Details

Time bar (total: 13.8s)

sample21.0ms

Algorithm
intervals
Results
11.0ms271×body80valid

simplify78.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
12111
23711
35811
48711
511111
done11111

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 2 expressions with local error:

2.1b
(* y (+ 1.0 (* z z)))
4.9b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 70
Calls
2 calls:
37.0ms
(* y (+ 1.0 (* z z)))
17.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series184.0ms

Counts
2 → 6
Calls
2 calls:
96.0ms
(* y (+ 1.0 (* z z)))
88.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify1.5s

Counts
76 → 76
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01561062
13951035
21322887
done5000885

prune188.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize10.0ms

Local error

Found 2 expressions with local error:

2.4b
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
4.8b
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
299×times-frac
199×add-sqr-sqrt
152×add-cube-cbrt *-un-lft-identity
79×sqrt-prod
72×associate-*r*
28×add-exp-log add-cbrt-cube
22×associate-*l* associate-/l*
12×cbrt-undiv div-exp unswap-sqr
10×div-inv
6×prod-exp cbrt-unprod
4×pow1 associate-/r/
3×associate-/r*
2×flip3-+ flip-+ add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
2 → 238
Calls
2 calls:
100.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
27.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

series341.0ms

Counts
2 → 6
Calls
2 calls:
208.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
133.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

simplify1.9s

Counts
244 → 244
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03635187
110584711
235404441
done50004401

prune786.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
0.7b
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
15.4b
(sqrt (+ 1.0 (* z z)))
15.4b
(sqrt (+ 1.0 (* z z)))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
497×times-frac
375×add-sqr-sqrt
231×*-un-lft-identity
221×add-cube-cbrt
155×sqrt-prod
84×associate-*r* associate-*l*
73×add-exp-log
45×add-cbrt-cube
39×div-exp
35×unswap-sqr
22×div-inv
21×cbrt-undiv
15×prod-exp
13×associate-/l*
10×sqrt-div
9×cbrt-unprod
8×pow1
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×rec-exp 1-exp add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 385
Calls
4 calls:
20.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
227.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
97.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
53.0ms
(sqrt (+ 1.0 (* z z)))
58.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.9s

Counts
397 → 397
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
050210067
114819020
242398075
done50008075

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1.0 y) (sqrt (+ 1.0 (* z z))))
2.0b
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
15.4b
(sqrt (+ 1.0 (* z z)))
15.4b
(sqrt (+ 1.0 (* z z)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
921×times-frac
446×add-sqr-sqrt
444×add-cube-cbrt *-un-lft-identity
204×sqrt-prod
97×associate-/l*
37×div-inv
18×add-exp-log add-cbrt-cube
14×sqrt-div
10×associate-/r/
9×cbrt-undiv div-exp associate-/r*
7×flip3-+ flip-+
6×pow1
4×add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 500
Calls
4 calls:
25.0ms
(/ (/ 1.0 y) (sqrt (+ 1.0 (* z z))))
64.0ms
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
7.0ms
(sqrt (+ 1.0 (* z z)))
8.0ms
(sqrt (+ 1.0 (* z z)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (/ 1.0 y) (sqrt (+ 1.0 (* z z))))
111.0ms
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
62.0ms
(sqrt (+ 1.0 (* z z)))
64.0ms
(sqrt (+ 1.0 (* z z)))

simplify2.2s

Counts
512 → 512
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
070012560
1161311481
2408711309
done500011309

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.0b

regimes176.0ms

Accuracy

0% (1.2b remaining)

Error of 6.2b against oracle of 5.0b and baseline of 6.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01423
11921
done1921

end0.0ms

sample611.0ms

Algorithm
intervals
Results
420.0ms8632×body80valid