Details

Time bar (total: 14.9s)

sample27.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms95×body80nan

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06162
18162
done8162

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
3 → 61
Calls
3 calls:
6.0ms
(sqrt (+ x 1.0))
13.0ms
(+ 1.0 (sqrt (+ x 1.0)))
29.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series287.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(sqrt (+ x 1.0))
54.0ms
(+ 1.0 (sqrt (+ x 1.0)))
186.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.5s

Counts
70 → 70
Iterations

Useful iterations: done (1.5s)

IterNodesCost
013722020
131617420
2149516694
done500016614

prune284.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×add-sqr-sqrt
26×times-frac
23×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×associate-/r* flip3-+ div-exp prod-exp associate-/r/ sqrt-prod flip-+
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 106
Calls
4 calls:
9.0ms
(sqrt (+ x 1.0))
13.0ms
(+ 1.0 (sqrt (+ x 1.0)))
29.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
77.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series386.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ x 1.0))
56.0ms
(+ 1.0 (sqrt (+ x 1.0)))
116.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
183.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.7s

Counts
118 → 118
Iterations

Useful iterations: 2 (679.0ms)

IterNodesCost
018336666
146627052
2245425176
done500225176

prune397.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ x (+ (* (+ x 1.0) (sqrt (+ x 1.0))) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.8b
(/ x (+ (* (+ x 1.0) (sqrt (+ x 1.0))) (* 1.0 (* 1.0 1.0))))

rewrite384.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-div
54×add-sqr-sqrt
44×*-un-lft-identity
34×flip3-+ flip-+
30×associate-*r/ add-cube-cbrt
26×sqrt-prod
25×times-frac associate-*l*
21×pow1
16×frac-sub
14×frac-times
13×add-cbrt-cube add-exp-log
11×swap-sqr
10×associate-*r*
9×associate-*l/
8×sqrt-pow1 pow1/2
7×cube-unmult pow3 sum-cubes
6×distribute-lft-out add-log-exp unswap-sqr
5×pow-prod-up
4×associate-/r* pow-prod-down associate-/r/ sub-div
3×prod-exp pow-sqr cbrt-unprod associate-/l*
2×cbrt-undiv div-exp *-commutative div-inv
1×pow2 distribute-rgt-in clear-num sub-neg rem-square-sqrt frac-2neg distribute-lft-in pow-plus flip3-- distribute-rgt-out-- sqrt-unprod diff-log flip--
Counts
4 → 171
Calls
4 calls:
271.0ms
(* (/ x (+ (* (+ x 1.0) (sqrt (+ x 1.0))) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
34.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
25.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
47.0ms
(/ x (+ (* (+ x 1.0) (sqrt (+ x 1.0))) (* 1.0 (* 1.0 1.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
801.0ms
(* (/ x (+ (* (+ x 1.0) (sqrt (+ x 1.0))) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
21.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
68.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
210.0ms
(/ x (+ (* (+ x 1.0) (sqrt (+ x 1.0))) (* 1.0 (* 1.0 1.0))))

simplify2.0s

Counts
183 → 183
Iterations

Useful iterations: done (2.0s)

IterNodesCost
038191422
1121771105
done500069658

prune769.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
56×add-sqr-sqrt
52×times-frac
39×add-cube-cbrt sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×associate-/r* flip3-+ associate-/r/ flip-+
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ *-commutative
Counts
4 → 132
Calls
4 calls:
12.0ms
(sqrt (+ x 1.0))
23.0ms
(+ 1.0 (sqrt (+ x 1.0)))
50.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
94.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series666.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(sqrt (+ x 1.0))
49.0ms
(+ 1.0 (sqrt (+ x 1.0)))
379.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
199.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify3.7s

Counts
144 → 144
Iterations

Useful iterations: done (3.7s)

IterNodesCost
021352783
154743830
2392941098
done500240818

prune542.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08203
113203
done13203

end0.0ms

sample604.0ms

Algorithm
intervals
Results
314.0ms7998×body80valid
112.0ms2729×body80nan
0.0ms2×body1280valid