bug329 (missed optimization)

Time bar (total: 1.7s)

analyze16.0ms (0.9%)

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: 9.0ms
ival-atan: 7.0ms (79% of total)
ival-div: 1.0ms (11.3% of total)
ival->=: 1.0ms (11.3% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample943.0ms (57.1%)

Results
710.0ms8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 197.0ms
ival-div: 88.0ms (44.7% of total)
ival-atan: 55.0ms (27.9% of total)
ival->=: 43.0ms (21.8% of total)
const: 7.0ms (3.6% of total)
backward-pass: 3.0ms (1.5% of total)
Bogosity

preprocess14.0ms (0.9%)

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))

explain42.0ms (2.6%)

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
30.0ms512×0valid
Compiler

Compiled 30 to 14 computations (53.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-div: 8.0ms (65.5% of total)
ival-atan: 3.0ms (24.6% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

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 (0.2%)

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

localize21.0ms (1.3%)

Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 y x)
✓accuracy100.0%
(atan.f64 (/.f64 y x))
Results
16.0ms256×0valid
Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-div: 3.0ms (62% of total)
ival-atan: 2.0ms (41.3% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series3.0ms (0.2%)

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)

rewrite86.0ms (5.2%)

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)

simplify6.0ms (0.4%)

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)

eval16.0ms (1%)

Compiler

Compiled 864 to 195 computations (77.4% saved)

prune9.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1072109
Fresh000
Picked011
Done000
Total1073110
Accuracy
100.0%
Counts
110 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(atan.f64 (/.f64 y x))
▶99.4%
(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
▶99.9%
(atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y))
Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify5.0ms (0.3%)

Algorithm
1×egg-herbie
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 x y)
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 x y))
✓cost-diff128
(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) x)
✓cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
✓cost-diff128
(atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y))
Rules
16×*-lowering-*.f32
16×*-lowering-*.f64
12×/-lowering-/.f32
12×/-lowering-/.f64
6×associate-*r*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0929
11625
22025
33025
43025
03025
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(atan (* (/ 1 x) y))
(* (/ 1 x) y)
(/ 1 x)
1
x
y
(atan (/ 1 (/ x y)))
(/ 1 (/ x y))
1
(/ x y)
x
y
Outputs
(atan (* (/ 1 x) y))
(atan.f64 (/.f64 y x))
(* (/ 1 x) y)
(/.f64 y x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
y
(atan (/ 1 (/ x y)))
(atan.f64 (/.f64 y x))
(/ 1 (/ x y))
(/.f64 y x)
1
#s(literal 1 binary64)
(/ x y)
(/.f64 x y)
x
y

localize43.0ms (2.6%)

Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 x y)
✓accuracy100.0%
(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
✓accuracy99.2%
(/.f64 #s(literal 1 binary64) (/.f64 x y))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) x)
✓accuracy100.0%
(atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y))
✓accuracy99.7%
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
Results
27.0ms256×0valid
Compiler

Compiled 37 to 10 computations (73% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-div: 7.0ms (52.9% of total)
ival-atan: 3.0ms (22.7% of total)
ival-mult: 2.0ms (15.1% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series4.0ms (0.2%)

Counts
6 → 132
Calls
Call 1
Inputs
#<alt (atan (* (/ 1 x) y))>
#<alt (* (/ 1 x) y)>
#<alt (/ 1 x)>
#<alt (atan (/ 1 (/ x y)))>
#<alt (/ 1 (/ x y))>
#<alt (/ x y)>
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)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 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 (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)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
Calls

33 calls:

TimeVariablePointExpression
1.0ms
y
@0
(/ x y)
0.0ms
x
@-inf
(/ x y)
0.0ms
x
@0
(/ x y)
0.0ms
x
@0
(/ 1 x)
0.0ms
y
@-inf
(/ x y)

rewrite238.0ms (14.4%)

