Details

Time bar (total: 17.9s)

sample33.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
5.0ms256×pre80true

simplify3.7s

Counts
1 → 1
Iterations
IterNodes
done5000
74574
61116
5522
4251
3115
252
123
09

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (* y y))
0.0b
(* (- x y) (+ y x))
17.7b
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
10×add-cbrt-cube add-exp-log
8×frac-times associate-/l/
7×add-cube-cbrt
6×flip3-+ flip3-- flip-+ flip--
5×pow1 associate-*l*
4×associate-*r* associate-*l/ associate-*r/
3×expm1-log1p-u associate-/r* times-frac log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in pow-prod-down *-commutative fma-udef div-inv distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 74
Calls
3 calls:
0.0ms
(fma x x (* y y))
35.0ms
(* (- x y) (+ y x))
25.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

series217.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(fma x x (* y y))
76.0ms
(* (- x y) (+ y x))
93.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

simplify1.7s

Counts
83 → 83
Iterations
IterNodes
done5001
22980
1385
0123

prune418.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot x y)
0.0b
(hypot x y)
0.0b
(* (/ (- x y) (hypot x y)) (/ (+ y x) (hypot x y)))
0.0b
(/ (- x y) (hypot x y))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
51×*-un-lft-identity
46×times-frac
31×add-cube-cbrt
19×associate-*l*
18×add-cbrt-cube add-exp-log
16×associate-*r*
7×distribute-lft-out-- difference-of-squares
6×pow1
5×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r* div-inv distribute-lft-out
2×hypot-udef associate-/l/
1×frac-times clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot x y)
0.0ms
(hypot x y)
85.0ms
(* (/ (- x y) (hypot x y)) (/ (+ y x) (hypot x y)))
27.0ms
(/ (- x y) (hypot x y))

series414.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(hypot x y)
84.0ms
(hypot x y)
140.0ms
(* (/ (- x y) (hypot x y)) (/ (+ y x) (hypot x y)))
118.0ms
(/ (- x y) (hypot x y))

simplify1.8s

Counts
133 → 133
Iterations
IterNodes
done5000
22644
1472
0153

prune886.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot x y)
0.0b
(expm1 (log1p (/ (* (/ (+ y x) (hypot x y)) (- x y)) (hypot x y))))
0.0b
(/ (* (/ (+ y x) (hypot x y)) (- x y)) (hypot x y))
1.3b
(log1p (/ (* (/ (+ y x) (hypot x y)) (- x y)) (hypot x y)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube add-exp-log
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×expm1-log1p-u associate-/l/
4×pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
3×associate-/r* times-frac
2×frac-times flip3-- prod-exp associate-*r/ cbrt-unprod flip--
1×log1p-udef expm1-log1p hypot-udef clear-num frac-2neg associate-*l/ log1p-expm1 div-inv associate-/l* expm1-udef
Counts
4 → 62
Calls
4 calls:
0.0ms
(hypot x y)
0.0ms
(expm1 (log1p (/ (* (/ (+ y x) (hypot x y)) (- x y)) (hypot x y))))
40.0ms
(/ (* (/ (+ y x) (hypot x y)) (- x y)) (hypot x y))
1.0ms
(log1p (/ (* (/ (+ y x) (hypot x y)) (- x y)) (hypot x y)))

series912.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(hypot x y)
393.0ms
(expm1 (log1p (/ (* (/ (+ y x) (hypot x y)) (- x y)) (hypot x y))))
151.0ms
(/ (* (/ (+ y x) (hypot x y)) (- x y)) (hypot x y))
304.0ms
(log1p (/ (* (/ (+ y x) (hypot x y)) (- x y)) (hypot x y)))

simplify1.2s

Counts
74 → 74
Iterations
IterNodes
done5000
21737
1323
0119

prune484.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y)))
0.0b
(/ (hypot x y) (- x y))
0.3b
(expm1 (/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y))))
1.0b
(log1p (log1p (expm1 (/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y))))))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
870×times-frac
585×*-un-lft-identity
453×add-sqr-sqrt
343×add-cube-cbrt
66×distribute-lft-out
55×distribute-lft-out-- difference-of-squares
41×div-inv
37×associate-/r/
26×associate-/r*
19×associate-/l*
18×flip3-- add-cbrt-cube add-exp-log flip--
9×cbrt-undiv div-exp
5×expm1-log1p-u log1p-expm1-u
4×pow1 add-log-exp
2×clear-num frac-2neg
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef associate-/l/
Counts
4 → 456
Calls
4 calls:
75.0ms
(/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y)))
18.0ms
(/ (hypot x y) (- x y))
1.0ms
(expm1 (/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y))))
1.0ms
(log1p (log1p (expm1 (/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y))))))

series898.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y)))
114.0ms
(/ (hypot x y) (- x y))
197.0ms
(expm1 (/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y))))
453.0ms
(log1p (log1p (expm1 (/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y))))))

simplify959.0ms

Counts
468 → 468
Iterations
IterNodes
done5001
12234
0632

prune2.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done13
113
012

end0.0ms

sample847.0ms

Algorithm
intervals
Results
468.0ms8000×body80valid
195.0ms8000×pre80true