sqrt E (should all be same)

Time bar (total: 1.0s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 10 to 6 computations (40% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
ival-add: 0.0ms (0% of total)
const: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)
ival-pow: 0.0ms (0% of total)

sample594.0ms (59.3%)

Results
440.0ms8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 256.0ms
ival-pow: 117.0ms (45.7% of total)
ival-sqrt: 75.0ms (29.3% of total)
ival-add: 51.0ms (19.9% of total)
const: 10.0ms (3.9% of total)
backward-pass: 3.0ms (1.2% of total)
Bogosity

preprocess25.0ms (2.5%)

Algorithm
2×egg-herbie
Rules
174×fmsub-define
174×fnmadd-define
160×fnmsub-define
114×fma-define
86×fmm-def
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01020
12010
24810
316710
438410
560210
674010
774310
056
173
2143
3173
0173
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(sqrt (+ (pow x 2) (pow x 2)))
Outputs
(sqrt (+ (pow x 2) (pow x 2)))
(hypot.f64 x x)
Call 2
Inputs
(sqrt (+ (pow x 2) (pow x 2)))
(sqrt (+ (pow (neg x) 2) (pow (neg x) 2)))
(neg (sqrt (+ (pow (neg x) 2) (pow (neg x) 2))))
Outputs
(sqrt (+ (pow x 2) (pow x 2)))
(hypot x x)
(sqrt (+ (pow (neg x) 2) (pow (neg x) 2)))
(hypot x x)
(neg (sqrt (+ (pow (neg x) 2) (pow (neg x) 2))))
(neg (hypot x x))
Symmetry

(abs x)

explain79.0ms (7.8%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1210-4(2.7194061164858503e-157)(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
00-0-x
00-0-(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
00-0-(pow.f64 x #s(literal 2 binary64))
00-0-#s(literal 2 binary64)
Results
51.0ms512×0valid
Compiler

Compiled 53 to 17 computations (67.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-pow: 6.0ms (40.8% of total)
ival-sqrt: 5.0ms (34% of total)
ival-add: 3.0ms (20.4% of total)
const: 1.0ms (6.8% of total)
backward-pass: 0.0ms (0% of total)

eval5.0ms (0.5%)

Compiler

Compiled 4 to 2 computations (50% saved)

prune1.0ms (0.1%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(hypot.f64 x x)
▶57.4%
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Compiler

Compiled 13 to 7 computations (46.2% saved)

simplify4.0ms (0.4%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(hypot.f64 x x)
✓cost-diff6336
(pow.f64 x #s(literal 2 binary64))
✓cost-diff12800
(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
✓cost-diff12992
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Rules
14×*-lowering-*.f32
14×*-lowering-*.f64
4×*-commutative
4×+-lowering-+.f64
4×count-2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
11317
21617
31917
01917
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt (+ (pow x 2) (pow x 2)))
(+ (pow x 2) (pow x 2))
(pow x 2)
x
2
(sqrt (+ (* x x) (* x x)))
x
Outputs
(sqrt (+ (pow x 2) (pow x 2)))
(hypot.f64 x x)
(+ (pow x 2) (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(pow x 2)
(*.f64 x x)
x
2
#s(literal 2 binary64)
(sqrt (+ (* x x) (* x x)))
(hypot.f64 x x)
x

localize36.0ms (3.6%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(hypot.f64 x x)
✓accuracy100.0%
(pow.f64 x #s(literal 2 binary64))
✓accuracy100.0%
(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
✓accuracy57.4%
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Results
26.0ms256×0valid
Compiler

Compiled 26 to 7 computations (73.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
compiled-spec: 7.0ms (32.7% of total)
ival-mult: 4.0ms (18.7% of total)
ival-sqrt: 4.0ms (18.7% of total)
ival-add: 3.0ms (14% of total)
ival-pow: 3.0ms (14% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series3.0ms (0.3%)

Counts
4 → 48
Calls
Call 1
Inputs
#<alt (sqrt (+ (pow x 2) (pow x 2)))>
#<alt (+ (pow x 2) (pow x 2))>
#<alt (pow x 2)>
#<alt (sqrt (+ (* x x) (* x x)))>
Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@0
(sqrt (+ (pow x 2) (pow x 2)))
1.0ms
x
@inf
(+ (pow x 2) (pow x 2))
0.0ms
x
@inf
(sqrt (+ (pow x 2) (pow x 2)))
0.0ms
x
@0
(+ (pow x 2) (pow x 2))
0.0ms
x
@-inf
(sqrt (+ (* x x) (* x x)))

rewrite51.0ms (5.1%)

