Details

Time bar (total: 11.1s)

analyze103.0ms (0.9%)

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
0%99.9%0.1%4
12.5%87.4%0.1%5
46.8%53.1%0.1%6
70.2%29.7%0.1%7
76.5%23.4%0.1%8
83.5%16.4%0.1%9
87%12.9%0.1%10
91.1%8.8%0.1%11
93.2%6.7%0.1%12
95.4%4.5%0.1%13
96.5%3.4%0.1%14
Compiler

Compiled 20 to 10 computations (50% saved)

sample935.0ms (8.4%)

Symmetry

(sort x y)

Results
813.0ms8256×body128valid
Compiler

Compiled 59 to 29 computations (50.8% saved)

simplify144.0ms (1.3%)

Algorithm
egg-herbie
Rules
985×associate-/l*_binary64
659×distribute-lft-out_binary64
601×*-commutative_binary64
469×distribute-rgt-out_binary64
356×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01025
13925
213523
347423
4153623
5212223
6258923
7256723
8262023
9267723
10277023
11395623
12408823
13445423
14498323
15496823
16496123

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
20.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
20.8b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
20.8b
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
Compiler

Compiled 109 to 47 computations (56.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
0.0b
(pow.f64 (+.f64 x y) 3)
20.6b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series100.0ms (0.9%)

Counts
3 → 72
Calls

3 calls:

79.0ms
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
12.0ms
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
9.0ms
(pow.f64 (+.f64 x y) 3)

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
3 → 62
Calls

3 calls:

5.0ms
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
3.0ms
(pow.f64 (+.f64 x y) 3)
0.0ms
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))

simplify149.0ms (1.3%)

Algorithm
egg-herbie
Rules
326×fma-def_binary64
301×times-frac_binary64
297×associate-+r+_binary64
257×associate-/l*_binary64
223×+-commutative_binary64
Counts
134 → 162
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03474819
110474272
247024260
349814260
449964260
549814260

prune175.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1557162
Fresh101
Picked101
Done000
Total1577164
Error
4.8b
Counts
164 → 7
Alt Table
StatusErrorProgram
20.8b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (*.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))))
9.8b
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
40.0b
(/.f64 x (pow.f64 y 2))
10.0b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (/.f64 y (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
40.7b
(/.f64 y (pow.f64 x 2))
38.3b
(/.f64 (/.f64 (*.f64 x y) (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
Compiler

Compiled 5975 to 3148 computations (47.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
0.0b
(pow.f64 (+.f64 x y) 3)
4.9b
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
8.5b
(/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series145.0ms (1.3%)

Counts
2 → 48
Calls

2 calls:

76.0ms
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
69.0ms
(/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64
34×times-frac_binary64
26×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
21×add-exp-log_binary64
Counts
2 → 85
Calls

2 calls:

8.0ms
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
2.0ms
(/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

simplify374.0ms (3.4%)

Algorithm
egg-herbie
Rules
428×times-frac_binary64
391×associate-/l*_binary64
391×fma-def_binary64
316×associate-/r*_binary64
246×associate-*r*_binary64
Counts
133 → 207
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04867311
114736634
249816634

prune453.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2961297
Fresh156
Picked011
Done000
Total2977304
Error
4.8b
Counts
304 → 7
Alt Table
StatusErrorProgram
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
32.3b
(*.f64 (*.f64 (/.f64 x 1) (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
20.8b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (*.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))))
9.8b
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
40.0b
(/.f64 x (pow.f64 y 2))
10.0b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (/.f64 y (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
40.7b
(/.f64 y (pow.f64 x 2))
Compiler

Compiled 11992 to 6603 computations (44.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
0.1b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (/.f64 y (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
16.5b
(/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
37.6b
(cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series3.7s (33.1%)

Counts
4 → 96
Calls

4 calls:

3.3s
(/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
207.0ms
(*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
91.0ms
(cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
80.0ms
(*.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (/.f64 y (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))

rewrite44.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt_binary64
32×add-exp-log_binary64
31×times-frac_binary64
30×*-un-lft-identity_binary64
30×cbrt-prod_binary64
Counts
4 → 139
Calls

4 calls:

12.0ms
(*.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (/.f64 y (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
4.0ms
(*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
4.0ms
(/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
1.0ms
(cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

simplify239.0ms (2.2%)

Algorithm
egg-herbie
Rules
693×*-commutative_binary64
391×fma-def_binary64
375×associate-+r+_binary64
230×associate-*l*_binary64
228×associate-*r*_binary64
Counts
235 → 294
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0162623365
1500423365

prune915.0ms (8.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4011402
Fresh055
Picked101
Done011
Total4027409
Error
4.8b
Counts
409 → 7
Alt Table
StatusErrorProgram
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
32.3b
(*.f64 (*.f64 (/.f64 x 1) (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
20.8b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (*.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))))
11.1b
(*.f64 (/.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))) (/.f64 y (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))))
9.8b
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
40.0b
(/.f64 x (pow.f64 y 2))
40.7b
(/.f64 y (pow.f64 x 2))
Compiler

Compiled 43150 to 26025 computations (39.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
4.9b
(*.f64 (/.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))) (/.f64 y (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))))
16.5b
(/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
37.6b
(cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series179.0ms (1.6%)

Counts
2 → 48
Calls

2 calls:

100.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
79.0ms
(*.f64 (/.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))) (/.f64 y (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))))

rewrite64.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
67×add-exp-log_binary64
59×add-sqr-sqrt_binary64
58×times-frac_binary64
45×cbrt-prod_binary64
40×add-cbrt-cube_binary64
Counts
2 → 112
Calls

2 calls:

19.0ms
(*.f64 (/.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))) (/.f64 y (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))))
1.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))

simplify257.0ms (2.3%)

Algorithm
egg-herbie
Rules
649×fma-def_binary64
498×times-frac_binary64
452×associate-/l*_binary64
246×*-commutative_binary64
163×+-commutative_binary64
Counts
160 → 260
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
075420532
1232115845
2515515845

prune1.9s (17.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New7361737
Fresh055
Picked101
Done011
Total7377744
Error
4.8b
Counts
744 → 7
Alt Table
StatusErrorProgram
9.8b
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
32.2b
(*.f64 (/.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))) (/.f64 y (cbrt.f64 (exp.f64 (log.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))))))
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
32.3b
(*.f64 (*.f64 (/.f64 x 1) (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
20.8b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (*.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))))
40.0b
(/.f64 x (pow.f64 y 2))
40.7b
(/.f64 y (pow.f64 x 2))
Compiler

Compiled 95908 to 52825 computations (44.9% saved)

regimes806.0ms (7.3%)

Accuracy

Total 2.8b remaining (34.9%)

Threshold costs 0b (0%)

Counts
130 → 3
Compiler

Compiled 12332 to 6005 computations (51.3% saved)

bsearch51.0ms (0.5%)

Steps
ItersRangePoint
9
-4.874974585594426e-199
-3.2615745078769454e-205
-3.3015405365043286e-205
8
-5.696834084397072e+106
-6.8537188811296636e+103
-2.1378619596082982e+105
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02676
12776
22776

end269.0ms (2.4%)

Compiler

Compiled 416 to 198 computations (52.4% saved)

Profiling

Loading profile data...