math.log/1 on complex, real part

Time bar (total: 1.9s)

analyze64.0ms (3.4%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
0%0%99.9%0.1%0%0%0%3
0%0%99.9%0.1%0%0%0%4
18.8%18.7%81.2%0.1%0%0%0%5
34.4%34.3%65.6%0.1%0%0%0%6
54.7%54.6%45.3%0.1%0%0%0%7
64.8%64.8%35.1%0.1%0%0%0%8
76.2%76.1%23.8%0.1%0%0%0%9
81.8%81.8%18.1%0.1%0%0%0%10
87.8%87.7%12.2%0.1%0%0%0%11
90.8%90.7%9.2%0.1%0%0%0%12
Compiler

Compiled 12 to 8 computations (33.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
ival-mult: 12.0ms (37.8% of total)
ival-log: 9.0ms (28.4% of total)
ival-sqrt: 7.0ms (22.1% of total)
ival-add: 4.0ms (12.6% of total)
const: 1.0ms (3.2% of total)

sample1.6s (83.8%)

Results
1.1s8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 491.0ms
ival-log: 213.0ms (43.4% of total)
ival-mult: 134.0ms (27.3% of total)
ival-sqrt: 76.0ms (15.5% of total)
ival-add: 57.0ms (11.6% of total)
const: 9.0ms (1.8% of total)
backward-pass: 4.0ms (0.8% of total)
Bogosity

preprocess50.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
52×fma-neg
45×fma-define
15×neg-sub0
14×distribute-lft-neg-in
14×unsub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028127
155127
2102127
3187127
4284127
5323127
6333127
Stop Event
1×saturated
Calls
Call 1
Inputs
(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))))
(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))))
(log.f64 (sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im))))
(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im)))))
(neg.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im)))))
(neg.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im))))))
(log.f64 (sqrt.f64 (+.f64 (*.f64 im im) (*.f64 re re))))
Outputs
(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))))
(log.f64 (hypot.f64 re im))
(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))))
(log.f64 (hypot.f64 re im))
(log.f64 (sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im))))
(log.f64 (hypot.f64 re im))
(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im)))))
(log.f64 (hypot.f64 re im))
(neg.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im)))))
(neg.f64 (log.f64 (hypot.f64 re im)))
(neg.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im))))))
(neg.f64 (log.f64 (hypot.f64 re im)))
(log.f64 (sqrt.f64 (+.f64 (*.f64 im im) (*.f64 re re))))
(log.f64 (hypot.f64 re im))
Symmetry

(abs re)

(abs im)

(sort re im)

explain89.0ms (4.8%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1280-4(6.343393040285866e-269 8.509633381194774e-162)(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
00-0-(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))))
00-0-im
00-0-(*.f64 im im)
00-0-(*.f64 re re)
00-0-re
00-0-(+.f64 (*.f64 re re) (*.f64 im im))
Results
57.0ms512×256valid
Compiler

Compiled 81 to 23 computations (71.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 26.0ms
ival-log: 9.0ms (35% of total)
ival-mult: 9.0ms (35% of total)
ival-sqrt: 4.0ms (15.5% of total)
ival-add: 3.0ms (11.7% of total)
const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(log.f64 (hypot.f64 re im))
Compiler

Compiled 6 to 4 computations (33.3% saved)

localize37.0ms (2%)

Results
30.0ms256×256valid
Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
composed: 9.0ms (41.7% of total)
ival-mult: 5.0ms (23.2% of total)
ival-log: 4.0ms (18.5% of total)
ival-sqrt: 2.0ms (9.3% of total)
ival-add: 1.0ms (4.6% of total)
const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done000
Total011
Accuracy
100.0%
Counts
1 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(log.f64 (hypot.f64 re im))
Compiler

Compiled 21 to 13 computations (38.1% saved)

regimes9.0ms (0.5%)

Accuracy

Total -30.4b remaining (-∞%)

Threshold costs -30.4b (-∞%)

Counts
2 → 1
Calls
Call 1
Inputs
(log.f64 (hypot.f64 re im))
(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))))
Outputs
(log.f64 (hypot.f64 re im))
Calls

7 calls:

2.0ms
(*.f64 im im)
1.0ms
im
1.0ms
re
1.0ms
(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))))
1.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Results
AccuracySegmentsBranch
100.0%1re
100.0%1im
100.0%1(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))))
100.0%1(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
100.0%1(+.f64 (*.f64 re re) (*.f64 im im))
100.0%1(*.f64 re re)
100.0%1(*.f64 im im)
Compiler

Compiled 46 to 28 computations (39.1% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01017
Stop Event
1×saturated
Calls
Call 1
Inputs
(log.f64 (hypot.f64 re im))
Outputs
(log.f64 (hypot.f64 re im))

soundness22.0ms (1.2%)

Rules
52×fma-neg
45×fma-define
15×neg-sub0
14×distribute-lft-neg-in
14×unsub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028127
155127
2102127
3187127
4284127
5323127
6333127
Stop Event
1×done
1×saturated
Compiler

Compiled 21 to 13 computations (38.1% saved)

preprocess27.0ms (1.5%)

Remove

(sort re im)

(abs im)

(abs re)

Compiler

Compiled 106 to 70 computations (34% saved)

end0.0ms (0%)

Profiling

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