Algorithm
1×batch-egg-rewrite
Rules
74×*-lowering-*.f32
74×*-lowering-*.f64
36×pow-lowering-pow.f64
36×pow-lowering-pow.f32
34×/-lowering-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0814
13212
020812
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
Counts
4 → 42
Calls
Call 1
Inputs
(sqrt (+ (pow x 2) (pow x 2)))
(+ (pow x 2) (pow x 2))
(pow x 2)
(sqrt (+ (* x x) (* x x)))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(hypot.f64 x x)
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (sqrt.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 x x)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(+.f64 (*.f64 x x) (*.f64 x x))
(-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)))
(fma.f64 x x (*.f64 x x))
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(/.f64 (neg.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (neg.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64))))
(*.f64 x (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64))))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) x) x)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(hypot.f64 x x)
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (sqrt.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 x x)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))

simplify14.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
106×sum3-define
98×fma-define
46×fma-lowering-fma.f32
46×fma-lowering-fma.f64
38×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08200
115200
232200
338200
442200
564200
696200
7108200
8139200
9232200
10235200
0235200
Stop Event
1×iter limit
1×saturated
Counts
48 → 48
Calls
Call 1
Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

eval9.0ms (0.9%)

Compiler

Compiled 854 to 105 computations (87.7% saved)

prune6.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1071108
Fresh000
Picked112
Done000
Total1082110
Accuracy
100.0%
Counts
110 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
▶99.3%
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify3.0ms (0.3%)

Algorithm
1×egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
Rules
4×*-lowering-*.f32
4×*-lowering-*.f64
2×*-commutative
2×sqrt-lowering-sqrt.f64
2×sqrt-lowering-sqrt.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048
158
058
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* x (sqrt 2))
x
(sqrt 2)
2
Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)

localize17.0ms (1.7%)

Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy99.3%
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
Results
11.0ms256×0valid
Compiler

Compiled 10 to 5 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 2.0ms (43.1% of total)
ival-sqrt: 2.0ms (43.1% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

Counts
2 → 12
Calls
Call 1
Inputs
#<alt (* x (sqrt 2))>
#<alt (sqrt 2)>
Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
(* x (sqrt 2))
0.0ms
x
@0
(* x (sqrt 2))
0.0ms
x
@inf
(* x (sqrt 2))

rewrite91.0ms (9.1%)

Algorithm
1×batch-egg-rewrite
Rules
564×*-lowering-*.f32
564×*-lowering-*.f64
200×associate-*r*
148×prod-exp
146×associate-*l*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046
176
2146
3336
4816
52176
010106
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
Counts
2 → 55
Calls
Call 1
Inputs
(* x (sqrt 2))
(sqrt 2)
Outputs
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64))))
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))))
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) x))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64))))
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64)))
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64))))
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)))
(*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64))))
(*.f64 (*.f64 x (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(*.f64 (*.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64)))
(exp.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(exp.f64 (*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 16 binary64)) #s(literal 1/8 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 8 binary64))
(pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 4 binary64)))
(pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 2 binary64))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/4 binary64)) (exp.f64 #s(literal 1/4 binary64))) (log.f64 #s(literal 2 binary64)))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 5/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/16 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 1 binary64)) (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/32 binary64)))

simplify4.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
4×*-lowering-*.f32
4×*-lowering-*.f64
2×*-commutative
2×sqrt-lowering-sqrt.f64
2×sqrt-lowering-sqrt.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0448
1548
0548
Stop Event
1×iter limit
1×saturated
Counts
12 → 12
Calls
Call 1
Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))

eval9.0ms (0.9%)

Compiler

Compiled 562 to 147 computations (73.8% saved)

prune7.0ms (0.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New67067
Fresh000
Picked011
Done011
Total67269
Accuracy
100.0%
Counts
69 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
✓99.3%
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
Compiler

Compiled 25 to 14 computations (44% saved)

regimes7.0ms (0.7%)

Accuracy

Total -27.5b remaining (-352496.3%)

Threshold costs -27.5b (-352496.3%)

Counts
3 → 1
Calls
Call 1
Inputs
(hypot.f64 x x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
Outputs
(hypot.f64 x x)
Calls

4 calls:

2.0ms
x
2.0ms
(pow.f64 x #s(literal 2 binary64))
2.0ms
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
2.0ms
(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
100.0%1(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
100.0%1(pow.f64 x #s(literal 2 binary64))
Compiler

Compiled 23 to 13 computations (43.5% saved)

simplify8.0ms (0.8%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
023
Stop Event
1×saturated
Calls
Call 1
Inputs
(hypot.f64 x x)
Outputs
(hypot.f64 x x)

soundness4.0ms (0.4%)

Rules
14×*-lowering-*.f32
14×*-lowering-*.f64
4×*-commutative
4×+-lowering-+.f64
4×count-2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
056
173
2143
3173
0173
Stop Event
1×done
1×iter limit
1×saturated
Compiler

Compiled 8 to 4 computations (50% saved)

preprocess23.0ms (2.3%)

Remove

(abs x)

Compiler

Compiled 42 to 22 computations (47.6% saved)

end0.0ms (0%)

Profiling

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