Details

Time bar (total: 11.4s)

sample19.0ms

Algorithm
intervals
Results
9.0ms277×body80valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604
done1604

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.0b

localize7.0ms

Local error

Found 2 expressions with local error:

4.2b
(* y (+ 1.0 (* z z)))
4.5b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite32.0ms

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×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u 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 → 74
Calls
2 calls:
15.0ms
(* y (+ 1.0 (* z z)))
15.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series110.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(* y (+ 1.0 (* z z)))
59.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify45.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0416531
12028428
25001420
done5001420

prune170.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
6.6b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
228×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×associate-/r*
2×pow1 expm1-log1p-u frac-2neg clear-num associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×flip3-+ flip-+
Counts
2 → 268
Calls
2 calls:
10.0ms
(/ (/ 1.0 y) x)
28.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series79.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(/ (/ 1.0 y) x)
60.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify99.0ms

Counts
274 → 274
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
011383012
145962854
250022850
done50022850

prune741.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (/ 1.0 y))
1.3b
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
17.5b
(sqrt (+ 1.0 (* z z)))
17.5b
(sqrt (+ 1.0 (* z z)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
846×times-frac
410×add-sqr-sqrt
406×add-cube-cbrt *-un-lft-identity
286×cbrt-prod
165×sqrt-prod
52×associate-/l*
30×div-inv
9×add-exp-log
8×add-cbrt-cube
6×pow1 sqrt-div associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ div-exp flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ hypot-def
1×cbrt-div frac-2neg pow1/3 clear-num associate-/l/
Counts
4 → 449
Calls
4 calls:
2.0ms
(cbrt (/ 1.0 y))
35.0ms
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
10.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(cbrt (/ 1.0 y))
177.0ms
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
48.0ms
(sqrt (+ 1.0 (* z z)))
41.0ms
(sqrt (+ 1.0 (* z z)))

simplify131.0ms

Counts
461 → 461
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
015427195
148296982
250016980
done50016980

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
2.7b
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
17.5b
(sqrt (+ 1.0 (* z z)))
17.5b
(sqrt (+ 1.0 (* z z)))

rewrite409.0ms

Algorithm
rewrite-expression-head
Rules
6882×times-frac
2952×add-sqr-sqrt
2948×add-cube-cbrt *-un-lft-identity
1836×sqrt-prod
307×associate-/l*
205×div-inv
27×add-exp-log add-cbrt-cube
22×sqrt-div
18×associate-/r/
16×cbrt-undiv div-exp
12×associate-/r*
11×flip3-+ flip-+
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def associate-/l/
Counts
4 → 2241
Calls
4 calls:
107.0ms
(/ (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
32.0ms
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
91.0ms
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
40.0ms
(sqrt (+ 1.0 (* z z)))
48.0ms
(sqrt (+ 1.0 (* z z)))

simplify414.0ms

Counts
2253 → 2253
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0500151372
done500151372

prune6.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.8b

regimes141.0ms

Accuracy

0% (1.2b remaining)

Error of 6.1b against oracle of 4.9b and baseline of 6.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01617
11617
done1617

end0.0ms

sample461.0ms

Algorithm
intervals
Results
234.0ms8627×body80valid