Details

Time bar (total: 20.4s)

sample44.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
7.0ms256×pre80true

simplify4.7s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize25.0ms

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)))

rewrite93.0ms

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:
53.0ms
(* (- x y) (+ y x))
0.0ms
(fma x x (* y y))
35.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

series212.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(* (- x y) (+ y x))
45.0ms
(fma x x (* y y))
93.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

simplify1.8s

Counts
83 → 83
Iterations
IterNodes
done5011
21676
1386
0123

prune522.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize39.0ms

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)))

rewrite127.0ms

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:
97.0ms
(* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y)))))
20.0ms
(/ (+ y x) (sqrt (fma x x (* y y))))
1.0ms
(sqrt (fma x x (* y y)))
1.0ms
(sqrt (fma x x (* y y)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y)))))
145.0ms
(/ (+ y x) (sqrt (fma x x (* y y))))
59.0ms
(sqrt (fma x x (* y y)))
69.0ms
(sqrt (fma x x (* y y)))

simplify2.0s

Counts
187 → 187
Iterations
IterNodes
done5010
22034
1521
0178

prune857.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 3 expressions with local error:

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

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
882×times-frac
601×*-un-lft-identity
461×add-sqr-sqrt
351×add-cube-cbrt
70×distribute-lft-out
55×distribute-lft-out-- difference-of-squares
42×div-inv
37×associate-/r/
29×associate-/r*
23×associate-/l*
19×add-cbrt-cube add-exp-log
18×flip3-- flip--
10×cbrt-undiv div-exp
3×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp associate-/l/
1×flip3-+ flip-+
Counts
3 → 469
Calls
3 calls:
55.0ms
(/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y)))
18.0ms
(/ (hypot x y) (- x y))
28.0ms
(/ (+ y x) (hypot x y))

series368.0ms

Counts
3 → 9
Calls
3 calls:
122.0ms
(/ (/ (+ y x) (hypot x y)) (/ (hypot x y) (- x y)))
115.0ms
(/ (hypot x y) (- x y))
131.0ms
(/ (+ y x) (hypot x y))

simplify2.1s

Counts
478 → 478
Iterations
IterNodes
done5000
12102
0604

prune2.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (hypot x y) (- x y))
0.0b
(cbrt (* (* (/ (hypot x y) (- x y)) (/ (hypot x y) (- x y))) (/ (hypot x y) (- x y))))
0.0b
(/ (+ y x) (hypot x y))
0.1b
(* (/ (hypot x y) (- x y)) (/ (hypot x y) (- x y)))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
121×*-un-lft-identity
107×add-sqr-sqrt
103×times-frac
63×add-cube-cbrt
27×swap-sqr
22×distribute-lft-out--
21×associate-*r* associate-*l*
20×add-cbrt-cube add-exp-log
16×difference-of-squares
11×pow1
10×associate-/r/
8×associate-/r*
7×cbrt-div associate-/l*
6×frac-times cbrt-undiv div-exp associate-*l/ div-inv
5×flip3-- flip--
4×expm1-log1p-u prod-exp associate-*r/ cbrt-unprod log1p-expm1-u distribute-lft-out add-log-exp unswap-sqr
2×clear-num frac-2neg associate-/l/
1×cbrt-prod pow2 flip3-+ pow-plus pow1/3 pow3 pow-prod-down pow-sqr *-commutative pow-prod-up rem-cbrt-cube flip-+
Counts
4 → 192
Calls
4 calls:
11.0ms
(/ (hypot x y) (- x y))
64.0ms
(cbrt (* (* (/ (hypot x y) (- x y)) (/ (hypot x y) (- x y))) (/ (hypot x y) (- x y))))
22.0ms
(/ (+ y x) (hypot x y))
78.0ms
(* (/ (hypot x y) (- x y)) (/ (hypot x y) (- x y)))

series504.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ (hypot x y) (- x y))
125.0ms
(cbrt (* (* (/ (hypot x y) (- x y)) (/ (hypot x y) (- x y))) (/ (hypot x y) (- x y))))
98.0ms
(/ (+ y x) (hypot x y))
168.0ms
(* (/ (hypot x y) (- x y)) (/ (hypot x y) (- x y)))

simplify2.0s

Counts
204 → 204
Iterations
IterNodes
done5001
22257
1718
0237

prune963.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes83.0ms

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
done14
114
010

end0.0ms

sample845.0ms

Algorithm
intervals
Results
427.0ms8000×body80valid
228.0ms8000×pre80true