Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A

Time bar (total: 2.9s)

analyze0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 11 to 10 computations (9.1% saved)

sample1.1s (38.3%)

Memory
26.4MiB live, 2 057.0MiB allocated
Samples
896.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 632.0ms
ival-sin: 251.0ms (39.7% of total)
ival-cos: 224.0ms (35.4% of total)
ival-mult: 107.0ms (16.9% of total)
ival-sub: 41.0ms (6.5% of total)
ival-true: 6.0ms (0.9% of total)
ival-assert: 3.0ms (0.5% of total)
Bogosity

preprocess54.0ms (1.8%)

Memory
-17.8MiB live, 68.4MiB allocated
Algorithm
egg-herbie
Rules
208×accelerator-lowering-fma.f32
208×accelerator-lowering-fma.f64
174×distribute-lft-neg-in
168×associate-*r*
162×cancel-sign-sub-inv
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03696
19393
217493
338593
469193
592093
6110293
7115393
8116193
9116593
089
1159
2279
3399
4609
5909
61489
72169
82769
93059
103219
03219
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(- (* x (cos y)) (* z (sin y)))
Outputs
(- (* x (cos y)) (* z (sin y)))
(fma.f64 (sin.f64 y) (-.f64 #s(literal 0 binary64) z) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
Call 2
Inputs
(- (* x (cos y)) (* z (sin y)))
(- (* (neg x) (cos y)) (* z (sin y)))
(- (* x (cos (neg y))) (* z (sin (neg y))))
(- (* x (cos y)) (* (neg z) (sin y)))
(neg (- (* (neg x) (cos y)) (* z (sin y))))
(neg (- (* x (cos (neg y))) (* z (sin (neg y)))))
(neg (- (* x (cos y)) (* (neg z) (sin y))))
(- (* y (cos x)) (* z (sin x)))
(- (* z (cos y)) (* x (sin y)))
(- (* x (cos z)) (* y (sin z)))
Outputs
(- (* x (cos y)) (* z (sin y)))
(- (* (neg x) (cos y)) (* z (sin y)))
(- (* x (neg (cos y))) (* z (sin y)))
(- (* x (cos (neg y))) (* z (sin (neg y))))
(+ (* x (cos y)) (* z (sin y)))
(- (* x (cos y)) (* (neg z) (sin y)))
(+ (* x (cos y)) (* z (sin y)))
(neg (- (* (neg x) (cos y)) (* z (sin y))))
(+ (* x (cos y)) (* z (sin y)))
(neg (- (* x (cos (neg y))) (* z (sin (neg y)))))
(- (* x (neg (cos y))) (* z (sin y)))
(neg (- (* x (cos y)) (* (neg z) (sin y))))
(- (* x (neg (cos y))) (* z (sin y)))
(- (* y (cos x)) (* z (sin x)))
(- (* z (cos y)) (* x (sin y)))
(- (* (cos y) z) (* x (sin y)))
(- (* x (cos z)) (* y (sin z)))

explain106.0ms (3.6%)

Memory
23.0MiB live, 178.8MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
00-0-(sin.f64 y)
00-0-y
00-0-(*.f64 x (cos.f64 y))
00-0-z
00-0-(cos.f64 y)
00-0-x
00-0-(*.f64 z (sin.f64 y))
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
50.0ms512×0valid
Compiler

Compiled 76 to 36 computations (52.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
ival-sin: 12.0ms (37.8% of total)
ival-cos: 10.0ms (31.5% of total)
ival-mult: 6.0ms (18.9% of total)
ival-sub: 2.0ms (6.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory
1.1MiB live, 1.1MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify19.0ms (0.7%)

Memory
-17.0MiB live, 21.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff-64
(*.f64 x (cos.f64 y))
cost-diff0
(sin.f64 y)
cost-diff0
(cos.f64 y)
cost-diff0
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
Rules
208×accelerator-lowering-fma.f32
208×accelerator-lowering-fma.f64
144×*-lowering-*.f32
144×*-lowering-*.f64
64×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0824
11524
22724
33924
46024
59024
614824
721624
827624
930524
1032124
032124
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(- (* x (cos y)) (* z (sin y)))
(* x (cos y))
x
(cos y)
y
(* z (sin y))
z
(sin y)
Outputs
(- (* x (cos y)) (* z (sin y)))
(fma.f64 (sin.f64 y) (-.f64 #s(literal 0 binary64) z) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
x
(cos y)
(cos.f64 y)
y
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
z
(sin y)
(sin.f64 y)

localize35.0ms (1.2%)

