Details

Time bar (total: 4.9s)

sample22.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify24.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0209
1409
2789
31349
42009
52339
62399
72399

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* (* y 4.0) y))
4.0b
(- (* x x) (* (* y 4.0) y))
31.5b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite19.0ms

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:
3.0ms
(+ (* x x) (* (* y 4.0) y))
3.0ms
(- (* x x) (* (* y 4.0) y))
12.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series28.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(+ (* x x) (* (* y 4.0) y))
8.0ms
(- (* x x) (* (* y 4.0) y))
13.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify48.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0254719
11175657
25001641

prune477.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

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

prune36.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
2.0b
(/ x (/ (fma x x (* (* y 4.0) y)) x))
17.1b
(/ (fma x x (* (* y 4.0) y)) y)
20.0b
(/ (fma x x (* (* y 4.0) y)) x)

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:
8.0ms
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
5.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
2.0ms
(/ (fma x x (* (* y 4.0) y)) y)
2.0ms
(/ (fma x x (* (* y 4.0) y)) x)

series43.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
9.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
12.0ms
(/ (fma x x (* (* y 4.0) y)) y)
12.0ms
(/ (fma x x (* (* y 4.0) y)) x)

simplify97.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06131740
132201580
250011575

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
2.0b
(/ x (/ (fma x x (* (* y 4.0) y)) x))
7.6b
(/ (pow x 2) y)
20.0b
(/ (fma x x (* (* y 4.0) y)) x)

rewrite21.0ms

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:
3.0ms
(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
5.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
4.0ms
(/ (pow x 2) y)
2.0ms
(/ (fma x x (* (* y 4.0) y)) x)

series36.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
9.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
4.0ms
(/ (pow x 2) y)
13.0ms
(/ (fma x x (* (* y 4.0) y)) x)

simplify96.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
05821433
130971281
250011279

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes285.0ms

Accuracy

77.9% (4.2b remaining)

Error of 4.6b against oracle of 0.3b and baseline of 19.5b

bsearch76.0ms

Steps
ItersRangePoint
9
3.7878992299232015e+133
1.2064922412751594e+141
1.1879481736734828e+141
9
1.0904804653520417e-193
4.279018400982983e-187
4.2299291990473933e-187
6
-1.9866354412666532e-138
-4.100696315228617e-139
-4.159944505818501e-139
10
-2.2059920124076508e+157
-2.5337000025306127e+146
-1.3594260967832104e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03426
13426

end0.0ms

sample545.0ms

Algorithm
intervals
Results
411.0ms8000×body80valid