Details

Time bar (total: 11.7s)

sample42.0ms

Algorithm
intervals
Results
8.0ms284×body80nan
7.0ms51×body1280valid
4.0ms141×body80valid
4.0ms31×body640valid
2.0ms25×body320valid
0.0ms8×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize5.0ms

Local error

Found 1 expressions with local error:

2.8b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
1 → 19
Calls
1 calls:
42.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series65.0ms

Counts
1 → 3
Calls
1 calls:
65.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.5s

Counts
22 → 22
Iterations

Useful iterations: done (1.5s)

IterNodesCost
059310
1133285
2336263
3802257
42104250
done5001246

prune39.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 55
Calls
2 calls:
30.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
43.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series194.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
135.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.2s

Counts
61 → 61
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0128947
1297865
2790788
32333774
done5001766

prune116.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.3b
(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite435.0ms

Algorithm
rewrite-expression-head
Rules
848×sqrt-prod
658×*-un-lft-identity
496×times-frac
412×add-sqr-sqrt
236×distribute-lft-out
229×add-cube-cbrt
126×swap-sqr
60×associate-*r* associate-*l*
25×unswap-sqr
20×add-exp-log add-cbrt-cube
18×associate-/r*
14×sqrt-div
12×pow1 associate-/r/ associate-/l*
7×flip3-+ flip-+
6×cbrt-undiv sqrt-undiv div-exp div-inv
4×prod-exp cbrt-unprod add-log-exp
2×frac-2neg clear-num
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 sqrt-unprod associate-*r/ pow-prod-down associate-*l/ rem-square-sqrt pow-sqr *-commutative pow-prod-up
Counts
4 → 483
Calls
4 calls:
39.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
46.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
45.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
261.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series974.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
340.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
324.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
155.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.5s

Counts
495 → 495
Iterations

Useful iterations: done (1.5s)

IterNodesCost
035115267
1102313155
2312211081
done500010755

prune657.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.1b
(/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b
(* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(* (/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

rewrite719.0ms

Algorithm
rewrite-expression-head
Rules
697×sqrt-prod
311×*-un-lft-identity
273×times-frac
207×add-sqr-sqrt
164×add-cube-cbrt
123×associate-*r*
84×distribute-lft-out
70×add-exp-log
62×sqrt-div
48×associate-*l*
34×add-cbrt-cube
33×associate-/l*
27×unpow-prod-down cube-prod
26×div-exp
24×prod-exp
20×flip3-+ associate-/r/ flip-+
18×pow1
16×unswap-sqr
13×frac-times associate-/r*
12×sqrt-pow1
10×cbrt-undiv cbrt-unprod
8×pow1/2
7×associate-*r/ associate-*l/
6×pow-to-exp pow-exp pow-prod-up
4×pow-prod-down div-inv add-log-exp
3×cube-mult unpow3 sqr-pow
2×frac-2neg pow-plus cube-unmult clear-num *-commutative
1×sqrt-undiv sqrt-unprod
Counts
4 → 470
Calls
4 calls:
65.0ms
(/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
49.0ms
(/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
191.0ms
(* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
387.0ms
(* (/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
602.0ms
(/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
462.0ms
(/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
357.0ms
(* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
168.0ms
(* (/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

simplify704.0ms

Counts
482 → 482
Iterations

Useful iterations: done (678.0ms)

IterNodesCost
055016131
1144014081
done500011097

prune1.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

end0.0ms

sample721.0ms

Algorithm
intervals
Results
141.0ms1699×body1280valid
141.0ms8130×body80nan
78.0ms1207×body640valid
77.0ms4169×body80valid
31.0ms617×body320valid
10.0ms308×body160valid