bug329 (missed optimization)

Time bar (total: 1.1s)

start0.0ms (0%)

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

analyze17.0ms (1.5%)

Memory
-29.4MiB live, 13.6MiB allocated; 12ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50%50%0%0%0%0
0%0%50%50%0%0%0%1
50%25%25%50%0%0%0%2
50%25%25%50%0%0%0%3
75%37.5%12.5%50%0%0%0%4
75%37.5%12.5%50%0%0%0%5
87.5%43.7%6.2%50%0%0%0%6
87.5%43.7%6.2%50%0%0%0%7
93.8%46.8%3.1%50%0%0%0%8
93.8%46.8%3.1%50%0%0%0%9
96.9%48.4%1.6%50%0%0%0%10
96.9%48.4%1.6%50%0%0%0%11
98.4%49.2%0.8%50%0%0%0%12
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample575.0ms (51.3%)

Memory
37.1MiB live, 647.3MiB allocated; 195ms collecting garbage
Samples
364.0ms8 255×0valid
0.0ms1×1valid
Precisions
Click to see histograms. Total time spent on operations: 137.0ms
ival-atan: 78.0ms (56.9% of total)
ival-div!: 57.0ms (41.6% of total)
adjust: 1.0ms (0.7% of total)
Bogosity

preprocess72.0ms (6.5%)

Memory
-18.7MiB live, 24.6MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
13326
28626
316226
442826
5242826
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(atan.f64 (/.f64 y x))
Symmetry

(negabs x)

(negabs y)

Compiler

Compiled 8 to 8 computations (0% saved)

rewrite129.0ms (11.5%)

Memory
-51.5MiB live, 101.7MiB allocated; 86ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049
069
1129
2329
3909
02959
Stop Event
1×iter-limit
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
4 → 21
Calls
Call 1
Inputs
(atan.f64 (/.f64 y x))
(/.f64 y x)
y
x
Outputs
(neg.f64 (atan.f64 (/.f64 (neg.f64 y) x)))
(atan.f64 (/.f64 y x))
(*.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 y) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 y) #s(literal -1 binary64)) x)
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 y)) x)
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 y)) (*.f64 #s(literal 2 binary64) (neg.f64 x)))
(/.f64 (*.f64 #s(literal 2 binary64) y) (*.f64 #s(literal 2 binary64) x))
(/.f64 (neg.f64 y) (neg.f64 x))
(/.f64 y x)
(neg.f64 (/.f64 (neg.f64 y) x))
y
x

eval2.0ms (0.2%)

Memory
4.2MiB live, 4.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 74 to 56 computations (24.3% saved)

prune1.0ms (0.1%)

Memory
2.0MiB live, 2.0MiB allocated; 0ms collecting garbage
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New16117
Fresh000
Picked011
Done000
Total16218
Accuracy
100.0%
Counts
18 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(atan.f64 (/.f64 y x))
▶99.7%
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
Compiler

Compiled 12 to 11 computations (8.3% saved)

rewrite20.0ms (1.8%)

Memory
22.7MiB live, 22.7MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0730
01130
12322
08122
Stop Event
1×iter-limit
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
7 → 24
Calls
Call 1
Inputs
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(pow.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)
y
Outputs
(atan.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) y))
(*.f64 (*.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) y)
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 y (pow.f64 x #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1/4 binary64))) (fabs.f64 (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) (neg.f64 (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal -1/2 binary64))
(fabs.f64 (pow.f64 x #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))))
x
#s(literal -1/2 binary64)
(*.f64 (*.f64 y (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))
(*.f64 y (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)
y

eval2.0ms (0.2%)

Memory
3.9MiB live, 3.9MiB allocated; 0ms collecting garbage
Compiler

Compiled 142 to 77 computations (45.8% saved)

prune2.0ms (0.1%)

Memory
2.6MiB live, 2.6MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New16218
Fresh000
Picked011
Done011
Total16420
Accuracy
100.0%
Counts
20 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(atan.f64 (/.f64 y x))
▶99.7%
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))))
▶99.7%
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))))
✓99.7%
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
Compiler

