Details

Time bar (total: 4.5s)

analyze19.0ms (0.4%)

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
0%99.9%0.1%4
49.9%49.9%0.1%5
74.9%25%0.1%6
87.4%12.5%0.1%7
93.6%6.2%0.1%8
96.7%3.1%0.1%9
98.3%1.6%0.1%10
99.1%0.8%0.1%11
99.5%0.4%0.1%12
99.7%0.2%0.1%13
99.8%0.1%0.1%14
Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.0s (22.9%)

Symmetry

(sort x y z)

Results
985.0ms8256×body128valid
Compiler

Compiled 53 to 35 computations (34% saved)

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
9×fma-def_binary64
5×+-commutative_binary64
3×associate-+r+_binary64
3×associate-+l+_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01219
11717
22717
33117
43117

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
37.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶37.5b
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
Compiler

Compiled 59 to 34 computations (42.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 z z (fma.f64 x x (*.f64 y y)))
✓0.1b
(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
✓34.8b
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

series131.0ms (2.9%)

Counts
3 → 108
Calls

3 calls:

88.0ms
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
26.0ms
(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
13.0ms
(fma.f64 z z (fma.f64 x x (*.f64 y y)))

rewrite58.0ms (1.3%)

Algorithm
2×batch-egg-rewrite
Rules
864×log1p-expm1-u_binary64
864×expm1-log1p-u_binary64
135×prod-diff_binary64
100×add-sqr-sqrt_binary64
94×add-log-exp_binary64
Counts
3 → 85
Calls

3 calls:

57.0ms
(fma.f64 z z (fma.f64 x x (*.f64 y y)))
57.0ms
(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
57.0ms
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01044
120635
2228535
3551735
000
100

simplify95.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
796×cancel-sign-sub-inv_binary64
354×fma-neg_binary64
351×sub-neg_binary64
281×fma-def_binary64
226×times-frac_binary64
Counts
193 → 182
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03043804
18923407
238123407
355883407

prune141.0ms (3.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1802182
Fresh000
Picked101
Done000
Total1812183
Error
0.0b
Counts
183 → 2
Alt Table
StatusErrorProgram
0.4b
(fabs.f64 (*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3)))
▶0.4b
(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))
Compiler

Compiled 5090 to 3545 computations (30.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(hypot.f64 z (hypot.f64 x y))
✓0.4b
(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))

series159.0ms (3.6%)

Counts
2 → 72
Calls

2 calls:

97.0ms
(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))
62.0ms
(hypot.f64 z (hypot.f64 x y))

rewrite50.0ms (1.1%)

Algorithm
2×batch-egg-rewrite
Rules
809×log1p-expm1-u_binary64
809×expm1-log1p-u_binary64
126×prod-diff_binary64
91×add-sqr-sqrt_binary64
87×add-log-exp_binary64
Counts
2 → 52
Calls

2 calls:

49.0ms
(hypot.f64 z (hypot.f64 x y))
49.0ms
(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0919
118519
2210419
3522919
000
100

simplify87.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
411×fma-def_binary64
272×times-frac_binary64
262×associate-/r*_binary64
254×associate--l+_binary64
240×associate-/l*_binary64
Counts
124 → 190
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04174742
113024402
251904402

prune160.0ms (3.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1900190
Fresh011
Picked011
Done000
Total1902192
Error
0.0b
Counts
192 → 2
Alt Table
StatusErrorProgram
▶0.4b
(fabs.f64 (*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3)))
✓0.4b
(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))
Compiler

Compiled 7212 to 5053 computations (29.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 z (hypot.f64 x y))
✓0.4b
(*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3))

series93.0ms (2.1%)

Counts
1 → 36
Calls

1 calls:

92.0ms
(*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3))

rewrite43.0ms (1%)

Algorithm
2×batch-egg-rewrite
Rules
717×log1p-expm1-u_binary64
717×expm1-log1p-u_binary64
155×expm1-udef_binary64
155×log1p-udef_binary64
102×prod-diff_binary64
Counts
1 → 15
Calls

1 calls:

42.0ms
(*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
117912
2189512
3508312
000
100

simplify74.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
819×cancel-sign-sub-inv_binary64
361×sub-neg_binary64
351×fma-neg_binary64
273×fma-def_binary64
226×times-frac_binary64
Counts
51 → 84
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02992697
18742555
237802555
355872555

prune280.0ms (6.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1720172
Fresh000
Picked011
Done011
Total1722174
Error
0.0b
Counts
174 → 2
Alt Table
StatusErrorProgram
✓0.4b
(fabs.f64 (*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3)))
✓0.4b
(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))
Compiler

Compiled 7049 to 5049 computations (28.4% saved)

regimes1.9s (42.2%)

Accuracy

Total 0.4b remaining (99.2%)

Threshold costs 0.4b (99.2%)

Counts
67 → 1
Compiler

Compiled 8703 to 6897 computations (20.8% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11315
21215

end136.0ms (3%)

Remove

(sort x y z)

Compiler

Compiled 75 to 57 computations (24% saved)

Profiling

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