Memory
-10.7MiB live, 78.4MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(cos.f64 y)
accuracy100.0%
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
accuracy99.8%
(*.f64 z (sin.f64 y))
accuracy99.8%
(*.f64 x (cos.f64 y))
Samples
28.0ms256×0valid
Compiler

Compiled 26 to 10 computations (61.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-cos: 9.0ms (47.9% of total)
ival-sin: 5.0ms (26.6% of total)
ival-mult: 3.0ms (16% of total)
ival-sub: 1.0ms (5.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series8.0ms (0.3%)

Memory
17.5MiB live, 17.5MiB allocated
Counts
5 → 108
Calls
Call 1
Inputs
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (cos y)>
#<alt (sin y)>
#<alt (* x (cos y))>
#<alt (* z (sin y))>
Outputs
#<alt (* -1 (* z (sin y)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (* x (cos y))>
#<alt (* x (+ (cos y) (* -1 (/ (* z (sin y)) x))))>
#<alt (* x (+ (cos y) (* -1 (/ (* z (sin y)) x))))>
#<alt (* x (+ (cos y) (* -1 (/ (* z (sin y)) x))))>
#<alt (* x (cos y))>
#<alt (* -1 (* x (+ (* -1 (cos y)) (/ (* z (sin y)) x))))>
#<alt (* -1 (* x (+ (* -1 (cos y)) (/ (* z (sin y)) x))))>
#<alt (* -1 (* x (+ (* -1 (cos y)) (/ (* z (sin y)) x))))>
#<alt x>
#<alt (+ x (* -1 (* y z)))>
#<alt (+ x (* y (- (* -1/2 (* x y)) z)))>
#<alt (+ x (* y (- (* y (+ (* -1/2 x) (* 1/6 (* y z)))) z)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (- (* x (cos y)) (* z (sin y)))>
#<alt (* x (cos y))>
#<alt (+ (* -1 (* z (sin y))) (* x (cos y)))>
#<alt (+ (* -1 (* z (sin y))) (* x (cos y)))>
#<alt (+ (* -1 (* z (sin y))) (* x (cos y)))>
#<alt (* -1 (* z (sin y)))>
#<alt (* z (- (/ (* x (cos y)) z) (sin y)))>
#<alt (* z (- (/ (* x (cos y)) z) (sin y)))>
#<alt (* z (- (/ (* x (cos y)) z) (sin y)))>
#<alt (* -1 (* z (sin y)))>
#<alt (* -1 (* z (- (* -1 (/ (* x (cos y)) z)) (* -1 (sin y)))))>
#<alt (* -1 (* z (- (* -1 (/ (* x (cos y)) z)) (* -1 (sin y)))))>
#<alt (* -1 (* z (- (* -1 (/ (* x (cos y)) z)) (* -1 (sin y)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow y 2)))>
#<alt (+ 1 (* (pow y 2) (- (* 1/24 (pow y 2)) 1/2)))>
#<alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/24 (* -1/720 (pow y 2)))) 1/2)))>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt y>
#<alt (* y (+ 1 (* -1/6 (pow y 2))))>
#<alt (* y (+ 1 (* (pow y 2) (- (* 1/120 (pow y 2)) 1/6))))>
#<alt (* y (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/120 (* -1/5040 (pow y 2)))) 1/6))))>
#<alt (sin y)>
#<alt (sin y)>
#<alt (sin y)>
#<alt (sin y)>
#<alt (sin y)>
#<alt (sin y)>
#<alt (sin y)>
#<alt (sin y)>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt x>
#<alt (+ x (* -1/2 (* x (pow y 2))))>
#<alt (+ x (* (pow y 2) (+ (* -1/2 x) (* 1/24 (* x (pow y 2))))))>
#<alt (+ x (* (pow y 2) (+ (* -1/2 x) (* (pow y 2) (+ (* -1/720 (* x (pow y 2))) (* 1/24 x))))))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* y z)>
#<alt (* y (+ z (* -1/6 (* (pow y 2) z))))>
#<alt (* y (+ z (* (pow y 2) (+ (* -1/6 z) (* 1/120 (* (pow y 2) z))))))>
#<alt (* y (+ z (* (pow y 2) (+ (* -1/6 z) (* (pow y 2) (+ (* -1/5040 (* (pow y 2) z)) (* 1/120 z)))))))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
Calls