Compiled 34 to 31 computations (8.8% saved)

rewrite43.0ms (3.9%)

Memory
-0.5MiB live, 43.9MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01492
02472
14968
015468
Stop Event
1×iter-limit
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
14 → 77
Calls
Call 1
Inputs
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y)))
(pow.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))
(pow.f64 x #s(literal -1/4 binary64))
#s(literal -1/4 binary64)
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) y)
y
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)
Outputs
(atan.f64 (*.f64 (pow.f64 x #s(literal -3/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y)))
(*.f64 (*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -1/4 binary64))) y)
(*.f64 (*.f64 (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -3/4 binary64))) y)
(*.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) y)
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)))
(*.f64 (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 y (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) (neg.f64 (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal -1/2 binary64))
(fabs.f64 (pow.f64 x #s(literal -1/2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -1/4 binary64) (*.f64 (log.f64 x) #s(literal -1/4 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))))
x
#s(literal -1/2 binary64)
(*.f64 (*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 y (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1/8 binary64))) (fabs.f64 (pow.f64 x #s(literal -1/8 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1/8 binary64))) (neg.f64 (pow.f64 x #s(literal -1/8 binary64))))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (pow.f64 x #s(literal -1/8 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -1/4 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/8 binary64))
(pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal -1/4 binary64))
(fabs.f64 (pow.f64 x #s(literal -1/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/4 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal -1/4 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal -1/4 binary64))))
#s(literal -1/4 binary64)
(*.f64 (*.f64 y (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) y))
(*.f64 y (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) y)
y
(atan.f64 (*.f64 (pow.f64 x #s(literal -3/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y)))
(*.f64 (*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -1/4 binary64))) y)
(*.f64 (*.f64 (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -3/4 binary64))) y)
(*.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) y)
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)))
(*.f64 (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 y (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (*.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 y (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))
(*.f64 (*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 y (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)

eval16.0ms (1.4%)

Memory
-22.9MiB live, 21.4MiB allocated; 7ms collecting garbage
Compiler

Compiled 522 to 262 computations (49.8% saved)

prune2.0ms (0.2%)

Memory
6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New67168
Fresh000
Picked112
Done112
Total69372
Accuracy
100.0%
Counts
72 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(atan.f64 (/.f64 y x))
▶99.8%
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)))
✓99.7%
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))))
Compiler

Compiled 24 to 23 computations (4.2% saved)

series142.0ms (12.6%)

Memory
23.5MiB live, 163.0MiB allocated; 28ms collecting garbage
Counts
9 → 11
Calls
Call 1
Inputs
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y))
(pow.f64 x #s(literal -1/4 binary64))
x
#s(literal -1/4 binary64)
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)
(pow.f64 x #s(literal -3/4 binary64))
#s(literal -3/4 binary64)
y
Outputs
#s(approx (atan (* (pow x -1/4) (* (pow x -3/4) y))) #s(hole binary64 (atan (* y (* (pow x -3/4) (pow x -1/4))))))
#s(approx (* (pow x -1/4) (* (pow x -3/4) y)) #s(hole binary64 (* y (* (pow x -3/4) (pow x -1/4)))))
#s(approx (pow x -1/4) #s(hole binary64 (pow x -1/4)))
#s(approx x #s(hole binary64 x))
#s(approx (* (pow x -3/4) y) #s(hole binary64 (* y (pow x -3/4))))
#s(approx (pow x -3/4) #s(hole binary64 (pow x -3/4)))
#s(approx (* (pow x -1/4) (* (pow x -3/4) y)) #s(hole binary64 (* y (* (pow (/ 1 x) 1/4) (pow (/ 1 x) 3/4)))))
#s(approx (pow x -1/4) #s(hole binary64 (pow (/ 1 x) 1/4)))
#s(approx (* (pow x -3/4) y) #s(hole binary64 (* y (pow (/ 1 x) 3/4))))
#s(approx (pow x -3/4) #s(hole binary64 (pow (/ 1 x) 3/4)))
#s(approx y #s(hole binary64 y))
Calls