Algorithm
1×batch-egg-rewrite
Rules
1538×*-lowering-*.f32
1538×*-lowering-*.f64
1216×+-lowering-+.f64
1216×+-lowering-+.f32
1110×prod-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0923
13619
214119
356419
4317619
0988619
Stop Event
1×iter limit
1×node limit
Counts
6 → 515
Calls
Call 1
Inputs
(atan (* (/ 1 x) y))
(* (/ 1 x) y)
(/ 1 x)
(atan (/ 1 (/ x y)))
(/ 1 (/ x y))
(/ x y)
Outputs
(-.f64 #s(literal 0 binary64) (atan.f64 (/.f64 y x)))
(atan.f64 (/.f64 y x))
(neg.f64 (atan.f64 (/.f64 y x)))
(*.f64 #s(literal -1 binary64) (atan.f64 (/.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 (log.f64 (/.f64 y x)))
(exp.f64 (*.f64 (log.f64 (/.f64 y x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 x y)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 x y))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 y x) (/.f64 y x))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (/.f64 x y))))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 y x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 (log.f64 (/.f64 x y)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 x y))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 y x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (log.f64 y) #s(literal 1 binary64))))
(exp.f64 (+.f64 (*.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (log.f64 y)))
(exp.f64 (+.f64 (*.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 y) #s(literal 1 binary64))))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal -1/2 binary64)) (log.f64 y)))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal -1/2 binary64)) (*.f64 (log.f64 y) #s(literal 1 binary64))))
(exp.f64 (+.f64 (log.f64 y) (*.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64))))
(exp.f64 (+.f64 (log.f64 y) (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 y) #s(literal 1 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) x))))
(exp.f64 (+.f64 (*.f64 (log.f64 y) #s(literal 1 binary64)) (*.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 y) #s(literal 1 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 x y)) #s(literal -1/2 binary64)) (*.f64 (log.f64 (/.f64 y x)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 y x)) #s(literal 1/2 binary64)) (*.f64 (log.f64 (/.f64 x y)) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 y x)) #s(literal 1/2 binary64)) (*.f64 (log.f64 (/.f64 y x)) #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 y x))
(sqrt.f64 (*.f64 (/.f64 y x) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64) (/.f64 y x))
(neg.f64 (/.f64 y x))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 x (*.f64 x (/.f64 x y)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 y)))
(/.f64 y x)
(/.f64 #s(literal -1 binary64) (/.f64 x y))
(/.f64 (/.f64 y x) #s(literal 1 binary64))
(/.f64 (/.f64 y x) #s(literal -1 binary64))
(/.f64 (/.f64 y x) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))))
(/.f64 (/.f64 y x) (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 (log.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))
(/.f64 (/.f64 y x) (pow.f64 (exp.f64 #s(literal -1 binary64)) (+.f64 (log.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))
(/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)))
(/.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y y) x))
(/.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 y y)))
(/.f64 (*.f64 y y) (*.f64 y x))
(/.f64 (*.f64 y y) (*.f64 x y))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x y)) (*.f64 x x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (/.f64 y x))) x)
(/.f64 (*.f64 (*.f64 y (*.f64 y y)) #s(literal -1 binary64)) (*.f64 (*.f64 y y) x))
(/.f64 (*.f64 (*.f64 y y) #s(literal -1 binary64)) (*.f64 y x))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 y (*.f64 y y))) (*.f64 y y))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 y y)) y)
(/.f64 (*.f64 (*.f64 y (*.f64 y y)) (/.f64 #s(literal 1 binary64) x)) (*.f64 y y))
(/.f64 (*.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) x)) y)
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal -1/2 binary64))) (pow.f64 y #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 (/.f64 y x) (/.f64 y x)) (/.f64 y x))) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (/.f64 y x) (/.f64 y x)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 y x) (/.f64 y x))) (/.f64 y x))
(/.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 (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 y))) x)
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))) (/.f64 x y))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 y x)))) (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (+.f64 #s(literal 0 binary64) (log.f64 #s(literal -1 binary64)))) (/.f64 x y))
(pow.f64 (/.f64 x y) #s(literal -1 binary64))
(pow.f64 (/.f64 y x) #s(literal 1 binary64))
(pow.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (/.f64 (/.f64 x y) (/.f64 y x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 y x) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 y x) (/.f64 y x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 x y)))
(pow.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 y #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (/.f64 (/.f64 x y) (/.f64 y x))) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (log.f64 (/.f64 x y)))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (log.f64 (/.f64 y x)))
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 y))))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) (/.f64 y x))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(*.f64 (/.f64 y x) #s(literal -1 binary64))
(*.f64 (/.f64 y x) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 y (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 y) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 y) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) x))
(*.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 y) (pow.f64 (*.f64 x (/.f64 x y)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 y) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))))
(*.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))) (neg.f64 (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 y x) #s(literal 1/4 binary64)) (pow.f64 (/.f64 x y) #s(literal -3/4 binary64)))
(*.f64 (pow.f64 (/.f64 y x) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (/.f64 y x) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 y (pow.f64 x #s(literal -1/2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 y x) (/.f64 y x)) (/.f64 x y))
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 y (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) (*.f64 y (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal -1/2 binary64))) (sqrt.f64 y))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (*.f64 y (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 y #s(literal -1/2 binary64))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 y #s(literal -1/2 binary64))))
(*.f64 (/.f64 (sqrt.f64 y) #s(literal 1 binary64)) (/.f64 (sqrt.f64 y) x))
(*.f64 (/.f64 (sqrt.f64 y) x) (/.f64 (sqrt.f64 y) #s(literal 1 binary64)))
(*.f64 (/.f64 (sqrt.f64 y) x) (/.f64 (sqrt.f64 y) #s(literal -1 binary64)))
(*.f64 (/.f64 (sqrt.f64 y) #s(literal -1 binary64)) (/.f64 (sqrt.f64 y) x))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 y)) (sqrt.f64 y))
(*.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal -1/2 binary64)) (sqrt.f64 y))
(*.f64 (*.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64))) (sqrt.f64 y))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (sqrt.f64 y)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 y x) #s(literal 1/4 binary64))) (pow.f64 (/.f64 y x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -3/4 binary64)) (pow.f64 (/.f64 y x) #s(literal 1/4 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 y x) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(*.f64 (/.f64 y (sqrt.f64 x)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 y (*.f64 y y)))) (/.f64 (/.f64 x y) (/.f64 y x)))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 x y) (/.f64 y x))) (/.f64 x y))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 y (*.f64 y y)))) (/.f64 (/.f64 x y) (/.f64 y x)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(*.f64 (/.f64 y (*.f64 x (*.f64 x x))) (*.f64 x x))
(*.f64 (/.f64 y (*.f64 x x)) x)
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 y))) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))) (/.f64 y x))
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(*.f64 (/.f64 x y) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 x y))
(*.f64 (/.f64 #s(literal 1 binary64) y) x)
(*.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 #s(literal -1 binary64) (pow.f64 (/.f64 x y) #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)) (neg.f64 (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 (/.f64 (/.f64 x y) (/.f64 y x)) (/.f64 y x))
(*.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 y (*.f64 y y))) (*.f64 (/.f64 y x) (/.f64 y x)))
(*.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 x (sqrt.f64 y)))
(*.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 y #s(literal -1/2 binary64)) (*.f64 (pow.f64 y #s(literal -1/2 binary64)) x))
(*.f64 (sqrt.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) y) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (neg.f64 (pow.f64 (/.f64 y x) #s(literal -1/2 binary64))) (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 y)) (pow.f64 y #s(literal -1/2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) (/.f64 x (sqrt.f64 y)))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -1/2 binary64))) (sqrt.f64 x))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (*.f64 x (pow.f64 y #s(literal -1/2 binary64))) (pow.f64 y #s(literal -1/2 binary64)))
(*.f64 (/.f64 x (*.f64 y (*.f64 y y))) (*.f64 y y))
(*.f64 (/.f64 x (*.f64 y y)) y)
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))) (/.f64 x y))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 y)) x)
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))))) (sqrt.f64 x))

