Details

Time bar (total: 20.1s)

sample25.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
4.0ms256×pre80true

simplify4.0s

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- x y) (+ y x))
0.0b
(fma x x (* y y))
16.4b
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

rewrite74.0ms

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:
40.0ms
(* (- x y) (+ y x))
0.0ms
(fma x x (* y y))
30.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

series196.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(* (- x y) (+ y x))
44.0ms
(fma x x (* y y))
92.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

simplify2.3s

Counts
83 → 83
Iterations
IterNodes
done5000
23024
1386
0123

prune514.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y)))))
0.0b
(/ (+ y x) (sqrt (fma x x (* y y))))
15.7b
(sqrt (fma x x (* y y)))
15.7b
(sqrt (fma x x (* y y)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
93×*-un-lft-identity
90×times-frac
55×add-cube-cbrt
54×sqrt-prod
34×associate-*l*
28×associate-*r*
18×add-cbrt-cube add-exp-log
13×distribute-lft-out
9×unswap-sqr
8×pow1
6×associate-/r* distribute-lft-out-- difference-of-squares
5×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u associate-/l* add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef hypot-def associate-/l/
1×frac-times clear-num frac-2neg flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+
Counts
4 → 175
Calls
4 calls:
89.0ms
(* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y)))))
30.0ms
(/ (+ y x) (sqrt (fma x x (* y y))))
2.0ms
(sqrt (fma x x (* y y)))
3.0ms
(sqrt (fma x x (* y y)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y)))))
110.0ms
(/ (+ y x) (sqrt (fma x x (* y y))))
81.0ms
(sqrt (fma x x (* y y)))
82.0ms
(sqrt (fma x x (* y y)))

simplify2.0s

Counts
187 → 187
Iterations
IterNodes
done5000
22666
1526
0178

prune922.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
66×add-sqr-sqrt
58×times-frac
40×add-cube-cbrt
20×add-cbrt-cube add-exp-log
19×associate-*r*
16×associate-*l*
9×associate-/l*
7×distribute-lft-out distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv associate-/r* div-exp
5×log1p-expm1-u
4×expm1-log1p-u prod-exp cbrt-unprod div-inv add-log-exp unswap-sqr associate-/l/
2×clear-num frac-2neg
1×frac-times expm1-log1p flip3-+ flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+ flip-- expm1-udef
Counts
4 → 147
Calls
4 calls:
27.0ms
(/ (- x y) (hypot x y))
60.0ms
(* (/ (+ y x) (hypot x y)) (/ (- x y) (hypot x y)))
15.0ms
(/ (+ y x) (hypot x y))
0.0ms
(expm1 (* (/ (+ y x) (hypot x y)) (/ (- x y) (hypot x y))))

series585.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ (- x y) (hypot x y))
141.0ms
(* (/ (+ y x) (hypot x y)) (/ (- x y) (hypot x y)))
154.0ms
(/ (+ y x) (hypot x y))
175.0ms
(expm1 (* (/ (+ y x) (hypot x y)) (/ (- x y) (hypot x y))))

simplify3.1s

Counts
159 → 159
Iterations
IterNodes
done5001
23168
1524
0183

prune766.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (/ (+ y x) (hypot x y)))
0.1b
(cbrt (/ (+ y x) (hypot x y)))
0.1b
(cbrt (/ (+ y x) (hypot x y)))
0.3b
(expm1 (* (* (* (cbrt (/ (+ y x) (hypot x y))) (cbrt (/ (+ y x) (hypot x y)))) (cbrt (/ (+ y x) (hypot x y)))) (/ (- x y) (hypot x y))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
48×cbrt-prod
46×*-un-lft-identity
36×times-frac
28×add-sqr-sqrt add-cube-cbrt
9×distribute-lft-out
5×log1p-expm1-u
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log add-log-exp
3×cbrt-div pow1/3 div-inv
1×expm1-log1p expm1-udef
Counts
4 → 92
Calls
4 calls:
4.0ms
(cbrt (/ (+ y x) (hypot x y)))
4.0ms
(cbrt (/ (+ y x) (hypot x y)))
5.0ms
(cbrt (/ (+ y x) (hypot x y)))
0.0ms
(expm1 (* (* (* (cbrt (/ (+ y x) (hypot x y))) (cbrt (/ (+ y x) (hypot x y)))) (cbrt (/ (+ y x) (hypot x y)))) (/ (- x y) (hypot x y))))

series722.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(cbrt (/ (+ y x) (hypot x y)))
165.0ms
(cbrt (/ (+ y x) (hypot x y)))
158.0ms
(cbrt (/ (+ y x) (hypot x y)))
229.0ms
(expm1 (* (* (* (cbrt (/ (+ y x) (hypot x y))) (cbrt (/ (+ y x) (hypot x y)))) (cbrt (/ (+ y x) (hypot x y)))) (/ (- x y) (hypot x y))))

simplify2.2s

Counts
104 → 104
Iterations
IterNodes
done5001
42285
3525
2196
1115
080

prune753.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes106.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done12
112
010

end0.0ms

sample960.0ms

Algorithm
intervals
Results
504.0ms8000×body80valid
244.0ms8000×pre80true