Difference of squares

Time bar (total: 9.6s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.1MiB live, 0.1MiB 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 9 to 7 computations (22.2% saved)

sample803.0ms (8.4%)

Memory
2.8MiB live, 564.4MiB allocated
Samples
532.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 286.0ms
ival-mult: 192.0ms (67.2% of total)
ival-sub: 83.0ms (29.1% of total)
ival-true: 7.0ms (2.5% of total)
ival-assert: 3.0ms (1.1% of total)
Bogosity

explain89.0ms (0.9%)

Memory
10.4MiB live, 49.8MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
170-0-(-.f64 (*.f64 a a) (*.f64 b b))
00-0-(*.f64 a a)
00-0-a
00-0-b
00-0-(*.f64 b b)
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (*.f64 a a) (*.f64 b b))nan-rescue170
(*.f64 a a)overflow57
(*.f64 b b)overflow63
Confusion
Predicted +Predicted -
+170
-0239
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+1700
-00239
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0239
117
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
22.0ms512×0valid
Compiler

Compiled 56 to 24 computations (57.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 7.0ms (71.3% of total)
ival-sub: 2.0ms (20.4% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess463.0ms (4.8%)

Memory
18.4MiB live, 248.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01338
15135
214435
336635
489235
5122335
6175435
7234035
8415235
9472735
10484035
11495435
12503435
13503435
14641535
15739335
16787735
17789335
18789335
057
087
1167
2277
3537
41147
53157
65677
712387
824957
941247
1049977
1153667
1255967
1357107
1457107
1566707
1668307
1771507
1871507
1975507
2077107
2177907
2277907
2377907
0102687
Stop Event
iter limit
node limit
iter limit
node limit
Calls
Call 1
Inputs
(-.f64 (*.f64 a a) (*.f64 b b))
Outputs
(-.f64 (*.f64 a a) (*.f64 b b))
(fma.f64 (neg.f64 b) b (*.f64 a a))
Symmetry

(abs b)

(abs a)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.8MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
93.4%
(-.f64 (*.f64 a a) (*.f64 b b))
Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.8s (50.3%)

Memory
5.3MiB live, 167.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 b b)
cost-diff0
(*.f64 a a)
cost-diff0
(-.f64 (*.f64 a a) (*.f64 b b))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0515
0815
11615
22715
35315
411415
531515
656715
7123815
8249515
9412415
10499715
11536615
12559615
13571015
14571015
15667015
16683015
17715015
18715015
19755015
20771015
21779015
22779015
23779015
01026815
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b
Outputs
(-.f64 (*.f64 a a) (*.f64 b b))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(*.f64 a a)
a
(*.f64 b b)
b

localize98.0ms (1%)

Memory
-4.4MiB live, 40.3MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 b b)
accuracy0
(*.f64 a a)
accuracy3.99997522996247
(-.f64 (*.f64 a a) (*.f64 b b))
Samples
94.0ms256×0valid
Compiler

Compiled 32 to 12 computations (62.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 53.0ms
ival-mult: 51.0ms (96.6% of total)
ival-sub: 1.0ms (1.9% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series33.0ms (0.3%)

Memory
-30.0MiB live, 9.0MiB allocated
Counts
3 → 7
Calls
Call 1
Inputs
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
(*.f64 b b)
Outputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(+ (* -1 (pow b 2)) (pow a 2))
(pow b 2)
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
Calls

6 calls:

TimeVariablePointExpression
31.0ms
a
@0
((- (* a a) (* b b)) (* a a) (* b b))
1.0ms
a
@inf
((- (* a a) (* b b)) (* a a) (* b b))
0.0ms
b
@-inf
((- (* a a) (* b b)) (* a a) (* b b))
0.0ms
b
@inf
((- (* a a) (* b b)) (* a a) (* b b))
0.0ms
a
@-inf
((- (* a a) (* b b)) (* a a) (* b b))

simplify249.0ms (2.6%)

Memory
30.7MiB live, 150.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01738
13938
211338
346938
4168938
5283938
6499438
0839738
Stop Event
iter limit
node limit
Counts
7 → 7
Calls
Call 1
Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(+ (* -1 (pow b 2)) (pow a 2))
(pow b 2)
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
Outputs
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow b 2)
(*.f64 b b)
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))

rewrite583.0ms (6.1%)