27 calls:

TimeVariablePointExpression
1.0ms
x
@0
(- (* x (cos y)) (* z (sin y)))
1.0ms
z
@0
(- (* x (cos y)) (* z (sin y)))
1.0ms
y
@-inf
(- (* x (cos y)) (* z (sin y)))
1.0ms
y
@inf
(- (* x (cos y)) (* z (sin y)))
0.0ms
y
@0
(- (* x (cos y)) (* z (sin y)))

rewrite487.0ms (16.6%)

Memory
-15.1MiB live, 792.4MiB allocated
Algorithm
batch-egg-rewrite
Rules
10 986×accelerator-lowering-fma.f32
10 986×accelerator-lowering-fma.f64
4 356×*-lowering-*.f32
4 356×*-lowering-*.f64
3 866×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0821
12821
220521
3198121
0836621
Stop Event
iter limit
node limit
Counts
5 → 232
Calls
Call 1
Inputs
(- (* x (cos y)) (* z (sin y)))
(cos y)
(sin y)
(* x (cos y))
(* z (sin y))
Outputs
(+.f64 (*.f64 x (cos.f64 y)) (-.f64 #s(literal 0 binary64) (*.f64 z (sin.f64 y))))
(+.f64 (-.f64 #s(literal 0 binary64) (*.f64 z (sin.f64 y))) (*.f64 x (cos.f64 y)))
(+.f64 (/.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 3 binary64)) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))) (neg.f64 (/.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64)) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (/.f64 (*.f64 x x) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (/.f64 (*.f64 z z) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))) #s(literal -1 binary64)))
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
(-.f64 (/.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 3 binary64)) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))) (/.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64)) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))
(-.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (/.f64 (*.f64 x x) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (/.f64 (*.f64 z z) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 z (sin.f64 y)) (*.f64 x (cos.f64 y))))
(-.f64 (fma.f64 x (cos.f64 y) #s(literal 0 binary64)) (*.f64 z (sin.f64 y)))
(-.f64 (/.f64 (/.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 9 binary64)) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 6 binary64)) (pow.f64 (*.f64 (cos.f64 y) (*.f64 x (*.f64 z (sin.f64 y)))) #s(literal 3 binary64))))) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))) (/.f64 (/.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 9 binary64)) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 6 binary64)) (pow.f64 (*.f64 (cos.f64 y) (*.f64 x (*.f64 z (sin.f64 y)))) #s(literal 3 binary64))))) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64)))) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))) (/.f64 (/.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64)))) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))
(-.f64 (/.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 3 binary64)) (fma.f64 z (*.f64 z (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (-.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (*.f64 (*.f64 x (cos.f64 y)) (-.f64 #s(literal 0 binary64) (*.f64 z (sin.f64 y))))))) (/.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64)) (fma.f64 z (*.f64 z (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (-.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (*.f64 (*.f64 x (cos.f64 y)) (-.f64 #s(literal 0 binary64) (*.f64 z (sin.f64 y))))))))
(-.f64 (/.f64 (/.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 9 binary64)) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 6 binary64)) (pow.f64 (*.f64 (cos.f64 y) (*.f64 x (*.f64 z (sin.f64 y)))) #s(literal 3 binary64))))) (fma.f64 z (*.f64 z (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (-.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (*.f64 (*.f64 x (cos.f64 y)) (-.f64 #s(literal 0 binary64) (*.f64 z (sin.f64 y))))))) (/.f64 (/.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 9 binary64)) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 6 binary64)) (pow.f64 (*.f64 (cos.f64 y) (*.f64 x (*.f64 z (sin.f64 y)))) #s(literal 3 binary64))))) (fma.f64 z (*.f64 z (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (-.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (*.f64 (*.f64 x (cos.f64 y)) (-.f64 #s(literal 0 binary64) (*.f64 z (sin.f64 y))))))))
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(*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 6 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 6 binary64))) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64)))))
(*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 6 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 6 binary64))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 z z) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (fma.f64 (*.f64 z z) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 4 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 4 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 4 binary64))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 z z) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))))))
(*.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (neg.f64 (*.f64 z z)) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64)))) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (-.f64 (*.f64 z (sin.f64 y)) (*.f64 x (cos.f64 y))))))
(*.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (neg.f64 (*.f64 z z)) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (neg.f64 (*.f64 z z)) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))))) (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
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(*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64))) (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 4 binary64)) (pow.f64 (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) #s(literal 2 binary64)))) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (neg.f64 (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 6 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 z z) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (fma.f64 (*.f64 z z) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 4 binary64)))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 4 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 z z) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 9 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 6 binary64)) (pow.f64 (*.f64 (cos.f64 y) (*.f64 x (*.f64 z (sin.f64 y)))) #s(literal 3 binary64))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 6 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64)))))
(cos.f64 y)
(sin.f64 y)
(exp.f64 (log.f64 (*.f64 x (cos.f64 y))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (cos.f64 y))) #s(literal 1 binary64)))
(pow.f64 (*.f64 x (cos.f64 y)) #s(literal 1 binary64))
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 (cos.f64 y) #s(literal 1 binary64)))
(*.f64 (pow.f64 (cos.f64 y) #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 (cos.f64 y))))
(*.f64 (exp.f64 (log.f64 (cos.f64 y))) (exp.f64 (log.f64 x)))
(exp.f64 (log.f64 (*.f64 z (sin.f64 y))))
(exp.f64 (*.f64 (log.f64 (*.f64 z (sin.f64 y))) #s(literal 1 binary64)))
(pow.f64 (*.f64 z (sin.f64 y)) #s(literal 1 binary64))
(*.f64 z (sin.f64 y))
(*.f64 (sin.f64 y) z)
(*.f64 (pow.f64 z #s(literal 1 binary64)) (pow.f64 (sin.f64 y) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sin.f64 y) #s(literal 1 binary64)) (pow.f64 z #s(literal 1 binary64)))
(*.f64 (exp.f64 (log.f64 (sin.f64 y))) (exp.f64 (log.f64 z)))
(*.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 (sin.f64 y))))

