Details

Time bar (total: 10.8s)

sample33.0ms

Algorithm
intervals
Results
18.0ms281×body80valid

simplify115.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize19.0ms

Local error

Found 2 expressions with local error:

2.4b
(* y (+ 1.0 (* z z)))
3.9b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite43.0ms

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:
16.0ms
(* y (+ 1.0 (* z z)))
24.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series193.0ms

Counts
2 → 6
Calls
2 calls:
77.0ms
(* y (+ 1.0 (* z z)))
116.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify653.0ms

Counts
76 → 76

prune213.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.9b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
16.2b
(sqrt (+ 1.0 (* z z)))
16.2b
(sqrt (+ 1.0 (* z z)))

rewrite142.0ms

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:
59.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
59.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
5.0ms
(sqrt (+ 1.0 (* z z)))
9.0ms
(sqrt (+ 1.0 (* z z)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
95.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
72.0ms
(sqrt (+ 1.0 (* z z)))
57.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.1s

Counts
129 → 129

prune472.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (* x (sqrt (+ 1.0 (* z z)))))
0.4b
(* (/ 1 (* y (sqrt (+ 1.0 (* z z))))) (/ 1.0 (* x (sqrt (+ 1.0 (* z z))))))
16.2b
(sqrt (+ 1.0 (* z z)))
16.2b
(sqrt (+ 1.0 (* z z)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
87×add-exp-log
45×add-cbrt-cube
38×prod-exp
28×div-exp
16×add-sqr-sqrt cbrt-unprod
14×cbrt-undiv
12×add-cube-cbrt *-un-lft-identity
10×sqrt-div
9×times-frac associate-*r* associate-*l*
8×pow1
7×associate-*r/
6×rec-exp 1-exp sqrt-prod associate-/r/
5×flip3-+ flip-+
4×add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num associate-/r* *-commutative unswap-sqr
Counts
4 → 114
Calls
4 calls:
16.0ms
(/ 1.0 (* x (sqrt (+ 1.0 (* z z)))))
142.0ms
(* (/ 1 (* y (sqrt (+ 1.0 (* z z))))) (/ 1.0 (* x (sqrt (+ 1.0 (* z z))))))
9.0ms
(sqrt (+ 1.0 (* z z)))
10.0ms
(sqrt (+ 1.0 (* z z)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ 1.0 (* x (sqrt (+ 1.0 (* z z)))))
74.0ms
(* (/ 1 (* y (sqrt (+ 1.0 (* z z))))) (/ 1.0 (* x (sqrt (+ 1.0 (* z z))))))
53.0ms
(sqrt (+ 1.0 (* z z)))
71.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.2s

Counts
126 → 126

prune450.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 4.2b

localize291.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (/ (/ 1 (* y (sqrt (+ 1.0 (* z z))))) x) (/ 1.0 (sqrt (+ 1.0 (* z z)))))
2.0b
(/ (/ 1 (* y (sqrt (+ 1.0 (* z z))))) x)
16.2b
(sqrt (+ 1.0 (* z z)))
16.2b
(sqrt (+ 1.0 (* z z)))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
100×times-frac
87×add-exp-log
74×add-sqr-sqrt
53×add-cube-cbrt *-un-lft-identity
45×add-cbrt-cube
41×div-exp
31×associate-*l*
25×prod-exp
24×associate-*r*
20×sqrt-div
19×cbrt-undiv
17×sqrt-prod
16×associate-/r/
15×associate-*r/
11×cbrt-unprod
10×flip3-+ flip-+ div-inv
9×associate-/l*
8×pow1
6×rec-exp 1-exp unswap-sqr
4×add-log-exp
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 187
Calls
4 calls:
150.0ms
(* (/ (/ 1 (* y (sqrt (+ 1.0 (* z z))))) x) (/ 1.0 (sqrt (+ 1.0 (* z z)))))
41.0ms
(/ (/ 1 (* y (sqrt (+ 1.0 (* z z))))) x)
9.0ms
(sqrt (+ 1.0 (* z z)))
9.0ms
(sqrt (+ 1.0 (* z z)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (/ (/ 1 (* y (sqrt (+ 1.0 (* z z))))) x) (/ 1.0 (sqrt (+ 1.0 (* z z)))))
134.0ms
(/ (/ 1 (* y (sqrt (+ 1.0 (* z z))))) x)
64.0ms
(sqrt (+ 1.0 (* z z)))
71.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.5s

Counts
199 → 199

prune678.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 4.2b

regimes194.0ms

Accuracy

-29.3% (1.1b remaining)

Error of 6.2b against oracle of 5.1b and baseline of 5.9b

bsearch0.0ms

simplify1.1s

end0.0ms

sample937.0ms

Algorithm
intervals
Results
477.0ms8630×body80valid