Details

Time bar (total: 17.1s)

sample34.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
7.0ms256×pre80true

simplify4.5s

Counts
1 → 1
Iterations
IterNodes
done5004
71738
6803
5457
4220
3107
250
123
09

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize35.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma x x (* y y))
18.8b
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/l/
7×add-cbrt-cube add-exp-log
4×add-sqr-sqrt frac-times *-un-lft-identity add-cube-cbrt
3×associate-/r* flip3-+ times-frac flip3-- flip-+ flip--
2×expm1-log1p-u pow1 cbrt-undiv div-exp associate-*l/ associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
1×clear-num frac-2neg prod-exp cbrt-unprod fma-udef div-inv associate-/l*
Counts
2 → 43
Calls
2 calls:
0.0ms
(fma x x (* y y))
34.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

series142.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(fma x x (* y y))
94.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

simplify1.8s

Counts
49 → 49
Iterations
IterNodes
done5000
21109
1250
084

prune208.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y))))
18.3b
(sqrt (fma x x (* y y)))
18.3b
(sqrt (fma x x (* y y)))
18.8b
(/ (* (- x y) (+ y x)) (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
18×add-cbrt-cube add-exp-log
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
8×swap-sqr associate-/l/
6×associate-*r* associate-*l*
5×prod-exp pow-prod-up cbrt-unprod
4×expm1-log1p-u frac-times cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×flip3-+ flip3-- pow-prod-down pow-sqr flip-+ flip--
2×rem-sqrt-square associate-*l/ associate-*r/ fma-udef hypot-def
1×pow2 clear-num associate-/r* rem-square-sqrt frac-2neg times-frac pow-plus sqrt-unprod *-commutative div-inv associate-/l*
Counts
4 → 118
Calls
4 calls:
19.0ms
(* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y))))
2.0ms
(sqrt (fma x x (* y y)))
2.0ms
(sqrt (fma x x (* y y)))
39.0ms
(/ (* (- x y) (+ y x)) (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))))

series261.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y))))
53.0ms
(sqrt (fma x x (* y y)))
55.0ms
(sqrt (fma x x (* y y)))
109.0ms
(/ (* (- x y) (+ y x)) (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))))

simplify1.7s

Counts
130 → 130
Iterations
IterNodes
done5004
21749
1379
0126

prune576.0ms

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
(/ 1 (/ (* (hypot x y) (/ (hypot x y) (+ y x))) (- x y)))
0.0b
(/ (* (hypot x y) (/ (hypot x y) (+ y x))) (- x y))
0.0b
(* (hypot x y) (/ (hypot x y) (+ y x)))
0.0b
(/ (hypot x y) (+ y x))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
83×times-frac
70×*-un-lft-identity
61×add-sqr-sqrt
54×add-exp-log
44×add-cube-cbrt
34×add-cbrt-cube
26×div-exp
20×associate-/r*
18×associate-*r*
15×associate-/r/
14×cbrt-undiv
10×prod-exp
8×div-inv
7×pow1 distribute-lft-out associate-/l*
6×cbrt-unprod distribute-lft-out-- difference-of-squares
5×flip3-- flip--
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l*
2×flip3-+ associate-*r/ flip-+ unswap-sqr
1×pow-prod-down *-commutative pow-flip inv-pow associate-/l/
Counts
4 → 188
Calls
4 calls:
63.0ms
(/ 1 (/ (* (hypot x y) (/ (hypot x y) (+ y x))) (- x y)))
48.0ms
(/ (* (hypot x y) (/ (hypot x y) (+ y x))) (- x y))
48.0ms
(* (hypot x y) (/ (hypot x y) (+ y x)))
12.0ms
(/ (hypot x y) (+ y x))

series544.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(/ 1 (/ (* (hypot x y) (/ (hypot x y) (+ y x))) (- x y)))
142.0ms
(/ (* (hypot x y) (/ (hypot x y) (+ y x))) (- x y))
138.0ms
(* (hypot x y) (/ (hypot x y) (+ y x)))
132.0ms
(/ (hypot x y) (+ y x))

simplify1.9s

Counts
200 → 200
Iterations
IterNodes
done5001
22234
1633
0246

prune731.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (hypot x y) (/ (hypot x y) (+ y x)))
0.0b
(log1p (expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ y x))))))
0.0b
(/ (hypot x y) (+ y x))
0.4b
(expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ y x)))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
27×add-sqr-sqrt
25×times-frac
22×add-cube-cbrt
18×associate-*r*
11×add-cbrt-cube add-exp-log
7×distribute-lft-out
6×pow1
5×log1p-expm1-u
4×expm1-log1p-u associate-/r* associate-/r/ insert-posit16 add-log-exp
3×associate-*l* associate-/l*
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv unswap-sqr
1×log1p-udef expm1-log1p clear-num frac-2neg pow-prod-down log1p-expm1 associate-*r/ *-commutative expm1-udef
Counts
4 → 100
Calls
4 calls:
51.0ms
(* (hypot x y) (/ (hypot x y) (+ y x)))
0.0ms
(log1p (expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ y x))))))
12.0ms
(/ (hypot x y) (+ y x))
1.0ms
(expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ y x)))))

series616.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (hypot x y) (/ (hypot x y) (+ y x)))
193.0ms
(log1p (expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ y x))))))
121.0ms
(/ (hypot x y) (+ y x))
169.0ms
(expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ y x)))))

simplify2.0s

Counts
112 → 112
Iterations
IterNodes
done5042
32974
2901
1289
0127

prune532.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes84.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done12
112
010

end0.0ms

sample1.0s

Algorithm
intervals
Results
642.0ms8000×body80valid
236.0ms8000×pre80true