bug329 (missed optimization)

Time bar (total: 985.0ms)

analyze16.0ms (1.6%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50%50%0%0%0%0
0%0%50%50%0%0%0%1
50%25%25%50%0%0%0%2
50%25%25%50%0%0%0%3
75%37.5%12.5%50%0%0%0%4
75%37.5%12.5%50%0%0%0%5
87.5%43.7%6.2%50%0%0%0%6
87.5%43.7%6.2%50%0%0%0%7
93.8%46.8%3.1%50%0%0%0%8
93.8%46.8%3.1%50%0%0%0%9
96.9%48.4%1.6%50%0%0%0%10
96.9%48.4%1.6%50%0%0%0%11
98.4%49.2%0.8%50%0%0%0%12
Compiler

Compiled 9 to 6 computations (33.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-atan: 5.0ms (76.5% of total)
ival-div: 1.0ms (15.3% of total)
ival->=: 1.0ms (15.3% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample705.0ms (71.6%)

Results
504.0ms8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 176.0ms
ival-div: 76.0ms (43.2% of total)
ival-atan: 55.0ms (31.3% of total)
ival->=: 33.0ms (18.8% of total)
const: 8.0ms (4.5% of total)
backward-pass: 3.0ms (1.7% of total)
Bogosity

preprocess16.0ms (1.6%)

Algorithm
2×egg-herbie
Rules
60×sum3-define
36×fma-define
30×sub-neg
20×fmsub-define
20×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01430
12530
23730
34730
46730
58730
611030
716030
816530
916730
044
044
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(atan (/ y x))
Outputs
(atan (/ y x))
(atan.f64 (/.f64 y x))
Call 2
Inputs
(atan (/ y x))
(atan (/ y (neg x)))
(atan (/ (neg y) x))
(neg (atan (/ y (neg x))))
(neg (atan (/ (neg y) x)))
(atan (/ x y))
Outputs
(atan (/ y x))
(atan (/ y (neg x)))
(atan (/ (neg y) x))
(atan (/ y (neg x)))
(neg (atan (/ y (neg x))))
(neg (atan (/ (neg y) x)))
(neg (atan (/ y (neg x))))
(atan (/ x y))

explain46.0ms (4.6%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-x
00-0-(atan.f64 (/.f64 y x))
00-0-y
00-0-(/.f64 y x)
Results
32.0ms512×0valid
Compiler

Compiled 30 to 14 computations (53.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-div: 5.0ms (56.7% of total)
ival-atan: 3.0ms (34% of total)
const: 1.0ms (11.3% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0.1%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(atan.f64 (/.f64 y x))
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify3.0ms (0.3%)

Algorithm
1×egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 y x)
✓cost-diff0
(atan.f64 (/.f64 y x))
Rules
2×atan-lowering-atan.f32
2×atan-lowering-atan.f64
2×/-lowering-/.f32
2×/-lowering-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049
049
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(atan (/ y x))
(/ y x)
y
x
Outputs
(atan (/ y x))
(atan.f64 (/.f64 y x))
(/ y x)
(/.f64 y x)
y
x

localize27.0ms (2.8%)

Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 y x)
✓accuracy100.0%
(atan.f64 (/.f64 y x))
Results
22.0ms256×0valid
Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-atan: 6.0ms (66.5% of total)
ival-div: 2.0ms (22.2% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series3.0ms (0.3%)

Counts
2 → 48
Calls
Call 1
Inputs
#<alt (atan (/ y x))>
#<alt (/ y x)>
Outputs
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
Calls

12 calls:

TimeVariablePointExpression
1.0ms
y
@inf
(/ y x)
1.0ms
x
@inf
(/ y x)
0.0ms
y
@-inf
(/ y x)
0.0ms
y
@0
(/ y x)
0.0ms
x
@0
(/ y x)

rewrite84.0ms (8.5%)

Algorithm
1×batch-egg-rewrite
Rules
522×*-lowering-*.f32
522×*-lowering-*.f64
470×/-lowering-/.f32
470×/-lowering-/.f64
136×--lowering--.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047
1127
2497
32277
012387
Stop Event
1×iter limit
1×iter limit
1×node limit
Counts
2 → 61
Calls
Call 1
Inputs
(atan (/ y x))
(/ y x)
Outputs
(-.f64 #s(literal 0 binary64) (atan.f64 (-.f64 #s(literal 0 binary64) (/.f64 y x))))
(atan.f64 (/.f64 y x))
(neg.f64 (atan.f64 (-.f64 #s(literal 0 binary64) (/.f64 y x))))
(*.f64 #s(literal -1 binary64) (atan.f64 (-.f64 #s(literal 0 binary64) (/.f64 y x))))
(+.f64 #s(literal 0 binary64) (/.f64 y x))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64)) (/.f64 y x))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 x y))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 y x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 y x)))
(/.f64 y x)
(/.f64 (/.f64 y x) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x y)))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) y))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 y x)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 y (*.f64 y y))) (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 y y)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (*.f64 (-.f64 #s(literal 0 binary64) x) y))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x y))) (-.f64 #s(literal 0 binary64) x)) (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (/.f64 x y))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) y)) (*.f64 x x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) y))) (*.f64 (-.f64 #s(literal 0 binary64) x) x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y (*.f64 y y))) #s(literal 1 binary64)) (*.f64 (*.f64 y y) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y (*.f64 y y))) #s(literal -1 binary64)) (*.f64 (*.f64 y y) x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) #s(literal 1 binary64)) (*.f64 y (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) #s(literal -1 binary64)) (*.f64 y x))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 y (*.f64 y y)))) (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 y y)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 y y))) (*.f64 (-.f64 #s(literal 0 binary64) x) y))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x (*.f64 y y)))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 y y))) (*.f64 x y))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (/.f64 y x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 y x)) (-.f64 #s(literal 0 binary64) (/.f64 y x))) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 y x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 y x)) (-.f64 #s(literal 0 binary64) (/.f64 y x)))) (-.f64 #s(literal 0 binary64) (/.f64 y x)))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 y (*.f64 y y)))) (*.f64 y y))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 y y))) y)
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y (*.f64 y y))) (/.f64 #s(literal -1 binary64) x)) (*.f64 y y))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x)) y)
(pow.f64 (/.f64 y x) #s(literal 1 binary64))
(pow.f64 (/.f64 x y) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 x y) (/.f64 x y)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 x y))) #s(literal -1 binary64))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 y x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 0 binary64) y))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 y x)) #s(literal -1 binary64))
(*.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 y x) #s(literal 1/2 binary64))) (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x x))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) (*.f64 x x))) x)

simplify28.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
2×atan-lowering-atan.f32
2×atan-lowering-atan.f64
2×/-lowering-/.f32
2×/-lowering-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04168
04168
Stop Event
1×iter limit
1×saturated
Counts
48 → 48
Calls
Call 1
Inputs
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
Outputs
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)

eval10.0ms (1.1%)

Compiler

Compiled 864 to 195 computations (77.4% saved)

prune10.0ms (1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New1090109
Fresh000
Picked011
Done000
Total1091110
Accuracy
100.0%
Counts
110 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(atan.f64 (/.f64 y x))
Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify6.0ms (0.7%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044
Stop Event
1×saturated
Calls
Call 1
Inputs
(atan.f64 (/.f64 y x))
Outputs
(atan.f64 (/.f64 y x))

soundness0.0ms (0%)

Stop Event
1×done
Compiler

Compiled 6 to 4 computations (33.3% saved)

preprocess29.0ms (2.9%)

Compiler

Compiled 34 to 22 computations (35.3% saved)

end0.0ms (0%)

Profiling

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