Details

Time bar (total: 17.4s)

sample80.0ms

Algorithm
intervals
Results
17.0ms72×body640valid
15.0ms309×body80nan
12.0ms38×body1280valid
8.0ms117×body80valid
4.0ms23×body320valid
1.0ms6×body160valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11211
21411
done1411

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.4b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
70×add-sqr-sqrt
69×times-frac
46×sqrt-prod
40×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l*
5×add-log-exp
4×div-inv
3×pow1
2×cbrt-undiv frac-2neg sqrt-div div-exp clear-num associate-/r/
1×sub-neg flip3-- flip3-+ diff-log frac-sub flip-- flip-+
Counts
3 → 117
Calls
3 calls:
29.0ms
(/ 1.0 (sqrt (+ x 1.0)))
12.0ms
(/ 1.0 (sqrt x))
144.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series334.0ms

Counts
3 → 9
Calls
3 calls:
96.0ms
(/ 1.0 (sqrt (+ x 1.0)))
54.0ms
(/ 1.0 (sqrt x))
184.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.3s

Counts
126 → 126
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02011764
113141616
done50001536

prune453.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 22.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.4b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×sqrt-prod
17×add-exp-log add-cbrt-cube
16×*-un-lft-identity
7×pow1 add-cube-cbrt associate-*r*
6×associate-*r/ associate-*l*
5×prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv sqrt-div div-exp difference-of-squares unswap-sqr
3×pow-prod-down distribute-lft-out--
2×flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/ distribute-lft-out
1×sub-neg frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
3 → 77
Calls
3 calls:
112.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
43.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series605.0ms

Counts
3 → 9
Calls
3 calls:
377.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
111.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
117.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify4.6s

Counts
86 → 86
Iterations

Useful iterations: done (4.6s)

IterNodesCost
01801446
140871300
done50001158

prune408.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
1.7b
(- (+ x 1.0) x)

rewrite335.0ms

Algorithm
rewrite-expression-head
Rules
113×*-un-lft-identity
46×add-sqr-sqrt
39×sqrt-prod
37×times-frac distribute-lft-out
29×add-exp-log add-cbrt-cube
22×add-cube-cbrt
16×distribute-lft-out--
9×cbrt-undiv div-exp add-log-exp
8×pow1 prod-exp cbrt-unprod difference-of-squares
7×associate-*r* associate-/r* associate-/l*
6×associate-*l*
5×associate-*r/
4×sqrt-div associate-/r/ unswap-sqr
3×flip3-+ pow-prod-down flip-+ associate-/l/
2×flip3-- frac-2neg sqrt-pow1 pow1/2 diff-log clear-num flip-- div-inv
1×sub-neg sqrt-unprod div-sub associate--l+ sum-log *-commutative
Counts
4 → 143
Calls
4 calls:
143.0ms
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
85.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
49.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
52.0ms
(- (+ x 1.0) x)

series1.1s

Counts
4 → 12
Calls
4 calls:
206.0ms
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
758.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
97.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(- (+ x 1.0) x)

simplify895.0ms

Counts
155 → 155
Iterations

Useful iterations: done (889.0ms)

IterNodesCost
02693162
done50002946

prune544.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite251.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
31×sqrt-prod
29×add-exp-log add-cbrt-cube
27×add-sqr-sqrt
21×distribute-lft-out
19×add-cube-cbrt times-frac
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×associate-*r* associate-/r*
6×associate-*l* add-log-exp
5×associate-*r/
4×flip3-+ sqrt-div associate-/r/ flip-+ associate-/l* unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 116
Calls
4 calls:
59.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
87.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
49.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
52.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
93.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
197.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
753.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
85.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify873.0ms

Counts
128 → 128
Iterations

Useful iterations: done (865.0ms)

IterNodesCost
02502311
done50012081

prune550.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01221
11921
done1921

end0.0ms

sample2.2s

Algorithm
intervals
Results
645.0ms4128×body80valid
416.0ms8101×body80nan
388.0ms1143×body1280valid
345.0ms1807×body640valid
76.0ms609×body320valid
26.0ms313×body160valid