Memory
-11.3MiB live, 184.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0513
0813
13213
221613
3196713
0877813
Stop Event
iter limit
node limit
iter limit
Counts
3 → 252
Calls
Call 1
Inputs
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
(*.f64 b b)
Outputs
(*.f64 (pow.f64 (/.f64 (fma.f64 b b (*.f64 a a)) (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 b b (*.f64 a a)) (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 4 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 a #s(literal 8 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 18 binary64)) (pow.f64 b #s(literal 18 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) #s(literal 2 binary64)))) (-.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (pow.f64 (*.f64 b a) #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 3 binary64)) (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 12 binary64)))) (fma.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 binary64))) (pow.f64 a #s(literal 8 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (pow.f64 a #s(literal 4 binary64))))
(*.f64 (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal -1 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))))
(*.f64 (pow.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))
(*.f64 #s(literal 1 binary64) (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (pow.f64 (neg.f64 (fma.f64 b b (*.f64 a a))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) #s(literal -1 binary64)))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(*.f64 (fma.f64 b b (*.f64 a a)) (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (fma.f64 b b (*.f64 a a))))
(*.f64 (fma.f64 b b (*.f64 a a)) (*.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(*.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (*.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (pow.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (fma.f64 a a #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 b #s(literal 6 binary64))) (fma.f64 (fma.f64 a a #s(literal 0 binary64)) (fma.f64 a a #s(literal 0 binary64)) (+.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 (fma.f64 a a #s(literal 0 binary64)) (*.f64 b b)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 b b) (*.f64 a a)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (-.f64 (*.f64 b b) (*.f64 a a)) (*.f64 #s(literal 0 binary64) (-.f64 (*.f64 b b) (*.f64 a a))))))
(/.f64 (+.f64 (pow.f64 (*.f64 b (-.f64 a b)) #s(literal 3 binary64)) (pow.f64 (*.f64 a (-.f64 a b)) #s(literal 3 binary64))) (fma.f64 (*.f64 b (-.f64 a b)) (*.f64 b (-.f64 a b)) (-.f64 (*.f64 (*.f64 a (-.f64 a b)) (*.f64 a (-.f64 a b))) (*.f64 (*.f64 b (-.f64 a b)) (*.f64 a (-.f64 a b))))))
(/.f64 (+.f64 (pow.f64 (*.f64 a (-.f64 a b)) #s(literal 3 binary64)) (pow.f64 (*.f64 b (-.f64 a b)) #s(literal 3 binary64))) (fma.f64 (*.f64 a (-.f64 a b)) (*.f64 a (-.f64 a b)) (-.f64 (*.f64 (*.f64 b (-.f64 a b)) (*.f64 b (-.f64 a b))) (*.f64 (*.f64 a (-.f64 a b)) (*.f64 b (-.f64 a b))))))
(/.f64 (+.f64 (pow.f64 (*.f64 a (+.f64 b a)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 b) (+.f64 b a)) #s(literal 3 binary64))) (fma.f64 (*.f64 a (+.f64 b a)) (*.f64 a (+.f64 b a)) (-.f64 (*.f64 (*.f64 (neg.f64 b) (+.f64 b a)) (*.f64 (neg.f64 b) (+.f64 b a))) (*.f64 (*.f64 a (+.f64 b a)) (*.f64 (neg.f64 b) (+.f64 b a))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (-.f64 a b) b) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 a b) a) #s(literal 3 binary64))) (fma.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) b) (-.f64 (*.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) a)) (*.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) a)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (-.f64 a b) a) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 a b) b) #s(literal 3 binary64))) (fma.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) a) (-.f64 (*.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) b)) (*.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) b)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (+.f64 b a) a) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 b a) (neg.f64 b)) #s(literal 3 binary64))) (fma.f64 (*.f64 (+.f64 b a) a) (*.f64 (+.f64 b a) a) (-.f64 (*.f64 (*.f64 (+.f64 b a) (neg.f64 b)) (*.f64 (+.f64 b a) (neg.f64 b))) (*.f64 (*.f64 (+.f64 b a) a) (*.f64 (+.f64 b a) (neg.f64 b))))))
(/.f64 (+.f64 (/.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 3 binary64))) (pow.f64 (neg.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) #s(literal 2 binary64)) (-.f64 (*.f64 (neg.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a)))) (neg.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))))) (*.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (neg.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (-.f64 (*.f64 (neg.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))))) (neg.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))) (*.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 b a))) (neg.f64 (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (neg.f64 (*.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (+.f64 b a))) (neg.f64 (+.f64 b a)))
(/.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (-.f64 a b))) (neg.f64 (fma.f64 b (-.f64 b a) (*.f64 a a))))
(/.f64 (neg.f64 (*.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (-.f64 a b))) (neg.f64 (-.f64 a b)))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal -1 binary64)))) (neg.f64 (+.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal -1 binary64)))) (neg.f64 (+.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 4 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 a #s(literal 8 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)))) (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))))
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(/.f64 (neg.f64 (*.f64 (-.f64 a b) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))) (neg.f64 (fma.f64 b (-.f64 b a) (*.f64 a a))))
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(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))) (/.f64 (/.f64 (pow.f64 b #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))) (/.f64 (/.f64 (pow.f64 b #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))) (/.f64 (/.f64 (pow.f64 b #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))) (/.f64 (/.f64 (pow.f64 b #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (/.f64 (pow.f64 b #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (/.f64 (pow.f64 b #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(-.f64 (fma.f64 a a #s(literal 0 binary64)) (*.f64 b b))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 b b) (*.f64 a a)))
(-.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(-.f64 (*.f64 a a) (*.f64 b b))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (*.f64 b (-.f64 a b)) (*.f64 a (-.f64 a b)))
(+.f64 (*.f64 a (-.f64 a b)) (*.f64 b (-.f64 a b)))
(+.f64 (*.f64 a (+.f64 b a)) (*.f64 (neg.f64 b) (+.f64 b a)))
(+.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) a))
(+.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) b))
(+.f64 (*.f64 (+.f64 b a) a) (*.f64 (+.f64 b a) (neg.f64 b)))
(+.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (neg.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a)))))
(+.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))))))
(+.f64 (*.f64 (neg.f64 b) b) (*.f64 a a))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 b) b))
(*.f64 a a)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 a))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
(*.f64 (neg.f64 b) (neg.f64 b))
(*.f64 b b)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 b))
(pow.f64 (neg.f64 b) #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 b #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))