6 calls:

TimeVariablePointExpression
46.0ms
x
@0
((atan (* (pow x -1/4) (* (pow x -3/4) y))) (* (pow x -1/4) (* (pow x -3/4) y)) (pow x -1/4) x -1/4 (* (pow x -3/4) y) (pow x -3/4) -3/4 y)
37.0ms
x
@-inf
((atan (* (pow x -1/4) (* (pow x -3/4) y))) (* (pow x -1/4) (* (pow x -3/4) y)) (pow x -1/4) x -1/4 (* (pow x -3/4) y) (pow x -3/4) -3/4 y)
36.0ms
y
@0
((atan (* (pow x -1/4) (* (pow x -3/4) y))) (* (pow x -1/4) (* (pow x -3/4) y)) (pow x -1/4) x -1/4 (* (pow x -3/4) y) (pow x -3/4) -3/4 y)
8.0ms
x
@inf
((atan (* (pow x -1/4) (* (pow x -3/4) y))) (* (pow x -1/4) (* (pow x -3/4) y)) (pow x -1/4) x -1/4 (* (pow x -3/4) y) (pow x -3/4) -3/4 y)
8.0ms
y
@-inf
((atan (* (pow x -1/4) (* (pow x -3/4) y))) (* (pow x -1/4) (* (pow x -3/4) y)) (pow x -1/4) x -1/4 (* (pow x -3/4) y) (pow x -3/4) -3/4 y)

rewrite55.0ms (4.9%)

Memory
-3.9MiB live, 41.5MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
038159
044123
197107
0389107
Stop Event
1×iter-limit
1×iter-limit
1×iter-limit
1×unsound
1×iter-limit
Counts
20 → 62
Calls
Call 1
Inputs
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y))
(pow.f64 x #s(literal -1/4 binary64))
x
#s(literal -1/4 binary64)
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)
(pow.f64 x #s(literal -3/4 binary64))
#s(literal -3/4 binary64)
y
#s(approx (atan (* (pow x -1/4) (* (pow x -3/4) y))) #s(hole binary64 (atan (* y (* (pow x -3/4) (pow x -1/4))))))
#s(approx (* (pow x -1/4) (* (pow x -3/4) y)) #s(hole binary64 (* y (* (pow x -3/4) (pow x -1/4)))))
#s(approx (pow x -1/4) #s(hole binary64 (pow x -1/4)))
#s(approx x #s(hole binary64 x))
#s(approx (* (pow x -3/4) y) #s(hole binary64 (* y (pow x -3/4))))
#s(approx (pow x -3/4) #s(hole binary64 (pow x -3/4)))
#s(approx (* (pow x -1/4) (* (pow x -3/4) y)) #s(hole binary64 (* y (* (pow (/ 1 x) 1/4) (pow (/ 1 x) 3/4)))))
#s(approx (pow x -1/4) #s(hole binary64 (pow (/ 1 x) 1/4)))
#s(approx (* (pow x -3/4) y) #s(hole binary64 (* y (pow (/ 1 x) 3/4))))
#s(approx (pow x -3/4) #s(hole binary64 (pow (/ 1 x) 3/4)))
#s(approx y #s(hole binary64 y))
Outputs
(atan.f64 (/.f64 y x))
(*.f64 (*.f64 (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) y) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/8 binary64)))
(*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (*.f64 y (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (*.f64 y #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) y) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)))
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) y) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) y))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) y))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (*.f64 y (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 y #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 y #s(literal 1 binary64)) x)
(/.f64 (*.f64 #s(literal -1 binary64) y) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) y) x)
(/.f64 y x)
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1/8 binary64))) (fabs.f64 (pow.f64 x #s(literal -1/8 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1/8 binary64))) (neg.f64 (pow.f64 x #s(literal -1/8 binary64))))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (pow.f64 x #s(literal -1/8 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -1/4 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/8 binary64))
(pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal -1/4 binary64))
(fabs.f64 (pow.f64 x #s(literal -1/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/4 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal -1/4 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal -1/4 binary64))))
x
#s(literal -1/4 binary64)
(*.f64 (*.f64 y (pow.f64 x #s(literal -3/8 binary64))) (pow.f64 x #s(literal -3/8 binary64)))
(*.f64 (pow.f64 x #s(literal -3/8 binary64)) (*.f64 (pow.f64 x #s(literal -3/8 binary64)) y))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)
(*.f64 y (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal -3/8 binary64))) (fabs.f64 (pow.f64 x #s(literal -3/8 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal -3/8 binary64))) (neg.f64 (pow.f64 x #s(literal -3/8 binary64))))
(*.f64 (pow.f64 x #s(literal -3/8 binary64)) (pow.f64 x #s(literal -3/8 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -3/4 binary64))
(pow.f64 (*.f64 x x) #s(literal -3/8 binary64))
(pow.f64 (pow.f64 x #s(literal -3/8 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal -3/4 binary64))
(fabs.f64 (pow.f64 x #s(literal -3/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -3/4 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal -3/4 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal -3/4 binary64))))
#s(literal -3/4 binary64)
y
#s(approx (atan (* (pow x -1/4) (* (pow x -3/4) y))) (atan.f64 (/.f64 y x)))
#s(approx (* (pow x -1/4) (* (pow x -3/4) y)) (/.f64 y x))
#s(approx (pow x -1/4) (pow.f64 x #s(literal -1/4 binary64)))
#s(approx x x)
#s(approx (* (pow x -3/4) y) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y))
#s(approx (pow x -3/4) (pow.f64 x #s(literal -3/4 binary64)))
#s(approx (* (pow x -1/4) (* (pow x -3/4) y)) (/.f64 y x))
#s(approx (pow x -1/4) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
#s(approx (* (pow x -3/4) y) (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) y))
#s(approx (pow x -3/4) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)))
#s(approx y y)

