Details

Time bar (total: 17.6s)

sample65.0ms

Algorithm
intervals
Results
12.0ms286×body80nan
10.0ms57×body640valid
10.0ms45×body1280valid
5.0ms122×body80valid
3.0ms20×body320valid
1.0ms12×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-exp-log sqrt-div add-cbrt-cube distribute-lft-out
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+
Counts
2 → 35
Calls
2 calls:
16.0ms
(sqrt (+ x 1.0))
106.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series171.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(sqrt (+ x 1.0))
122.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.2s

Counts
41 → 41
Iterations

Useful iterations: done (2.2s)

IterNodesCost
084488
1188440
2638410
32563402
done5000400

prune235.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
16×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 71
Calls
3 calls:
14.0ms
(sqrt (+ x 1.0))
63.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
88.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series412.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(sqrt (+ x 1.0))
113.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
245.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.2s

Counts
80 → 80
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01521125
13611018
21505937
done5001929

prune473.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite655.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 250
Calls
4 calls:
75.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
75.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
77.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
391.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
566.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
220.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
216.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
263.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.3s

Counts
262 → 262
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03116170
17034400
232204128
done50024073

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
203×*-un-lft-identity
168×sqrt-prod
141×times-frac
131×add-sqr-sqrt
77×add-cube-cbrt
68×distribute-lft-out
60×associate-*l*
37×associate-*r*
34×add-exp-log
22×add-cbrt-cube
18×unswap-sqr
16×sqrt-div
15×pow1 associate-/r*
11×div-exp
10×associate-/r/
9×prod-exp
6×cbrt-undiv frac-times associate-*r/ pow-prod-down associate-/l*
5×sqrt-pow1 flip3-+ cbrt-unprod flip-+ div-inv
4×associate-*l/ add-log-exp
3×rec-exp pow-flip pow1/2 1-exp
2×frac-2neg clear-num *-commutative
1×sqrt-unprod swap-sqr inv-pow
Counts
4 → 262
Calls
4 calls:
92.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
76.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
408.0ms
(* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
550.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
438.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
225.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
214.0ms
(* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
255.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

simplify808.0ms

Counts
274 → 274
Iterations

Useful iterations: done (788.0ms)

IterNodesCost
04077103
111136491
done50005808

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes102.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01533
12133
done2133

end0.0ms

sample2.3s

Algorithm
intervals
Results
482.0ms329×body160valid
369.0ms1773×body1280valid
369.0ms7916×body80nan
298.0ms1235×body640valid
253.0ms4046×body80valid
67.0ms617×body320valid