eval25.0ms (0.3%)

Memory
11.6MiB live, 49.4MiB allocated
Compiler

Compiled 8 269 to 758 computations (90.8% saved)

prune96.0ms (1%)

Memory
-23.9MiB live, 14.6MiB allocated
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2542256
Fresh000
Picked101
Done000
Total2552257
Accuracy
100.0%
Counts
257 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(*.f64 (-.f64 a b) (+.f64 b a))
51.5%
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify432.0ms (4.5%)

Memory
27.8MiB live, 267.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 b a)
cost-diff0
(-.f64 a b)
cost-diff0
(*.f64 (-.f64 a b) (+.f64 b a))
cost-diff0
(neg.f64 b)
cost-diff0
(*.f64 (neg.f64 b) b)
cost-diff0
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01134
01634
13434
25934
313934
428134
558434
6147334
7287034
8396634
9453334
10477234
11490234
12492434
13492434
14492434
0865834
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 b) b)
(neg.f64 b)
b
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
a
b
(+.f64 b a)
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 b) b)
(neg.f64 b)
b
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(-.f64 a b)
a
b
(+.f64 b a)

localize75.0ms (0.8%)

Memory
-5.7MiB live, 33.2MiB allocated
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 a b)
accuracy0
(+.f64 b a)
accuracy0
(*.f64 (-.f64 a b) (+.f64 b a))
accuracy0
(*.f64 (neg.f64 b) b)
accuracy0
(neg.f64 b)
accuracy31.014017261573088
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Samples
68.0ms256×0valid
Compiler