eval12.0ms (1.1%)

Memory
-39.3MiB live, 12.9MiB allocated; 12ms collecting garbage
Compiler

Compiled 311 to 202 computations (35% saved)

prune6.0ms (0.5%)

Memory
10.4MiB live, 10.4MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New51051
Fresh000
Picked011
Done022
Total51354
Accuracy
100.0%
Counts
54 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(atan.f64 (/.f64 y x))
✓99.8%
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)))
✓99.7%
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))))
Compiler

Compiled 53 to 46 computations (13.2% saved)

regimes7.0ms (0.6%)

Memory
19.2MiB live, 19.2MiB allocated; 0ms collecting garbage
Accuracy

Total -0.3b remaining (-2545.3%)

Threshold costs -0.3b (-2545.3%)

Counts
5 → 1
Calls
Call 1
Inputs
(atan.f64 (/.f64 y x))
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -3/4 binary64)) y)))
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) y))))
(atan.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))))
Outputs
(atan.f64 (/.f64 y x))
Calls

4 calls:

2.0ms
y
2.0ms
x
2.0ms
(/.f64 y x)
1.0ms
(atan.f64 (/.f64 y x))
Results
AccuracySegmentsBranch
100.0%1(/.f64 y x)
100.0%1(atan.f64 (/.f64 y x))
100.0%1x
100.0%1y
Compiler

Compiled 9 to 11 computations (-22.2% saved)

derivations0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Stop Event
1×done
Compiler

Compiled 4 to 4 computations (0% saved)

preprocess17.0ms (1.5%)

Memory
-14.3MiB live, 30.9MiB allocated; 6ms collecting garbage
Remove

(negabs y)

(negabs x)

Compiler

Compiled 24 to 24 computations (0% saved)

end0.0ms (0%)

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

Profiling

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