Details

Time bar (total: 15.8s)

sample39.0ms

Algorithm
intervals
Results
8.0ms59×body640valid
7.0ms39×body1280valid
7.0ms248×body80nan
4.0ms124×body80valid
2.0ms22×body320valid
1.0ms12×body160valid

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08242
111242
214242
done14242

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.6b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-cbrt-cube add-exp-log distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
17.0ms
(/ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ 1.0 (sqrt x))
71.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series398.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(sqrt (+ x 1.0))
102.0ms
(/ 1.0 (sqrt (+ x 1.0)))
66.0ms
(/ 1.0 (sqrt x))
199.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.9s

Counts
145 → 145
Iterations

Useful iterations: done (2.9s)

IterNodesCost
021648307
146241169
2115840281
3346440121
done500240081

prune677.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.6b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×*-un-lft-identity sqrt-prod
11×add-cbrt-cube add-exp-log add-cube-cbrt
9×pow1
7×associate-*r*
6×sqrt-div associate-*l* add-log-exp
4×associate-*r/ unswap-sqr
3×sqrt-pow1 flip3-+ times-frac pow1/2 pow-prod-down flip-+ associate-/l*
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod flip-- distribute-lft-out associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Counts
4 → 87
Calls
4 calls:
6.0ms
(sqrt (+ x 1.0))
38.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
25.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
13.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series542.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(sqrt (+ x 1.0))
323.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
70.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
117.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify2.4s

Counts
99 → 99
Iterations

Useful iterations: done (2.4s)

IterNodesCost
019335661
154529716
2199727270
done500126708

prune575.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
0.3b
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
0.5b
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
1.7b
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
37×pow-prod-down
30×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
16×add-sqr-sqrt associate-*r/
14×sqrt-div
11×sqrt-prod
10×*-un-lft-identity
9×associate-*r*
8×associate-*l* pow-sqr pow-prod-up add-cube-cbrt
7×flip3-+ flip-+
6×add-log-exp
4×frac-times pow-plus unswap-sqr
3×*-commutative
2×pow2 sqrt-pow1 pow1/2 swap-sqr associate-*l/
1×sub-neg flip3-- sqrt-unprod diff-log flip-- distribute-lft-out difference-of-squares
Counts
4 → 122
Calls
4 calls:
22.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
65.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
39.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
75.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

series187.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
49.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
32.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
22.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

simplify1.6s

Counts
134 → 134
Iterations

Useful iterations: done (1.6s)

IterNodesCost
017233284
146326282
2143223398
done500222758

prune454.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
0.2b
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
0.2b
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
38×add-sqr-sqrt
32×*-un-lft-identity
30×add-cube-cbrt
20×add-cbrt-cube add-exp-log
18×associate-/l*
11×sqrt-prod
8×pow1 associate-/r/
7×cbrt-undiv div-exp associate-*r*
6×flip3-+ associate-*l* flip-+ add-log-exp
4×associate-/r* sqrt-div associate-*r/ div-inv unswap-sqr
3×pow-prod-down prod-exp cbrt-unprod
2×clear-num frac-2neg sqrt-pow1 pow1/2
1×+-commutative sum-log sqrt-unprod *-commutative distribute-lft-out associate-/l/
Counts
4 → 125
Calls
4 calls:
11.0ms
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
19.0ms
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
43.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
26.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series930.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
193.0ms
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
572.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
64.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify2.6s

Counts
137 → 137
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
028064576
177056966
2269255053
done500455053

prune500.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
013442
119442
done19442

end0.0ms

sample1.3s

Algorithm
intervals
Results
313.0ms4088×body80valid
267.0ms7971×body80nan
263.0ms1837×body640valid
185.0ms1105×body1280valid
95.0ms664×body320valid
19.0ms306×body160valid