Details

Time bar (total: 11.2s)

sample33.0ms

Algorithm
intervals
Results
14.0ms276×body80valid

simplify97.0ms

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: 5.4b

localize14.0ms

Local error

Found 2 expressions with local error:

3.2b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
3.6b
(* y (+ 1.0 (* z z)))

rewrite59.0ms

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:
26.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
29.0ms
(* y (+ 1.0 (* z z)))

series156.0ms

Counts
2 → 6
Calls
2 calls:
74.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
81.0ms
(* y (+ 1.0 (* z z)))

simplify1.4s

Counts
76 → 76
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01561062
13951035
21321887
done5000885

prune223.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.8b

localize16.0ms

Local error

Found 2 expressions with local error:

2.5b
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
3.7b
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

rewrite139.0ms

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:
85.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
27.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

series367.0ms

Counts
2 → 6
Calls
2 calls:
225.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
143.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

simplify1.8s

Counts
244 → 244
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03635187
110584711
235404441
done50004401

prune697.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
1.4b
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
14.9b
(sqrt (+ 1.0 (* z z)))
14.9b
(sqrt (+ 1.0 (* z z)))

rewrite300.0ms

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:
21.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
222.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
7.0ms
(sqrt (+ 1.0 (* z z)))
7.0ms
(sqrt (+ 1.0 (* z z)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
88.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
74.0ms
(sqrt (+ 1.0 (* z z)))
50.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.8s

Counts
397 → 397
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
050210067
114819020
242398075
done50008075

prune914.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ 1.0 (* y (* (+ 1.0 (* z z)) x)))
2.4b
(* y (* (+ 1.0 (* z z)) x))
3.6b
(* (+ 1.0 (* z z)) x)

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
10×pow1 add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×prod-exp cbrt-unprod
6×associate-*l* associate-*l/
4×associate-*r/ associate-*r* pow-prod-down
3×cbrt-undiv flip3-+ times-frac div-exp flip-+ associate-/l* add-log-exp
2×associate-/r/ *-commutative
1×frac-2neg clear-num associate-/r* div-inv unswap-sqr
Counts
3 → 65
Calls
3 calls:
27.0ms
(/ 1.0 (* y (* (+ 1.0 (* z z)) x)))
24.0ms
(* y (* (+ 1.0 (* z z)) x))
16.0ms
(* (+ 1.0 (* z z)) x)

series173.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ 1.0 (* y (* (+ 1.0 (* z z)) x)))
56.0ms
(* y (* (+ 1.0 (* z z)) x))
38.0ms
(* (+ 1.0 (* z z)) x)

simplify1.1s

Counts
74 → 74
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01241004
1322968
21286780
done5000778

prune187.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.8b

regimes185.0ms

Accuracy

0% (1.8b remaining)

Error of 6.5b against oracle of 4.8b and baseline of 6.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11211
done1211

end0.0ms

sample1.2s

Algorithm
intervals
Results
456.0ms8567×body80valid