Details

Time bar (total: 45.1s)

sample63.0ms

Algorithm
intervals
Results
19.0ms256×body80valid

simplify513.0ms

Counts
1 → 1
Iterations
IterNodes
done186
7186
6177
5152
4109
367
238
119
09

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize128.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* (* y 4.0) y))
2.0b
(- (* x x) (* (* y 4.0) y))
29.8b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite154.0ms

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:
20.0ms
(+ (* x x) (* (* y 4.0) y))
20.0ms
(- (* x x) (* (* y 4.0) y))
106.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series331.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(+ (* x x) (* (* y 4.0) y))
98.0ms
(- (* x x) (* (* y 4.0) y))
167.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify5.5s

Counts
73 → 73
Iterations
IterNodes
done5000
21116
1270
098

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize293.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* (* y 4.0) y))
1.3b
(fma x x (- (* (* y 4.0) y)))
29.8b
(/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube add-log-exp
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log fma-udef div-inv
Counts
3 → 55
Calls
3 calls:
24.0ms
(+ (* x x) (* (* y 4.0) y))
1.0ms
(fma x x (- (* (* y 4.0) y)))
39.0ms
(/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y)))

series686.0ms

Counts
3 → 9
Calls
3 calls:
169.0ms
(+ (* x x) (* (* y 4.0) y))
208.0ms
(fma x x (- (* (* y 4.0) y)))
296.0ms
(/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y)))

simplify10.5s

Counts
64 → 64
Iterations
IterNodes
done5000
32622
2661
1212
087

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
0.0b
(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
2.0b
(- (* x x) (* (* y 4.0) y))
29.8b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
30×exp-prod
27×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
16×log-pow
7×add-log-exp
6×add-exp-log associate-/r/ add-cbrt-cube
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×log-prod flip3-+ div-sub associate-/r* flip-+ div-inv associate-/l*
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg fma-neg diff-log div-exp rem-log-exp prod-diff clear-num rem-exp-log
Counts
4 → 106
Calls
4 calls:
82.0ms
(exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
80.0ms
(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
30.0ms
(- (* x x) (* (* y 4.0) y))
59.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series607.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
185.0ms
(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
108.0ms
(- (* x x) (* (* y 4.0) y))
128.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify10.4s

Counts
118 → 118
Iterations
IterNodes
done5000
34993
21041
1316
0148

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (- (/ (* x x) (fma (* y 4.0) y (* x x))) (* y (/ (* y 4.0) (fma (* y 4.0) y (* x x))))))
1.5b
(* y (/ (* y 4.0) (fma (* y 4.0) y (* x x))))
18.4b
(/ (* y 4.0) (fma (* y 4.0) y (* x x)))
20.2b
(/ (* x x) (fma (* y 4.0) y (* x x)))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log add-cbrt-cube
13×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×times-frac
7×associate-*r*
6×pow1 cbrt-undiv div-exp prod-exp associate-/r* cbrt-unprod
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×associate-*l* div-inv
2×frac-2neg clear-num associate-/l*
1×expm1-log1p associate-*r/ pow-prod-down *-commutative expm1-udef unswap-sqr
Counts
4 → 86
Calls
4 calls:
1.0ms
(expm1 (- (/ (* x x) (fma (* y 4.0) y (* x x))) (* y (/ (* y 4.0) (fma (* y 4.0) y (* x x))))))
134.0ms
(* y (/ (* y 4.0) (fma (* y 4.0) y (* x x))))
21.0ms
(/ (* y 4.0) (fma (* y 4.0) y (* x x)))
21.0ms
(/ (* x x) (fma (* y 4.0) y (* x x)))

series792.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(expm1 (- (/ (* x x) (fma (* y 4.0) y (* x x))) (* y (/ (* y 4.0) (fma (* y 4.0) y (* x x))))))
147.0ms
(* y (/ (* y 4.0) (fma (* y 4.0) y (* x x))))
221.0ms
(/ (* y 4.0) (fma (* y 4.0) y (* x x)))
168.0ms
(/ (* x x) (fma (* y 4.0) y (* x x)))

simplify5.7s

Counts
98 → 98
Iterations
IterNodes
done5002
21355
1346
0131

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes1.1s

Accuracy

53.5% (14.4b remaining)

Error of 14.8b against oracle of 0.4b and baseline of 31.4b

bsearch766.0ms

Steps
ItersRangePoint
3
7.789660942933776e+102
1.051930614453769e+103
1.0275620942826353e+103
9
5.347374519482908e+72
1.0345609728310515e+79
5.419438360639095e+72
9
3.73636363912113e+55
6.757399575956964e+60
4.117086201251835e+60
8
2.5839679515350884e-125
7.533563991116118e-123
4.4279729591410875e-125
10
-8.380652639018829e+71
-6.542924687516393e+55
-1.3024737343616896e+64

simplify17.0ms

Iterations
IterNodes
done41
141
035

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.3s8000×body80valid