simplify504.0ms (17.2%)

Memory
-14.6MiB live, 463.3MiB allocated
Algorithm
egg-herbie
Rules
12 936×accelerator-lowering-fma.f32
12 936×accelerator-lowering-fma.f64
4 366×*-lowering-*.f32
4 366×*-lowering-*.f64
2 310×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0112686
1339681
2929669
32675663
44616663
57378663
08249636
Stop Event
iter limit
node limit
Counts
108 → 108
Calls
Call 1
Inputs
(* -1 (* z (sin y)))
(- (* x (cos y)) (* z (sin y)))
(- (* x (cos y)) (* z (sin y)))
(- (* x (cos y)) (* z (sin y)))
(* x (cos y))
(* x (+ (cos y) (* -1 (/ (* z (sin y)) x))))
(* x (+ (cos y) (* -1 (/ (* z (sin y)) x))))
(* x (+ (cos y) (* -1 (/ (* z (sin y)) x))))
(* x (cos y))
(* -1 (* x (+ (* -1 (cos y)) (/ (* z (sin y)) x))))
(* -1 (* x (+ (* -1 (cos y)) (/ (* z (sin y)) x))))
(* -1 (* x (+ (* -1 (cos y)) (/ (* z (sin y)) x))))
x
(+ x (* -1 (* y z)))
(+ x (* y (- (* -1/2 (* x y)) z)))
(+ x (* y (- (* y (+ (* -1/2 x) (* 1/6 (* y z)))) z)))
(- (* x (cos y)) (* z (sin y)))
(- (* x (cos y)) (* z (sin y)))
(- (* x (cos y)) (* z (sin y)))
(- (* x (cos y)) (* z (sin y)))
(- (* x (cos y)) (* z (sin y)))
(- (* x (cos y)) (* z (sin y)))
(- (* x (cos y)) (* z (sin y)))
(- (* x (cos y)) (* z (sin y)))
(* x (cos y))
(+ (* -1 (* z (sin y))) (* x (cos y)))
(+ (* -1 (* z (sin y))) (* x (cos y)))
(+ (* -1 (* z (sin y))) (* x (cos y)))
(* -1 (* z (sin y)))
(* z (- (/ (* x (cos y)) z) (sin y)))
(* z (- (/ (* x (cos y)) z) (sin y)))
(* z (- (/ (* x (cos y)) z) (sin y)))
(* -1 (* z (sin y)))
(* -1 (* z (- (* -1 (/ (* x (cos y)) z)) (* -1 (sin y)))))
(* -1 (* z (- (* -1 (/ (* x (cos y)) z)) (* -1 (sin y)))))
(* -1 (* z (- (* -1 (/ (* x (cos y)) z)) (* -1 (sin y)))))
1
(+ 1 (* -1/2 (pow y 2)))
(+ 1 (* (pow y 2) (- (* 1/24 (pow y 2)) 1/2)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/24 (* -1/720 (pow y 2)))) 1/2)))
(cos y)
(cos y)
(cos y)
(cos y)
(cos y)
(cos y)
(cos y)
(cos y)
y
(* y (+ 1 (* -1/6 (pow y 2))))
(* y (+ 1 (* (pow y 2) (- (* 1/120 (pow y 2)) 1/6))))
(* y (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/120 (* -1/5040 (pow y 2)))) 1/6))))
(sin y)
(sin y)
(sin y)
(sin y)
(sin y)
(sin y)
(sin y)
(sin y)
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
x
(+ x (* -1/2 (* x (pow y 2))))
(+ x (* (pow y 2) (+ (* -1/2 x) (* 1/24 (* x (pow y 2))))))
(+ x (* (pow y 2) (+ (* -1/2 x) (* (pow y 2) (+ (* -1/720 (* x (pow y 2))) (* 1/24 x))))))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* x (cos y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* y z)
(* y (+ z (* -1/6 (* (pow y 2) z))))
(* y (+ z (* (pow y 2) (+ (* -1/6 z) (* 1/120 (* (pow y 2) z))))))
(* y (+ z (* (pow y 2) (+ (* -1/6 z) (* (pow y 2) (+ (* -1/5040 (* (pow y 2) z)) (* 1/120 z)))))))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
(* z (sin y))
Outputs
(* -1 (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) #s(literal 0 binary64))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (+ (cos y) (* -1 (/ (* z (sin y)) x))))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* x (+ (cos y) (* -1 (/ (* z (sin y)) x))))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* x (+ (cos y) (* -1 (/ (* z (sin y)) x))))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* -1 (* x (+ (* -1 (cos y)) (/ (* z (sin y)) x))))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* -1 (* x (+ (* -1 (cos y)) (/ (* z (sin y)) x))))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* -1 (* x (+ (* -1 (cos y)) (/ (* z (sin y)) x))))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
x
(+ x (* -1 (* y z)))
(-.f64 x (fma.f64 z y #s(literal 0 binary64)))
(+ x (* y (- (* -1/2 (* x y)) z)))
(fma.f64 y (-.f64 (fma.f64 x (*.f64 y #s(literal -1/2 binary64)) #s(literal 0 binary64)) z) x)
