Details

Time bar (total: 4.4s)

analyze167.0ms (3.8%)

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%53.1%22%7
25%46.8%28.2%8
25%33.6%41.5%9
28.1%18%54%10
31.6%12.1%56.3%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 32 to 20 computations (37.5% saved)

sample102.0ms (2.3%)

Algorithm
intervals
Results
21.0ms256×body128valid
0.0msbody128invalid
Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify60.0ms (1.3%)

Algorithm
egg-herbie
Rules
620×fma-def_binary64
556×cancel-sign-sub-inv_binary64
552×unswap-sqr_binary64
357×unsub-neg_binary64
344×+-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01939
15737
216837
349237
4160433
5289133
6430933
7521433

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 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -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 3 a))))) 1)
Compiler

Compiled 166 to 104 computations (37.3% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.0b
(pow.f64 (hypot.f64 a b) 4)
0.1b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
1.3b
(*.f64 (*.f64 b b) (+.f64 a 3))

series102.0ms (2.3%)

Counts
4 → 96
Calls

4 calls:

42.0ms
(pow.f64 (hypot.f64 a b) 4)
40.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
11.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))

rewrite18.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-exp-log_binary64
10×pow1_binary64
add-cube-cbrt_binary64
Counts
4 → 78
Calls

4 calls:

9.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))
4.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
2.0ms
(pow.f64 (hypot.f64 a b) 4)
0.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))

simplify89.0ms (2%)

Algorithm
egg-herbie
Rules
574×associate-+l+_binary64
469×distribute-rgt-in_binary64
453×distribute-lft-in_binary64
338×associate--l+_binary64
219×cancel-sign-sub-inv_binary64
Counts
174 → 162
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01743413
14643143
215563045
350743045

prune240.0ms (5.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1584162
Fresh101
Picked011
Done000
Total1595164
Error
0b
Counts
164 → 5
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
11.3b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (*.f64 a (+.f64 4 (*.f64 2 a))) 12)) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
0.2b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.5b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
12.1b
(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
Compiler

Compiled 5053 to 2958 computations (41.5% 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) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.1b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
0.4b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
1.3b
(*.f64 (*.f64 b b) (+.f64 a 3))

series47.0ms (1.1%)

Counts
2 → 48
Calls

2 calls:

34.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
13.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

rewrite13.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
fma-def_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
unpow-prod-down_binary64
add-cube-cbrt_binary64
Counts
2 → 43
Calls

2 calls:

7.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
4.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

simplify96.0ms (2.2%)

Algorithm
egg-herbie
Rules
833×fma-neg_binary64
753×fma-def_binary64
561×associate-+l+_binary64
335×associate--l+_binary64
227×distribute-rgt-in_binary64
Counts
91 → 96
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01112281
13192122
29741866
347011852
454091852

prune244.0ms (5.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1690169
Fresh033
Picked011
Done011
Total1695174
Error
0b
Counts
174 → 5
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
11.3b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (*.f64 a (+.f64 4 (*.f64 2 a))) 12)) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
0.2b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.5b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
12.1b
(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
Compiler

Compiled 5781 to 3033 computations (47.5% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
0.4b
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
1.3b
(*.f64 (*.f64 b b) (+.f64 a 3))
17.4b
(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

series156.0ms (3.5%)

Counts
3 → 72
Calls

3 calls:

64.0ms
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
51.0ms
(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))
40.0ms
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))

rewrite32.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
69×cbrt-prod_binary64
47×add-sqr-sqrt_binary64
29×pow1_binary64
27×unpow-prod-down_binary64
20×associate-*r*_binary64
Counts
3 → 127
Calls

3 calls:

11.0ms
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
8.0ms
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
1.0ms
(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

simplify191.0ms (4.3%)

Algorithm
egg-herbie
Rules
475×fma-neg_binary64
388×fma-def_binary64
356×cancel-sign-sub-inv_binary64
346×*-commutative_binary64
305×sqr-pow_binary64
Counts
199 → 198
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02024349
14524264
212863883
325093825
437313345
548063345
649873345
749063345

prune466.0ms (10.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New3170317
Fresh022
Picked011
Done022
Total3175322
Error
0b
Counts
322 → 5
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
11.3b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (*.f64 a (+.f64 4 (*.f64 2 a))) 12)) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
0.2b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.5b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
12.1b
(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
Compiler

Compiled 14656 to 8667 computations (40.9% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
0.0b
(*.f64 a (+.f64 4 (*.f64 2 a)))
0.1b
(*.f64 (pow.f64 a 3) (-.f64 a 4))
1.7b
(*.f64 (*.f64 b b) (+.f64 (*.f64 a (+.f64 4 (*.f64 2 a))) 12))

series29.0ms (0.7%)

Counts
4 → 60
Calls

4 calls:

20.0ms
(*.f64 (*.f64 b b) (+.f64 (*.f64 a (+.f64 4 (*.f64 2 a))) 12))
3.0ms
(*.f64 (pow.f64 a 3) (-.f64 a 4))
3.0ms
(fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
3.0ms
(*.f64 a (+.f64 4 (*.f64 2 a)))

rewrite33.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
25×add-cube-cbrt_binary64
18×prod-diff_binary64
16×associate-*l*_binary64
Counts
4 → 122
Calls

4 calls:

13.0ms
(*.f64 (*.f64 b b) (+.f64 (*.f64 a (+.f64 4 (*.f64 2 a))) 12))
8.0ms
(*.f64 (pow.f64 a 3) (-.f64 a 4))
5.0ms
(*.f64 a (+.f64 4 (*.f64 2 a)))
0.0ms
(fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

simplify123.0ms (2.8%)

Algorithm
egg-herbie
Rules
670×fma-neg_binary64
649×exp-prod_binary64
401×associate-*l*_binary64
342×associate-*r*_binary64
210×log-prod_binary64
Counts
182 → 208
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02413003
15362361
222222357
340092318
447952318
550422318

prune280.0ms (6.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New2080208
Fresh011
Picked011
Done033
Total2085213
Error
0b
Counts
213 → 5
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
11.3b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (*.f64 a (+.f64 4 (*.f64 2 a))) 12)) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
0.2b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.5b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
12.1b
(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
Compiler

Compiled 7557 to 5099 computations (32.5% saved)

regimes810.0ms (18.3%)

Accuracy

Total 0.0b remaining (64.4%)

Threshold costs 0.0b (64.4%)

Counts
123 → 1
Compiler

Compiled 18405 to 12707 computations (31% saved)

simplify3.0ms (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
01733
12433
22733
32933
43033
52933

end1.0ms (0%)

Compiler

Compiled 25 to 17 computations (32% saved)

sample1.1s (23.7%)

Algorithm
intervals
Results
717.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 195 to 130 computations (33.3% saved)

Profiling

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