Details

Time bar (total: 8.6s)

analyze377.0ms (4.4%)

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)

sample54.0ms (0.6%)

Algorithm
intervals
Results
39.0ms256×body128valid
Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify70.0ms (0.8%)

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

prune9.0ms (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)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (hypot.f64 a b) 4)
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))
0.1b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
0.6b
(*.f64 (*.f64 b b) (+.f64 a 3))

series170.0ms (2%)

Counts
4 → 96
Calls

4 calls:

68.0ms
(+.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))
64.0ms
(pow.f64 (hypot.f64 a b) 4)
21.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
16.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))

rewrite33.0ms (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:

12.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))
8.0ms
(+.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))
3.0ms
(pow.f64 (hypot.f64 a b) 4)
2.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))

simplify147.0ms (1.7%)

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

prune413.0ms (4.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1593162
Fresh011
Picked101
Done000
Total1604164
Error
0.0b
Counts
164 → 4
Alt Table
StatusErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
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)
16.2b
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
19.6b
(cbrt.f64 (*.f64 (*.f64 (+.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)) (+.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))) (+.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))))
Compiler

Compiled 5208 to 3059 computations (41.3% saved)

localize47.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
0.2b
(*.f64 12 (pow.f64 b 2))
0.5b
(*.f64 a (pow.f64 b 2))
2.7b
(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series106.0ms (1.2%)

Counts
4 → 20
Calls

4 calls:

62.0ms
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
22.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))
15.0ms
(*.f64 a (pow.f64 b 2))
6.0ms
(*.f64 12 (pow.f64 b 2))

rewrite153.0ms (1.8%)

Algorithm
rewrite-expression-head
Rules
64×add-log-exp_binary64
52×add-sqr-sqrt_binary64
36×sum-log_binary64
26×add-exp-log_binary64
24×associate-*r*_binary64
Counts
4 → 158
Calls

4 calls:

93.0ms
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
13.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))
8.0ms
(*.f64 12 (pow.f64 b 2))
8.0ms
(*.f64 a (pow.f64 b 2))

simplify296.0ms (3.4%)

Algorithm
egg-herbie
Rules
499×fma-neg_binary64
466×cancel-sign-sub-inv_binary64
280×associate-*l*_binary64
255×associate-*r*_binary64
247×unswap-sqr_binary64
Counts
178 → 252
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03085762
17545158
229555021
349745017
450835017

prune1.1s (12.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New2511252
Fresh123
Picked101
Done000
Total2533256
Error
0b
Counts
256 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 1 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (neg.f64 (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))))))) (fma.f64 (neg.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))))))
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)
16.2b
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
Compiler

Compiled 15490 to 11785 computations (23.9% saved)

localize65.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 12 (pow.f64 b 2))
0.5b
(*.f64 a (pow.f64 b 2))
2.7b
(*.f64 (pow.f64 a 2) (pow.f64 b 2))
16.4b
(fma.f64 (neg.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))))))

series177.0ms (2.1%)

Counts
1 → 12
Calls

1 calls:

177.0ms
(fma.f64 (neg.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))))))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

1.0ms
(fma.f64 (neg.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))))))

simplify110.0ms (1.3%)

Algorithm
egg-herbie
Rules
980×fma-neg_binary64
659×cancel-sign-sub-inv_binary64
464×distribute-rgt-in_binary64
277×exp-prod_binary64
240×distribute-rgt-neg-in_binary64
Counts
22 → 28
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
065749
1170645
2519514
32097294
44412279
54915279
64888279

prune1.4s (16.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1890189
Fresh022
Picked011
Done000
Total1893192
Error
0b
Counts
192 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 1 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (neg.f64 (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))))))) (fma.f64 (neg.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))))))
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)
16.2b
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
Compiler

Compiled 23594 to 19894 computations (15.7% saved)

localize29.0ms (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 3 a)))))
0.1b
(*.f64 (*.f64 a a) (-.f64 1 a))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.6b
(*.f64 (*.f64 b b) (+.f64 3 a))

series95.0ms (1.1%)

Counts
4 → 84
Calls

4 calls:

53.0ms
(+.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 3 a)))))
22.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
14.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
5.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))

rewrite65.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity_binary64
29×add-sqr-sqrt_binary64
24×add-cube-cbrt_binary64
18×prod-diff_binary64
15×distribute-lft-in_binary64
Counts
4 → 121
Calls

4 calls:

14.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
13.0ms
(+.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 3 a)))))
12.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
11.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

simplify180.0ms (2.1%)

Algorithm
egg-herbie
Rules
511×associate-+l+_binary64
383×associate-*l*_binary64
299×associate-*r*_binary64
268×cancel-sign-sub-inv_binary64
211×unswap-sqr_binary64
Counts
205 → 209
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02413743
16003419
223883054
348823054

prune452.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2090209
Fresh011
Picked011
Done011
Total2093212
Error
0b
Counts
212 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 1 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (neg.f64 (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))))))) (fma.f64 (neg.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3)))) (cbrt.f64 (+.f64 1 (*.f64 4 (pow.f64 a 3))))))))
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)
16.2b
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
Compiler

Compiled 7831 to 4051 computations (48.3% saved)

regimes2.0s (22.6%)

Accuracy

Total 0.0b remaining (59.4%)

Threshold costs 0.0b (59.4%)

Counts
259 → 1
Compiler

Compiled 52239 to 37375 computations (28.5% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
distribute-lft-neg-in_binary64
distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02767
15067
25767
36167
46467
56567
66267

end1.0ms (0%)

Compiler

Compiled 47 to 38 computations (19.1% saved)

sample1.1s (12.4%)

Algorithm
intervals
Results
624.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 301 to 226 computations (24.9% saved)

Profiling

Loading profile data...