(+ x (* y (- (* y (+ (* -1/2 x) (* 1/6 (* y z)))) z)))
(fma.f64 y (fma.f64 y (fma.f64 x #s(literal -1/2 binary64) (*.f64 (fma.f64 z y #s(literal 0 binary64)) #s(literal 1/6 binary64))) (-.f64 #s(literal 0 binary64) z)) x)
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(+ (* -1 (* z (sin y))) (* x (cos y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(+ (* -1 (* z (sin y))) (* x (cos y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(+ (* -1 (* z (sin y))) (* x (cos y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* -1 (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) #s(literal 0 binary64))
(* z (- (/ (* x (cos y)) z) (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* z (- (/ (* x (cos y)) z) (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* z (- (/ (* x (cos y)) z) (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* -1 (* z (sin y)))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) #s(literal 0 binary64))
(* -1 (* z (- (* -1 (/ (* x (cos y)) z)) (* -1 (sin y)))))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* -1 (* z (- (* -1 (/ (* x (cos y)) z)) (* -1 (sin y)))))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(* -1 (* z (- (* -1 (/ (* x (cos y)) z)) (* -1 (sin y)))))
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow y 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 1/24 (pow y 2)) 1/2)))
(fma.f64 y (*.f64 y (fma.f64 (*.f64 y y) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/24 (* -1/720 (pow y 2)))) 1/2)))
(fma.f64 (*.f64 y y) (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 y #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
y
(* y (+ 1 (* -1/6 (pow y 2))))
(*.f64 y (fma.f64 y (*.f64 y #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* y (+ 1 (* (pow y 2) (- (* 1/120 (pow y 2)) 1/6))))
(*.f64 y (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 y #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* y (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/120 (* -1/5040 (pow y 2)))) 1/6))))
(*.f64 y (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 y (fma.f64 (*.f64 y y) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(sin y)
(sin.f64 y)
(sin y)
(sin.f64 y)
(sin y)
(sin.f64 y)
(sin y)
(sin.f64 y)
(sin y)
(sin.f64 y)
(sin y)
(sin.f64 y)
(sin y)
(sin.f64 y)
(sin y)
(sin.f64 y)
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
x
(+ x (* -1/2 (* x (pow y 2))))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 y y) #s(literal 1 binary64)) #s(literal 0 binary64))
(+ x (* (pow y 2) (+ (* -1/2 x) (* 1/24 (* x (pow y 2))))))
(*.f64 x (fma.f64 y (*.f64 y (fma.f64 (*.f64 y y) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(+ x (* (pow y 2) (+ (* -1/2 x) (* (pow y 2) (+ (* -1/720 (* x (pow y 2))) (* 1/24 x))))))
(fma.f64 (*.f64 x (*.f64 y y)) (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 y #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) x)
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* y z)
(fma.f64 z y #s(literal 0 binary64))
(* y (+ z (* -1/6 (* (pow y 2) z))))
(*.f64 (fma.f64 z y #s(literal 0 binary64)) (fma.f64 y (*.f64 y #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* y (+ z (* (pow y 2) (+ (* -1/6 z) (* 1/120 (* (pow y 2) z))))))
(*.f64 z (*.f64 y (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 y #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(* y (+ z (* (pow y 2) (+ (* -1/6 z) (* (pow y 2) (+ (* -1/5040 (* (pow y 2) z)) (* 1/120 z)))))))
(*.f64 y (*.f64 z (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 y (fma.f64 (*.f64 y y) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))

