Details

Time bar (total: 5.4s)

sample21.0ms

Algorithm
intervals
Results
9.0ms276×body80valid

simplify6.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize8.0ms

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)))

rewrite41.0ms

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:
24.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
15.0ms
(* y (+ 1.0 (* z z)))

series119.0ms

Counts
2 → 6
Calls
2 calls:
64.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
54.0ms
(* y (+ 1.0 (* z z)))

simplify42.0ms

Counts
76 → 76

prune159.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.2b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
14.9b
(sqrt (+ 1.0 (* z z)))
14.9b
(sqrt (+ 1.0 (* z z)))

rewrite104.0ms

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:
43.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
46.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
65.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
48.0ms
(sqrt (+ 1.0 (* z z)))
45.0ms
(sqrt (+ 1.0 (* z z)))

simplify62.0ms

Counts
129 → 129

prune319.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
650×times-frac
443×add-sqr-sqrt
293×add-cube-cbrt *-un-lft-identity
191×sqrt-prod
138×associate-*r*
127×cbrt-prod
63×add-exp-log
52×add-cbrt-cube
48×associate-*l*
35×unswap-sqr
30×cbrt-undiv div-exp
22×div-inv associate-/l*
15×prod-exp cbrt-unprod
10×sqrt-div
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 → 464
Calls
4 calls:
21.0ms
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
180.0ms
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
10.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
154.0ms
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
52.0ms
(sqrt (+ 1.0 (* z z)))
48.0ms
(sqrt (+ 1.0 (* z z)))

simplify84.0ms

Counts
476 → 476

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

localize26.0ms

Local error

Found 4 expressions with local error:

14.9b
(sqrt (+ 1.0 (* z z)))
15.5b
(cbrt (+ 1.0 (* z z)))
15.5b
(cbrt (+ 1.0 (* z z)))
15.5b
(cbrt (+ 1.0 (* z z)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
9.0ms
(sqrt (+ 1.0 (* z z)))
13.0ms
(cbrt (+ 1.0 (* z z)))
3.0ms
(cbrt (+ 1.0 (* z z)))
3.0ms
(cbrt (+ 1.0 (* z z)))

series627.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(sqrt (+ 1.0 (* z z)))
184.0ms
(cbrt (+ 1.0 (* z z)))
187.0ms
(cbrt (+ 1.0 (* z z)))
211.0ms
(cbrt (+ 1.0 (* z z)))

simplify122.0ms

Counts
66 → 66

prune376.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.8b

regimes276.0ms

Accuracy

0% (1.1b remaining)

Error of 5.8b against oracle of 4.8b and baseline of 5.8b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample714.0ms

Algorithm
intervals
Results
400.0ms8567×body80valid