Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

Time bar (total: 1.7s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze5.0ms (0.3%)

Memory
-38.9MiB live, 8.1MiB allocated; 5ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%50%0%0%50%0%3
50%25%25%0%0%50%0%4
75%37.5%12.5%0%0%50%0%5
87.5%43.7%6.2%0%0%50%0%6
93.8%46.9%3.1%0%0%50%0%7
96.9%48.4%1.6%0%0%50%0%8
98.4%49.2%0.8%0%0%50%0%9
99.2%49.6%0.4%0%0%50%0%10
99.6%49.8%0.2%0%0%50%0%11
99.8%49.9%0.1%0%0%50%0%12
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample703.0ms (41.7%)

Memory
57.5MiB live, 991.9MiB allocated; 172ms collecting garbage
Samples
458.0ms8 256×0valid
0.0ms3×0invalid
Precisions
Click to see histograms. Total time spent on operations: 262.0ms
ival-mult: 138.0ms (52.7% of total)
ival-sqrt: 58.0ms (22.2% of total)
ival-sub: 49.0ms (18.7% of total)
ival-true: 6.0ms (2.3% of total)
exact: 5.0ms (1.9% of total)
ival-assert: 3.0ms (1.1% of total)
adjust: 2.0ms (0.8% of total)
Bogosity

explain126.0ms (7.4%)

Memory
-3.7MiB live, 84.9MiB allocated; 23ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
00-0-#s(literal 1 binary64)
00-0-(-.f64 #s(literal 1 binary64) (*.f64 x x))
00-0-(*.f64 x x)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
90.0ms512×0valid
Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-sub: 27.0ms (74.5% of total)
ival-mult: 4.0ms (11% of total)
ival-sqrt: 4.0ms (11% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess238.0ms (14.1%)

Memory
0.5MiB live, 246.5MiB allocated; 55ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
12113
24813
37213
413113
533813
6240513
7596713
056
086
1166
2406
3796
41386
53456
624076
759716
082106
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
Outputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
Compiler

Compiled 6 to 5 computations (16.7% saved)

series3.0ms (0.2%)

Memory
9.2MiB live, 9.2MiB allocated; 0ms collecting garbage
Counts
5 → 17
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x
Outputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(+ 1 (* -1 (pow x 2)))
(pow x 2)
x
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((sqrt (- 1 (* x x))) (- 1 (* x x)) 1 (* x x) x)
1.0ms
x
@-inf
((sqrt (- 1 (* x x))) (- 1 (* x x)) 1 (* x x) x)
1.0ms
x
@0
((sqrt (- 1 (* x x))) (- 1 (* x x)) 1 (* x x) x)

simplify77.0ms (4.6%)

Memory
-7.5MiB live, 131.7MiB allocated; 8ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
062221
1156220
2542204
02743198
Stop Event
1×iter limit
1×iter limit
1×node limit
Counts
17 → 16
Calls
Call 1
Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(+ 1 (* -1 (pow x 2)))
(pow x 2)
x
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
x
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) x)
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (neg.f64 (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(*.f64 (-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (neg.f64 (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64)))) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) x)
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) x)
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(*.f64 (neg.f64 x) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (neg.f64 (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(*.f64 (neg.f64 x) (-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (neg.f64 (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64)))))

rewrite103.0ms (6.1%)

Memory
7.8MiB live, 146.8MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0516
0813
13813
027313
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
5 → 55
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x
Outputs
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))
(pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))))
(sin.f64 (+.f64 (asin.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (acos.f64 (neg.f64 x)))
(sin.f64 (acos.f64 (fabs.f64 x)))
(sin.f64 (acos.f64 x))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(cos.f64 (neg.f64 (asin.f64 x)))
(cos.f64 (asin.f64 (neg.f64 x)))
(cos.f64 (asin.f64 (fabs.f64 x)))
(cos.f64 (asin.f64 x))
(exp.f64 (*.f64 (log1p.f64 (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (neg.f64 x)) (-.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) (fabs.f64 x)) (-.f64 #s(literal 1 binary64) (fabs.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (neg.f64 x) x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(fma.f64 x (neg.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 x)) x))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
#s(literal 1 binary64)
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)))
(*.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x))
(*.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 #s(literal 1 binary64) x) x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
x

eval15.0ms (0.9%)