Compiled 65 to 23 computations (64.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 6.0ms (53.3% of total)
ival-sub: 2.0ms (17.8% of total)
ival-add: 1.0ms (8.9% of total)
ival-neg: 1.0ms (8.9% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory
8.7MiB live, 8.7MiB allocated
Counts
6 → 31
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 b) b)
(neg.f64 b)
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
(+.f64 b a)
Outputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(* -1 b)
(- a b)
b
(+ a b)
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
a
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (/ b a)))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ a (* -1 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* b (- (/ a b) 1))
(* b (+ 1 (/ a b)))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (- (* -1 (/ a b)) 1)))
Calls

6 calls:

TimeVariablePointExpression
1.0ms
b
@-inf
((- (* a a) (* b b)) (* (neg b) b) (neg b) (* (- a b) (+ b a)) (- a b) (+ b a))
1.0ms
b
@inf
((- (* a a) (* b b)) (* (neg b) b) (neg b) (* (- a b) (+ b a)) (- a b) (+ b a))
1.0ms
a
@inf
((- (* a a) (* b b)) (* (neg b) b) (neg b) (* (- a b) (+ b a)) (- a b) (+ b a))
1.0ms
a
@-inf
((- (* a a) (* b b)) (* (neg b) b) (neg b) (* (- a b) (+ b a)) (- a b) (+ b a))
1.0ms
b
@0
((- (* a a) (* b b)) (* (neg b) b) (neg b) (* (- a b) (+ b a)) (- a b) (+ b a))

simplify198.0ms (2.1%)

Memory
-11.6MiB live, 116.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
092132
1281132
2837132
33582132
08444132
Stop Event
iter limit
node limit
Counts
31 → 29
Calls
Call 1
Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(* -1 b)
(- a b)
b
(+ a b)
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
a
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (/ b a)))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ a (* -1 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* b (- (/ a b) 1))
(* b (+ 1 (/ a b)))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (- (* -1 (/ a b)) 1)))
Outputs
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(*.f64 (neg.f64 b) b)
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* -1 b)
(neg.f64 b)
(- a b)
(-.f64 a b)
b
(+ a b)
(+.f64 b a)
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(*.f64 a a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
a
(* a (+ 1 (* -1 (/ b a))))
(-.f64 a b)
(* a (+ 1 (/ b a)))
(+.f64 b a)
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* -1 (* a (- (/ b a) 1)))
(-.f64 a b)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+.f64 b a)
(+ (* -1 (pow b 2)) (pow a 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ (* b (+ a (* -1 a))) (pow a 2))
(*.f64 a a)
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ a (* -1 b))
(-.f64 a b)
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(*.f64 (neg.f64 b) b)
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* b (- (/ a b) 1))
(-.f64 a b)
(* b (+ 1 (/ a b)))
(+.f64 b a)
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(*.f64 (neg.f64 b) b)
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 a b)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(+.f64 b a)

rewrite209.0ms (2.2%)