simplify26.0ms (1.6%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
07432
110432
010432
Stop Event
1×iter limit
1×saturated
Counts
132 → 132
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)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 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))
(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)
(/ 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)
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)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) 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))
(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)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)

eval68.0ms (4.1%)

Compiler

Compiled 6851 to 1217 computations (82.2% saved)

prune62.0ms (3.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New6470647
Fresh000
Picked022
Done011
Total6473650
Accuracy
100.0%
Counts
650 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(atan.f64 (/.f64 y x))
✓99.4%
(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
✓99.9%
(atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y))
Compiler

Compiled 40 to 27 computations (32.5% saved)

regimes7.0ms (0.4%)

Accuracy

Total -0.5b remaining (-3959.4%)

Threshold costs -0.5b (-3959.4%)

Counts
3 → 1
Calls
Call 1
Inputs
(atan.f64 (/.f64 y x))
(atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y))
(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
Outputs
(atan.f64 (/.f64 y x))
Calls

4 calls:

2.0ms
(/.f64 y x)
2.0ms
x
2.0ms
y
2.0ms
(atan.f64 (/.f64 y x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(atan.f64 (/.f64 y x))
100.0%1(/.f64 y x)
Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify8.0ms (0.5%)

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)

preprocess28.0ms (1.7%)

Compiler

Compiled 34 to 22 computations (35.3% saved)

end0.0ms (0%)

Profiling

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