Details

Time bar (total: 2.6s)

sample18.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify19.0ms

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: 29.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* (* y 4.0) y))
3.0b
(- (* x x) (* (* y 4.0) y))
29.3b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
9.0ms
(+ (* x x) (* (* y 4.0) y))
9.0ms
(- (* x x) (* (* y 4.0) y))
28.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series126.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(+ (* x x) (* (* y 4.0) y))
39.0ms
(- (* x x) (* (* y 4.0) y))
54.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify41.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0254719
11175657
25001641

prune162.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ x (/ (fma x x (* (* y 4.0) y)) x))
2.3b
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
17.8b
(/ (fma x x (* (* y 4.0) y)) x)
17.9b
(/ (fma x x (* (* y 4.0) y)) y)

rewrite41.0ms

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:
9.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
16.0ms
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
5.0ms
(/ (fma x x (* (* y 4.0) y)) x)
5.0ms
(/ (fma x x (* (* y 4.0) y)) y)

series216.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
52.0ms
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
58.0ms
(/ (fma x x (* (* y 4.0) y)) x)
58.0ms
(/ (fma x x (* (* y 4.0) y)) y)

simplify91.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06131740
132201580
250011580

prune409.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ x (/ (fma x x (* (* y 4.0) y)) x))
2.3b
(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
6.7b
(/ (pow x 2) y)
17.8b
(/ (fma x x (* (* y 4.0) y)) x)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
111×times-frac
73×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×associate-/r*
21×add-exp-log
18×add-cbrt-cube
15×associate-/l*
12×unpow-prod-down
9×div-exp
8×div-inv
7×cbrt-undiv
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u unpow2 add-log-exp sqr-pow
1×pow-to-exp pow-exp prod-exp associate-/r/ cbrt-unprod
Counts
4 → 175
Calls
4 calls:
9.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
10.0ms
(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
12.0ms
(/ (pow x 2) y)
5.0ms
(/ (fma x x (* (* y 4.0) y)) x)

series193.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
62.0ms
(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
17.0ms
(/ (pow x 2) y)
65.0ms
(/ (fma x x (* (* y 4.0) y)) x)

simplify83.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05821433
130971281
250011279

prune504.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes62.0ms

Accuracy

80.6% (3.5b remaining)

Error of 3.8b against oracle of 0.3b and baseline of 18.6b

bsearch111.0ms

Steps
ItersRangePoint
3
5.3555028086657875e+144
6.500549118149246e+144
6.373484080558642e+144
9
3.106715750607624e-169
6.710944371906917e-163
6.596793469983034e-163
7
-2.551704287482641e-161
-9.635173331890047e-163
-1.5707844452269527e-162
10
-8.37881605524702e+155
-3.831289382677712e+145
-1.3318871728471391e+154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03222
13222

end0.0ms

sample399.0ms

Algorithm
intervals
Results
223.0ms8000×body80valid