eval44.0ms (1.5%)

Memory
22.3MiB live, 59.3MiB allocated
Compiler

Compiled 15 762 to 736 computations (95.3% saved)

prune65.0ms (2.2%)

Memory
21.4MiB live, 59.6MiB allocated
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New32614340
Fresh000
Picked011
Done000
Total32615341
Accuracy
99.9%
Counts
341 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
58.7%
(fma.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (neg.f64 (*.f64 z z))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (*.f64 z (sin.f64 y)))) (*.f64 x (cos.f64 y)))
71.3%
(fma.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (/.f64 x (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (/.f64 (*.f64 z z) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))
37.2%
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) #s(literal 0 binary64))
50.4%
(fma.f64 y (fma.f64 y (fma.f64 x #s(literal -1/2 binary64) (*.f64 (fma.f64 z y #s(literal 0 binary64)) #s(literal 1/6 binary64))) (-.f64 #s(literal 0 binary64) z)) x)
50.3%
(fma.f64 y (-.f64 (fma.f64 x (*.f64 y #s(literal -1/2 binary64)) #s(literal 0 binary64)) z) x)
64.2%
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
48.6%
(/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (neg.f64 (*.f64 z z)) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))
42.8%
(/.f64 (+.f64 (neg.f64 (pow.f64 (*.f64 x (cos.f64 y)) #s(literal 3 binary64))) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (*.f64 (*.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))
99.6%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
55.3%
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (*.f64 y (fma.f64 y (*.f64 y #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
99.8%
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
51.8%
(-.f64 x (fma.f64 z y #s(literal 0 binary64)))
74.3%
(-.f64 x (*.f64 z (sin.f64 y)))
48.6%
(*.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (neg.f64 (*.f64 z z)) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
40.3%
x
Compiler

