Details

Time bar (total: 12.8s)

sample28.0ms

Algorithm
intervals
Results
5.0ms284×body80nan
5.0ms51×body1280valid
3.0ms141×body80valid
2.0ms31×body640valid
1.0ms25×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))

rewrite49.0ms

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:
48.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series75.0ms

Counts
1 → 3
Calls
1 calls:
75.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.5s

Counts
22 → 22
Iterations

Useful iterations: done (1.5s)

IterNodesCost
059310
1133285
2336263
3802257
42104250
done5001246

prune45.0ms

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)))

rewrite83.0ms

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:
33.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
48.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series199.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
138.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.3s

Counts
61 → 61
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0128947
1297865
2790788
32333774
done5001766

prune125.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

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)))))

rewrite458.0ms

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:
42.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
51.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
50.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
266.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
166.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
343.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
351.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
170.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.6s

Counts
495 → 495
Iterations

Useful iterations: done (1.6s)

IterNodesCost
035115267
1102313155
2312211081
done500010755

prune1.0s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize17.0ms

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
(* (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

rewrite749.0ms

Algorithm
rewrite-expression-head
Rules
697×sqrt-prod
311×*-un-lft-identity
273×times-frac
207×add-sqr-sqrt
164×add-cube-cbrt
126×associate-*l*
84×distribute-lft-out
70×add-exp-log
62×sqrt-div
45×associate-*r*
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:
75.0ms
(/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
56.0ms
(/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
190.0ms
(* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
392.0ms
(* (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
649.0ms
(/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
482.0ms
(/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
368.0ms
(* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
163.0ms
(* (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

simplify685.0ms

Counts
482 → 482
Iterations

Useful iterations: done (667.0ms)

IterNodesCost
052016182
1130014772
done500111275

prune1.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes81.0ms

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

sample761.0ms

Algorithm
intervals
Results
149.0ms1699×body1280valid
147.0ms8130×body80nan
81.0ms1207×body640valid
81.0ms4169×body80valid
35.0ms617×body320valid
11.0ms308×body160valid