Details

Time bar (total: 5.4s)

analyze173.0ms (3.2%)

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
0%99.9%0.1%4
25%74.9%0.1%5
25%68.7%6.3%6
25%56.2%18.8%7
25%48.4%26.6%8
25%35.1%39.9%9
28.1%18.3%53.6%10
31.6%12.3%56.1%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 34 to 22 computations (35.3% saved)

sample80.0ms (1.5%)

Algorithm
intervals
Results
24.0ms256×body128valid
Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify58.0ms (1.1%)

Algorithm
egg-herbie
Rules
725×fma-def_binary64
669×unsub-neg_binary64
596×cancel-sign-sub-inv_binary64
340×+-commutative_binary64
277×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02042
16340
217036
354236
4186732
5328132
6488132
7495832

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
0.2b
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
Compiler

Compiled 172 to 108 computations (37.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a -3 1)
0.0b
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.1b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
0.3b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series61.0ms (1.1%)

Counts
4 → 84
Calls

4 calls:

36.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
13.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
9.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
2.0ms
(fma.f64 a -3 1)

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
add-sqr-sqrt_binary64
fma-udef_binary64
Counts
4 → 53
Calls

4 calls:

5.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
0.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
0.0ms
(fma.f64 a -3 1)
0.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))

simplify106.0ms (1.9%)

Algorithm
egg-herbie
Rules
786×fma-def_binary64
528×fma-neg_binary64
415×associate-+l+_binary64
313×cancel-sign-sub-inv_binary64
229×associate-+r+_binary64
Counts
137 → 125
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01252754
13182352
29692192
331842169
448182143
549832143

prune176.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1232125
Fresh011
Picked011
Done000
Total1234127
Error
0.0b
Counts
127 → 4
Alt Table
StatusErrorProgram
0.2b
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
10.5b
(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1)
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
0.5b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
Compiler

Compiled 3712 to 2071 computations (44.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))
0.1b
(*.f64 (*.f64 a a) (+.f64 1 a))
0.3b
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

series56.0ms (1%)

Counts
4 → 84
Calls

4 calls:

30.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))
14.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
9.0ms
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
3.0ms
(*.f64 (*.f64 a a) (+.f64 1 a))

rewrite32.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
15×add-exp-log_binary64
15×pow1_binary64
14×add-cbrt-cube_binary64
14×*-un-lft-identity_binary64
14×add-sqr-sqrt_binary64
Counts
4 → 102
Calls

4 calls:

10.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))
6.0ms
(*.f64 (*.f64 a a) (+.f64 1 a))
6.0ms
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
4.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

simplify89.0ms (1.6%)

Algorithm
egg-herbie
Rules
870×distribute-rgt-in_binary64
807×distribute-lft-in_binary64
278×cancel-sign-sub-inv_binary64
257×associate-*l*_binary64
213×associate-*r*_binary64
Counts
186 → 195
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02093661
15773211
219973007
358193007

prune268.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1950195
Fresh022
Picked011
Done011
Total1954199
Error
0.0b
Counts
199 → 4
Alt Table
StatusErrorProgram
0.2b
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
10.5b
(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1)
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
0.5b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
Compiler

Compiled 7461 to 4237 computations (43.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))
0.3b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
0.5b
(*.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))
8.4b
(cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))

series620.0ms (11.4%)

Counts
3 → 72
Calls

3 calls:

417.0ms
(*.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))
163.0ms
(cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))
39.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))

rewrite25.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
24×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
16×pow1/3_binary64
14×*-un-lft-identity_binary64
Counts
3 → 93
Calls

3 calls:

7.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))
5.0ms
(*.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))
1.0ms
(cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))

simplify252.0ms (4.6%)

Algorithm
egg-herbie
Rules
507×associate-+l+_binary64
310×*-commutative_binary64
201×+-commutative_binary64
185×associate--l+_binary64
181×fma-def_binary64
Counts
165 → 192
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
078213856
1247012464
2495712460
3505012460

prune989.0ms (18.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New4010401
Fresh011
Picked011
Done022
Total4014405
Error
0.0b
Counts
405 → 4
Alt Table
StatusErrorProgram
0.2b
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
10.5b
(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1)
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
0.5b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
Compiler

Compiled 41975 to 25608 computations (39% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))
0.0b
(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1)
1.7b
(*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b)))))

series68.0ms (1.2%)

Counts
3 → 72
Calls

3 calls:

34.0ms
(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1)
23.0ms
(*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b)))))
11.0ms
(+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))

rewrite34.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
14×associate-*r/_binary64
11×flip-+_binary64
11×flip3-+_binary64
10×add-log-exp_binary64
frac-add_binary64
Counts
3 → 67
Calls

3 calls:

11.0ms
(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1)
10.0ms
(*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b)))))
8.0ms
(+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))

simplify132.0ms (2.4%)

Algorithm
egg-herbie
Rules
496×associate-+l+_binary64
279×associate-*l*_binary64
247×associate-*r*_binary64
226×fma-neg_binary64
214×distribute-rgt-in_binary64
Counts
139 → 147
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01683831
15982999
224752965
349452965
449952965
549382965

prune225.0ms (4.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1461147
Fresh000
Picked101
Done033
Total1474151
Error
0.0b
Counts
151 → 4
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
0.5b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
10.5b
(fma.f64 a (*.f64 a (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4))) -1)
0.2b
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
Compiler

Compiled 4638 to 2872 computations (38.1% saved)

regimes857.0ms (15.8%)

Accuracy

Total 0.0b remaining (57.8%)

Threshold costs 0.0b (57.8%)

Counts
137 → 1
Compiler

Compiled 20230 to 13340 computations (34.1% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01632
12032
21932

end1.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

sample1.1s (19.5%)

Algorithm
intervals
Results
725.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 209 to 128 computations (38.8% saved)

Profiling

Loading profile data...