Compiled 620 to 360 computations (41.9% saved)

simplify488.0ms (16.6%)

Memory
-18.3MiB live, 413.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (neg.f64 (*.f64 z z)) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))
cost-diff192
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))
cost-diff192
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))
cost-diff6784
(fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (neg.f64 (*.f64 z z)) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))))
cost-diff0
(sin.f64 y)
cost-diff0
(-.f64 #s(literal 0 binary64) (sin.f64 y))
cost-diff0
(fma.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y)) #s(literal 0 binary64))
cost-diff0
(fma.f64 z y #s(literal 0 binary64))
cost-diff0
(fma.f64 x #s(literal -1/2 binary64) (*.f64 (fma.f64 z y #s(literal 0 binary64)) #s(literal 1/6 binary64)))
cost-diff0
(fma.f64 y (fma.f64 x #s(literal -1/2 binary64) (*.f64 (fma.f64 z y #s(literal 0 binary64)) #s(literal 1/6 binary64))) (-.f64 #s(literal 0 binary64) z))
cost-diff0
(fma.f64 y (fma.f64 y (fma.f64 x #s(literal -1/2 binary64) (*.f64 (fma.f64 z y #s(literal 0 binary64)) #s(literal 1/6 binary64))) (-.f64 #s(literal 0 binary64) z)) x)
cost-diff0
(cos.f64 y)
cost-diff0
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
cost-diff0
(/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
cost-diff1408
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
Rules
9 736×accelerator-lowering-fma.f32
9 736×accelerator-lowering-fma.f64
3 454×*-lowering-*.f32
3 454×*-lowering-*.f64
1 900×--lowering--.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
041250
1110246
2285246
3737246
41716242
53422240
65700240
08056227
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(/ 1 (/ 1 (- (* x (cos y)) (* z (sin y)))))
1
(/ 1 (- (* x (cos y)) (* z (sin y))))
(- (* x (cos y)) (* z (sin y)))
(* x (cos y))
x
(cos y)
y
(* z (sin y))
z
(sin y)
x
(+ (* y (+ (* y (+ (* x -1/2) (* (+ (* z y) 0) 1/6))) (- 0 z))) x)
y
(+ (* y (+ (* x -1/2) (* (+ (* z y) 0) 1/6))) (- 0 z))
(+ (* x -1/2) (* (+ (* z y) 0) 1/6))
x
-1/2
(* (+ (* z y) 0) 1/6)
(+ (* z y) 0)
z
0
1/6
(- 0 z)
(+ (* z (- 0 (sin y))) 0)
z
(- 0 (sin y))
0
(sin y)
y
(/ (+ (* (- 1/2 (* 1/2 (cos (+ y y)))) (neg (* z z))) (* (* x x) (+ 1/2 (* 1/2 (cos (+ y y)))))) (+ (* x (cos y)) (* z (sin y))))
(+ (* (- 1/2 (* 1/2 (cos (+ y y)))) (neg (* z z))) (* (* x x) (+ 1/2 (* 1/2 (cos (+ y y))))))
(- 1/2 (* 1/2 (cos (+ y y))))
1/2
(* 1/2 (cos (+ y y)))
(cos (+ y y))
(+ y y)
y
(neg (* z z))
(* z z)
z
(* (* x x) (+ 1/2 (* 1/2 (cos (+ y y)))))
(* x x)
x
(+ 1/2 (* 1/2 (cos (+ y y))))
(+ (* x (cos y)) (* z (sin y)))
(cos y)
(* z (sin y))
(sin y)
Outputs
(/ 1 (/ 1 (- (* x (cos y)) (* z (sin y)))))
(fma.f64 x (cos.f64 y) (fma.f64 (sin.f64 y) (-.f64 #s(literal 0 binary64) z) #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(/ 1 (- (* x (cos y)) (* z (sin y))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (cos.f64 y) (fma.f64 (sin.f64 y) (-.f64 #s(literal 0 binary64) z) #s(literal 0 binary64))))