Memory
-2.5MiB live, 39.6MiB allocated; 10ms collecting garbage
Compiler

Compiled 811 to 240 computations (70.4% saved)

prune2.0ms (0.1%)

Memory
9.5MiB live, 9.5MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New70272
Fresh000
Picked011
Done000
Total70373
Accuracy
100.0%
Counts
73 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶99.6%
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶99.3%
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
Compiler

Compiled 27 to 22 computations (18.5% saved)

series2.0ms (0.1%)

Memory
6.2MiB live, 6.1MiB allocated; 0ms collecting garbage
Counts
7 → 16
Calls
Call 1
Inputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
Outputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(pow x 2)
x
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2)
1.0ms
x
@-inf
((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2)
0.0ms
x
@0
((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2)

simplify232.0ms (13.7%)

Memory
2.6MiB live, 339.4MiB allocated; 85ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
060212
1149212
2498196
32273187
08363179
Stop Event
1×iter limit
1×node limit
Counts
16 → 15
Calls
Call 1
Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(pow x 2)
x
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
x
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64)))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(neg.f64 (fma.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(neg.f64 (fma.f64 (-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64)))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))

rewrite60.0ms (3.6%)

Memory
-11.6MiB live, 88.1MiB allocated; 9ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01033
01327
15727
043627
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
7 → 51
Calls
Call 1
Inputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
Outputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 (* x x))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 x (*.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))))
(-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (neg.f64 x) x) #s(literal -1/2 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) x)))
(+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)))
(*.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x))
(*.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 #s(literal 1 binary64) x) x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
x
#s(literal -1/2 binary64)

eval10.0ms (0.6%)

Memory
-23.6MiB live, 22.1MiB allocated; 5ms collecting garbage
Compiler

Compiled 1 165 to 213 computations (81.7% saved)

prune2.0ms (0.1%)

Memory
8.0MiB live, 8.0MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New67067
Fresh000
Picked022
Done011
Total67370
Accuracy
100.0%
Counts
70 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓99.6%
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓99.3%
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
Compiler

Compiled 54 to 35 computations (35.2% saved)

regimes5.0ms (0.3%)

Memory
15.5MiB live, 15.5MiB allocated; 0ms collecting garbage
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
Outputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
Calls

4 calls:

1.0ms
x
1.0ms
(*.f64 x x)
1.0ms
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
1.0ms
(-.f64 #s(literal 1 binary64) (*.f64 x x))
Results
AccuracySegmentsBranch
100.0%1(*.f64 x x)
100.0%1(-.f64 #s(literal 1 binary64) (*.f64 x x))
100.0%1(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
100.0%1x
Compiler

Compiled 15 to 12 computations (20% saved)

regimes4.0ms (0.3%)

Memory
16.3MiB live, 16.3MiB allocated; 0ms collecting garbage
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
Outputs
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
Calls

4 calls:

1.0ms
x
1.0ms
(*.f64 x x)
1.0ms
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
1.0ms
(-.f64 #s(literal 1 binary64) (*.f64 x x))
Results
AccuracySegmentsBranch
99.6%1(*.f64 x x)
99.6%1(-.f64 #s(literal 1 binary64) (*.f64 x x))
99.6%1(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
99.6%1x
Compiler

Compiled 15 to 12 computations (20% saved)

regimes5.0ms (0.3%)

Memory
-29.7MiB live, 17.1MiB allocated; 2ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
Outputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
Calls

4 calls:

2.0ms
x
1.0ms
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
1.0ms
(*.f64 x x)
1.0ms
(-.f64 #s(literal 1 binary64) (*.f64 x x))
Results
AccuracySegmentsBranch
99.3%1(*.f64 x x)
99.3%1(-.f64 #s(literal 1 binary64) (*.f64 x x))
99.3%1(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
99.3%1x
Compiler

Compiled 15 to 12 computations (20% saved)

simplify48.0ms (2.8%)

Memory
5.2MiB live, 52.1MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01227
12527
25727
39927
414927
535327
6270527
7682127
Stop Event
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
Outputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

derivations24.0ms (1.4%)

Memory
-18.1MiB live, 31.7MiB allocated; 5ms collecting garbage
Stop Event
1×done
Compiler

Compiled 27 to 13 computations (51.9% saved)

preprocess22.0ms (1.3%)

Memory
2.2MiB live, 48.3MiB allocated; 5ms collecting garbage
Remove

(abs x)

Compiler

Compiled 90 to 56 computations (37.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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