Memory
-1.0MiB live, 158.1MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01131
01631
16731
250431
3674924
0927824
Stop Event
iter limit
node limit
iter limit
Counts
6 → 723
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 b) b)
(neg.f64 b)
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
(+.f64 b a)
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 b b))
(*.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)))
(*.f64 #s(literal 1 binary64) (*.f64 b b))
(*.f64 #s(literal -1 binary64) (*.f64 b b))
(*.f64 (*.f64 b b) #s(literal 1 binary64))
(*.f64 (*.f64 b b) #s(literal -1 binary64))
(*.f64 b b)
(pow.f64 (exp.f64 (log.f64 b)) #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 b #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) #s(literal 0 binary64)) (-.f64 (*.f64 b b) #s(literal 0 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 b #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 b b)))))
(/.f64 (+.f64 (pow.f64 b #s(literal 6 binary64)) #s(literal 0 binary64)) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 b b) #s(literal 0 binary64)))))
(/.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 b b))
(/.f64 (pow.f64 b #s(literal 6 binary64)) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 b b)))))
(/.f64 (pow.f64 b #s(literal 3 binary64)) b)
(neg.f64 (*.f64 b b))
(fma.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 b b) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 b b) #s(literal 0 binary64))
(fma.f64 (*.f64 b b) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (*.f64 b b) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 b b #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(exp.f64 (*.f64 (*.f64 (log.f64 b) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 b))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 b b))
(+.f64 (*.f64 b b) #s(literal 0 binary64))
(*.f64 (pow.f64 b #s(literal 1/2 binary64)) (pow.f64 b #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) b)
(*.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 (*.f64 b b) #s(literal -1 binary64)))
(*.f64 (*.f64 b b) (pow.f64 b #s(literal -1 binary64)))
(*.f64 b (/.f64 b b))
(*.f64 b #s(literal -1 binary64))
(pow.f64 (pow.f64 b #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (*.f64 b b) (pow.f64 b #s(literal 3 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 b (*.f64 b b)) #s(literal -1 binary64))
(pow.f64 b #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 b b) (pow.f64 b #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 b (*.f64 b b)))
(/.f64 (pow.f64 b #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 b b) #s(literal 0 binary64))))
(/.f64 (pow.f64 b #s(literal 3 binary64)) (*.f64 b b))
(/.f64 (*.f64 b b) b)
(neg.f64 b)
(fma.f64 (pow.f64 b #s(literal 1/2 binary64)) (pow.f64 b #s(literal 1/2 binary64)) #s(literal 0 binary64))
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(+.f64 (*.f64 (/.f64 (-.f64 a b) (-.f64 b a)) b) (*.f64 (/.f64 (-.f64 a b) (-.f64 b a)) (neg.f64 a)))
(+.f64 (*.f64 (/.f64 (pow.f64 (-.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (-.f64 a b) a)) (*.f64 (/.f64 (pow.f64 (-.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 b b)))
(+.f64 (*.f64 (/.f64 (pow.f64 (-.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 b b)) (*.f64 (/.f64 (pow.f64 (-.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (-.f64 a b) a)))
(+.f64 (-.f64 a #s(literal 0 binary64)) b)
(+.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (-.f64 a b) b (*.f64 a a))) (neg.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 b b (*.f64 (-.f64 b a) a)))))
(+.f64 (*.f64 b (/.f64 b (-.f64 b a))) (neg.f64 (*.f64 a (/.f64 a (-.f64 b a)))))
(+.f64 (*.f64 a (/.f64 a (-.f64 a b))) (neg.f64 (*.f64 b (/.f64 b (-.f64 b a)))))
(+.f64 #s(literal 0 binary64) (-.f64 a b))
(+.f64 b (neg.f64 (neg.f64 a)))
(+.f64 b a)
(+.f64 a (*.f64 #s(literal 1 binary64) b))
(+.f64 a b)

eval95.0ms (1%)

Memory
-2.4MiB live, 114.7MiB allocated
Compiler

Compiled 12 091 to 1 341 computations (88.9% saved)

prune9.0ms (0.1%)

Memory
0.9MiB live, 38.7MiB allocated
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New5321533
Fresh000
Picked022
Done000
Total5323535
Accuracy
100.0%
Counts
535 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(*.f64 (-.f64 a b) (+.f64 b a))
51.5%
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
53.8%
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify367.0ms (3.8%)

Memory
25.9MiB live, 215.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 a a)
cost-diff0
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
0815
11615
22715
35315
411515
531815
658015
7125715
8253115
9417015
10503715
11540615
12563615
13575015
14575015
15671015
16687015
17719015
18719015
19759015
20775015
21783015
22783015
23783015
01039715
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
a
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
a

localize16.0ms (0.2%)

Memory
-6.7MiB live, 30.7MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 a a)
accuracy29.570392595004783
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Samples
12.0ms256×0valid
Compiler

Compiled 28 to 14 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 3.0ms (66.1% of total)
ival-sub: 1.0ms (22% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0%)

Memory
4.7MiB live, 4.7MiB allocated
Counts
2 → 6
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
Outputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(+ (* -1 (pow b 2)) (pow a 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
Calls

6 calls:

TimeVariablePointExpression
0.0ms
a
@-inf
((- (* a a) (* b b)) (* a a))
0.0ms
a
@inf
((- (* a a) (* b b)) (* a a))
0.0ms
a
@0
((- (* a a) (* b b)) (* a a))
0.0ms
b
@inf
((- (* a a) (* b b)) (* a a))
0.0ms
b
@-inf
((- (* a a) (* b b)) (* a a))

simplify169.0ms (1.8%)