(- (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 (sin.f64 y) (-.f64 #s(literal 0 binary64) z) #s(literal 0 binary64)))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
x
(cos y)
(cos.f64 y)
y
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
z
(sin y)
(sin.f64 y)
x
(+ (* y (+ (* y (+ (* x -1/2) (* (+ (* z y) 0) 1/6))) (- 0 z))) x)
(fma.f64 (fma.f64 y (fma.f64 y (fma.f64 z #s(literal -1/6 binary64) #s(literal 0 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64))) z) (-.f64 #s(literal 0 binary64) y) x)
y
(+ (* y (+ (* x -1/2) (* (+ (* z y) 0) 1/6))) (- 0 z))
(fma.f64 y (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (fma.f64 y z #s(literal 0 binary64)) #s(literal 1/6 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) z))
(+ (* x -1/2) (* (+ (* z y) 0) 1/6))
(fma.f64 x #s(literal -1/2 binary64) (fma.f64 (fma.f64 y z #s(literal 0 binary64)) #s(literal 1/6 binary64) #s(literal 0 binary64)))
x
-1/2
#s(literal -1/2 binary64)
(* (+ (* z y) 0) 1/6)
(fma.f64 (fma.f64 y z #s(literal 0 binary64)) #s(literal 1/6 binary64) #s(literal 0 binary64))
(+ (* z y) 0)
(fma.f64 y z #s(literal 0 binary64))
z
0
#s(literal 0 binary64)
1/6
#s(literal 1/6 binary64)
(- 0 z)
(-.f64 #s(literal 0 binary64) z)
(+ (* z (- 0 (sin y))) 0)
(fma.f64 (sin.f64 y) (-.f64 #s(literal 0 binary64) z) #s(literal 0 binary64))
z
(- 0 (sin y))
(-.f64 #s(literal 0 binary64) (sin.f64 y))
0
#s(literal 0 binary64)
(sin y)
(sin.f64 y)
y
(/ (+ (* (- 1/2 (* 1/2 (cos (+ y y)))) (neg (* z z))) (* (* x x) (+ 1/2 (* 1/2 (cos (+ y y)))))) (+ (* x (cos y)) (* z (sin y))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 y y)) (fma.f64 x x (fma.f64 z z #s(literal 0 binary64))) (fma.f64 (-.f64 x z) (+.f64 x z) #s(literal 0 binary64))) #s(literal 0 binary64)) (fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64))))
(+ (* (- 1/2 (* 1/2 (cos (+ y y)))) (neg (* z z))) (* (* x x) (+ 1/2 (* 1/2 (cos (+ y y))))))
(fma.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 y y)) (fma.f64 x x (fma.f64 z z #s(literal 0 binary64))) (fma.f64 (-.f64 x z) (+.f64 x z) #s(literal 0 binary64))) #s(literal 0 binary64))
(- 1/2 (* 1/2 (cos (+ y y))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* 1/2 (cos (+ y y)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal 0 binary64))
(cos (+ y y))
(cos.f64 (+.f64 y y))
(+ y y)
(+.f64 y y)
y
(neg (* z z))
(-.f64 #s(literal 0 binary64) (fma.f64 z z #s(literal 0 binary64)))
(* z z)
(fma.f64 z z #s(literal 0 binary64))
z
(* (* x x) (+ 1/2 (* 1/2 (cos (+ y y)))))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal 1/2 binary64)) #s(literal 0 binary64))
(* x x)
(fma.f64 x x #s(literal 0 binary64))
x
(+ 1/2 (* 1/2 (cos (+ y y))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal 1/2 binary64))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(cos y)
(cos.f64 y)
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(sin y)
(sin.f64 y)

localize1.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Compiler

Compiled 257 to 43 computations (83.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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