Details

Time bar (total: 2.8s)

sample16.0ms

Algorithm
intervals
Results
7.0ms256×body80valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0209
1409
2789
31349
42009
52339
62399
72399

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize12.0ms

Local error

Found 2 expressions with local error:

2.8b
(- (* x x) (* (* y 4.0) y))
31.7b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff clear-num flip-+ div-inv
Counts
2 → 50
Calls
2 calls:
3.0ms
(- (* x x) (* (* y 4.0) y))
11.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series123.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(- (* x x) (* (* y 4.0) y))
69.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify46.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0237617
11114565
25002555

prune165.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

prune9.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ x (/ (fma x x (* (* y 4.0) y)) x))
1.4b
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
18.8b
(/ (fma x x (* (* y 4.0) y)) x)
20.2b
(/ (fma x x (* (* y 4.0) y)) y)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
124×times-frac
76×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×associate-/r*
25×add-exp-log add-cbrt-cube
11×cbrt-undiv div-exp
10×div-inv associate-/l*
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×prod-exp associate-/r/ cbrt-unprod
Counts
4 → 178
Calls
4 calls:
5.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
6.0ms
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
2.0ms
(/ (fma x x (* (* y 4.0) y)) x)
2.0ms
(/ (fma x x (* (* y 4.0) y)) y)

series283.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
59.0ms
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
81.0ms
(/ (fma x x (* (* y 4.0) y)) x)
76.0ms
(/ (fma x x (* (* y 4.0) y)) y)

simplify98.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
06131740
132201580
250011580

prune510.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (* x x) (* (* y 4.0) y))
30.2b
(sqrt (+ (* x x) (* (* y 4.0) y)))
30.2b
(sqrt (+ (* x x) (* (* y 4.0) y)))
30.3b
(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num div-inv
Counts
4 → 96
Calls
4 calls:
3.0ms
(- (* x x) (* (* y 4.0) y))
4.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
4.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
12.0ms
(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

series287.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* x x) (* (* y 4.0) y))
65.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
64.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
114.0ms
(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

simplify54.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
02941179
111991104
250011085

prune328.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.6b

regimes207.0ms

Accuracy

58.2% (13.1b remaining)

Error of 13.5b against oracle of 0.4b and baseline of 31.7b

bsearch181.0ms

Steps
ItersRangePoint
9
4.283497980630725e+128
1.2086931281044804e+136
2.4967207998252852e+132
8
4.2706539415928307e+104
2.1878188410446244e+107
2.0587973952335703e+107
7
4.816160122085315e-63
1.371182844040792e-61
1.198566414608277e-62
7
-2.4883474419946845e-96
-1.2073393430268885e-97
-1.580626566055513e-97
7
-2.854726066546375e+174
-4.469800189377323e+172
-4.542223976096402e+172

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03224
13224

end0.0ms

sample367.0ms

Algorithm
intervals
Results
233.0ms8000×body80valid