Details

Time bar (total: 12.4s)

sample31.0ms

Algorithm
intervals
Results
14.0ms271×body80valid

simplify97.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
12111
23711
35811
48711
511111
done11111

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize8.0ms

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))))

rewrite54.0ms

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:
32.0ms
(* y (+ 1.0 (* z z)))
17.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series149.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(* y (+ 1.0 (* z z)))
79.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify1.5s

Counts
76 → 76
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01561062
13951035
21322887
done5000885

prune197.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize13.0ms

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)))

rewrite158.0ms

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:
109.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
27.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

series376.0ms

Counts
2 → 6
Calls
2 calls:
226.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
150.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

simplify1.7s

Counts
244 → 244
Iterations

Useful iterations: done (1.7s)

IterNodesCost
03635187
110584711
235404441
done50004401

prune808.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite561.0ms

Algorithm
rewrite-expression-head
Rules
878×times-frac
629×add-sqr-sqrt
448×sqrt-prod
389×add-cube-cbrt *-un-lft-identity
138×associate-*r* associate-*l*
49×unswap-sqr
45×add-exp-log add-cbrt-cube
22×div-inv associate-/l*
21×cbrt-undiv div-exp
10×sqrt-div
9×prod-exp cbrt-unprod
8×pow1
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×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 → 562
Calls
4 calls:
33.0ms
(/ (/ (sqrt 1.0) x) (sqrt (+ 1.0 (* z z))))
444.0ms
(* (/ (/ (sqrt 1.0) y) (sqrt (+ 1.0 (* z z)))) (/ (/ (sqrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
6.0ms
(sqrt (+ 1.0 (* z z)))
6.0ms
(sqrt (+ 1.0 (* z z)))

series515.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (/ (sqrt 1.0) x) (sqrt (+ 1.0 (* z z))))
273.0ms
(* (/ (/ (sqrt 1.0) y) (sqrt (+ 1.0 (* z z)))) (/ (/ (sqrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
44.0ms
(sqrt (+ 1.0 (* z z)))
63.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.2s

Counts
574 → 574
Iterations

Useful iterations: done (1.2s)

IterNodesCost
061916028
1186614896
done500014094

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) x))
1.8b
(/ (/ 1.0 (* (sqrt (+ 1.0 (* z z))) x)) y)
15.4b
(sqrt (+ 1.0 (* z z)))
15.4b
(sqrt (+ 1.0 (* z z)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
28×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube
14×sqrt-div
12×associate-/l*
10×associate-*l/ associate-/r/
7×cbrt-undiv flip3-+ div-exp flip-+
6×pow1 sqrt-prod div-inv
4×associate-/r* add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod
1×associate-/l/
Counts
4 → 109
Calls
4 calls:
26.0ms
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) x))
34.0ms
(/ (/ 1.0 (* (sqrt (+ 1.0 (* z z))) x)) y)
8.0ms
(sqrt (+ 1.0 (* z z)))
8.0ms
(sqrt (+ 1.0 (* z z)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) x))
130.0ms
(/ (/ 1.0 (* (sqrt (+ 1.0 (* z z))) x)) y)
65.0ms
(sqrt (+ 1.0 (* z z)))
59.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.1s

Counts
121 → 121
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02182016
15111863
216201701
done50001683

prune418.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.0b

regimes189.0ms

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
01321
11719
done1719

end0.0ms

sample913.0ms

Algorithm
intervals
Results
491.0ms8632×body80valid