Memory
-34.4MiB live, 133.8MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01735
13935
211335
346935
4168935
5283935
6499435
0839735
Stop Event
iter limit
node limit
Counts
6 → 6
Calls
Call 1
Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(+ (* -1 (pow b 2)) (pow a 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
Outputs
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))

rewrite162.0ms (1.7%)

Memory
11.4MiB live, 290.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
0814
13214
221614
3196914
0878014
Stop Event
iter limit
node limit
iter limit
Counts
2 → 7
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 a))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))

eval1.0ms (0%)

Memory
3.5MiB live, 3.5MiB allocated
Compiler

Compiled 129 to 32 computations (75.2% saved)

prune2.0ms (0%)

Memory
4.9MiB live, 4.9MiB allocated
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New10010
Fresh000
Picked011
Done022
Total10313
Accuracy
100.0%
Counts
13 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(*.f64 (-.f64 a b) (+.f64 b a))
51.5%
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
53.8%
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Compiler

Compiled 67 to 35 computations (47.8% saved)

regimes11.0ms (0.1%)

Memory
-12.8MiB live, 25.7MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 (*.f64 a a) (*.f64 b b))
Outputs
(*.f64 (-.f64 a b) (+.f64 b a))
Calls

5 calls:

3.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
2.0ms
b
2.0ms
a
2.0ms
(*.f64 b b)
2.0ms
(*.f64 a a)
Results
AccuracySegmentsBranch
100.0%1a
100.0%1b
100.0%1(-.f64 (*.f64 a a) (*.f64 b b))
100.0%1(*.f64 a a)
100.0%1(*.f64 b b)
Compiler

Compiled 15 to 15 computations (0% saved)

regimes8.0ms (0.1%)

Memory
20.0MiB live, 20.0MiB allocated
Counts
2 → 3
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Calls

5 calls:

2.0ms
b
1.0ms
a
1.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
1.0ms
(*.f64 b b)
1.0ms
(*.f64 a a)
Results
AccuracySegmentsBranch
82.5%2a
82.6%2b
97.3%3(-.f64 (*.f64 a a) (*.f64 b b))
82.5%2(*.f64 a a)
82.6%2(*.f64 b b)
Compiler

Compiled 15 to 15 computations (0% saved)

regimes10.0ms (0.1%)

Memory
-25.1MiB live, 18.6MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Calls

5 calls:

5.0ms
b
1.0ms
a
1.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
1.0ms
(*.f64 a a)
1.0ms
(*.f64 b b)
Results
AccuracySegmentsBranch
53.8%1a
53.8%1(*.f64 a a)
53.8%1b
53.8%1(*.f64 b b)
53.8%1(-.f64 (*.f64 a a) (*.f64 b b))
Compiler

Compiled 15 to 15 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.1MiB live, 1.1MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
+inf
NaN
0.0ms
-5e-324
0.0
Compiler

Compiled 10 to 10 computations (0% saved)

simplify22.0ms (0.2%)

Memory
26.2MiB live, 65.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02173
13273
23873
34173
44273
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 (-.f64 a b) (+.f64 b a))
(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -1/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)) (if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal +inf.0 binary64)) #s(approx (- (* a a) (* b b)) (*.f64 a a)) #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Outputs
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -1/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)) (if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal +inf.0 binary64)) #s(approx (- (* a a) (* b b)) (*.f64 a a)) #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))))
#s(approx (- (* a a) (* b b)) (*.f64 a a))

soundness476.0ms (5%)

Memory
-40.5MiB live, 288.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01738
13938
211338
346938
4168938
5283938
6499438
0839738
092132
1281132
2837132
33582132
08444132
0513
0813
13213
221613
3196713
0877813
Stop Event
done
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 105 to 47 computations (55.2% saved)

preprocess61.0ms (0.6%)

Memory
0.1MiB live, 38.9MiB allocated
Remove

(abs a)

(abs b)

Compiler

Compiled 230 to 102 computations (55.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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