Details

Time bar (total: 5.8s)

sample17.0ms

Algorithm
intervals
Results
8.0ms279×body80valid

simplify49.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
12111
23611
35711
48511
510011
done10011

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.0b

localize7.0ms

Local error

Found 2 expressions with local error:

3.5b
(* y (+ 1.0 (* z z)))
4.3b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite17.0ms

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:
7.0ms
(* y (+ 1.0 (* z z)))
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series120.0ms

Counts
2 → 6
Calls
2 calls:
58.0ms
(* y (+ 1.0 (* z z)))
62.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify598.0ms

Counts
76 → 76
Iterations

Useful iterations: 2 (136.0ms)

IterNodesCost
01561062
14101035
21854887
done5000887

prune171.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
4.3b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-exp-log add-cbrt-cube
28×sqrt-div
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
16×associate-*r/
14×flip3-+ flip-+
13×associate-/l*
11×pow1
9×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod
8×frac-times associate-/r/
6×associate-*r*
4×associate-*l/ add-log-exp
3×pow-prod-down div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 117
Calls
4 calls:
20.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
24.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series206.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
61.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
43.0ms
(sqrt (+ 1.0 (* z z)))
49.0ms
(sqrt (+ 1.0 (* z z)))

simplify895.0ms

Counts
129 → 129
Iterations

Useful iterations: 2 (204.0ms)

IterNodesCost
02172776
16102090
227631728
done50001728

prune344.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ 1.0 (* x (* y (+ (* z z) 1.0))))
3.5b
(* y (+ (* z z) 1.0))
4.1b
(* x (* y (+ (* z z) 1.0)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
10×pow1 add-sqr-sqrt associate-*r/
8×add-cube-cbrt *-un-lft-identity
7×prod-exp cbrt-unprod
6×associate-*l*
5×distribute-rgt-in distribute-lft-in
4×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 → 71
Calls
3 calls:
13.0ms
(/ 1.0 (* x (* y (+ (* z z) 1.0))))
14.0ms
(* y (+ (* z z) 1.0))
13.0ms
(* x (* y (+ (* z z) 1.0)))

series373.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(/ 1.0 (* x (* y (+ (* z z) 1.0))))
252.0ms
(* y (+ (* z z) 1.0))
61.0ms
(* x (* y (+ (* z z) 1.0)))

simplify559.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
01241034
13411010
21614820
done5001820

prune168.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (- 1.0) (- (* x (* y (+ (* z z) 1.0)))))
3.5b
(* y (+ (* z z) 1.0))
4.1b
(* x (* y (+ (* z z) 1.0)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
40×add-sqr-sqrt
38×add-cube-cbrt *-un-lft-identity
32×distribute-lft-neg-in distribute-rgt-neg-in
18×neg-mul-1
12×add-exp-log add-cbrt-cube
10×pow1 associate-*r/ associate-/l*
6×associate-*l* associate-/r*
5×distribute-rgt-in distribute-lft-in
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
3×flip3-+ flip-+ add-log-exp
2×associate-/r/ *-commutative distribute-neg-frac
1×cbrt-undiv neg-sub0 frac-2neg div-sub distribute-frac-neg div-exp clear-num div-inv unswap-sqr
Counts
3 → 138
Calls
3 calls:
7.0ms
(/ (- 1.0) (- (* x (* y (+ (* z z) 1.0)))))
11.0ms
(* y (+ (* z z) 1.0))
13.0ms
(* x (* y (+ (* z z) 1.0)))

series201.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(/ (- 1.0) (- (* x (* y (+ (* z z) 1.0)))))
52.0ms
(* y (+ (* z z) 1.0))
65.0ms
(* x (* y (+ (* z z) 1.0)))

simplify938.0ms

Counts
147 → 147
Iterations

Useful iterations: 2 (191.0ms)

IterNodesCost
02442504
15892435
227542280
done50002280

prune322.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

regimes247.0ms

Accuracy

0% (1.8b remaining)

Error of 6.5b against oracle of 4.7b and baseline of 6.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
12013
22813
33113
43413
done3413

end0.0ms

sample410.0ms

Algorithm
intervals
Results
236.0ms8608×body80valid