Details

Time bar (total: 14.6s)

sample63.0ms

Algorithm
intervals
Results
13.0ms63×body640valid
11.0ms275×body80nan
9.0ms33×body1280valid
7.0ms136×body80valid
2.0ms17×body320valid
1.0ms7×body160valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0811
11111
21411
done1411

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
2.3b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
18.0ms
(/ 1.0 (sqrt (+ x 1.0)))
7.0ms
(/ 1.0 (sqrt x))
115.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series426.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(sqrt (+ x 1.0))
113.0ms
(/ 1.0 (sqrt (+ x 1.0)))
69.0ms
(/ 1.0 (sqrt x))
191.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.1s

Counts
145 → 145
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02151942
14631778
216801704
done50011700

prune476.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
0.3b
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.5b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
2.3b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite540.0ms

Algorithm
rewrite-expression-head
Rules
362×times-frac
331×*-un-lft-identity
258×add-sqr-sqrt
180×sqrt-prod
174×add-cube-cbrt
88×distribute-lft-out
67×swap-sqr
49×associate-*r* associate-*l*
30×add-exp-log add-cbrt-cube
19×div-inv
18×pow1 frac-sub unswap-sqr
16×difference-of-squares
14×frac-times associate-*r/ associate-*l/ associate-/r*
11×associate-/r/ associate-/l/
9×cbrt-undiv div-exp
8×sqrt-div prod-exp cbrt-unprod
6×add-log-exp
5×flip3-+ flip-+
4×associate-/l*
2×pow2 flip3-- pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up flip--
1×sub-neg frac-2neg diff-log div-sub frac-add clear-num
Counts
4 → 354
Calls
4 calls:
108.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
297.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
83.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
25.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series672.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
515.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
31.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
92.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify1.1s

Counts
366 → 366
Iterations

Useful iterations: done (1.1s)

IterNodesCost
051910724
117689736
done50009262

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.3b
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.7b
(- (+ x 1.0) x)

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
303×*-un-lft-identity
296×times-frac
124×sqrt-prod
117×distribute-lft-out
108×add-sqr-sqrt
106×add-cube-cbrt
37×add-exp-log add-cbrt-cube
35×associate-/r/
34×div-inv
30×associate-*r/
27×associate-/r*
17×flip3-+ flip-+
15×cbrt-undiv div-exp
13×associate-/l*
9×prod-exp cbrt-unprod add-log-exp
4×pow1
3×frac-2neg clear-num
2×sqrt-div diff-log distribute-lft-out--
1×sub-neg flip3-- frac-add associate--l+ sum-log flip-- associate-/l/ difference-of-squares
Counts
4 → 248
Calls
4 calls:
23.0ms
(/ 1.0 (sqrt (+ x 1.0)))
12.0ms
(/ 1.0 (sqrt x))
238.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
49.0ms
(- (+ x 1.0) x)

series909.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ 1.0 (sqrt (+ x 1.0)))
81.0ms
(/ 1.0 (sqrt x))
721.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.0ms
(- (+ x 1.0) x)

simplify1.0s

Counts
260 → 260
Iterations

Useful iterations: done (1.0s)

IterNodesCost
04677637
113587143
done50006683

prune960.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.7b
(/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0)))
4.6b
(/ (/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite315.0ms

Algorithm
rewrite-expression-head
Rules
298×*-un-lft-identity
297×times-frac
124×sqrt-prod
116×distribute-lft-out
106×add-sqr-sqrt add-cube-cbrt
58×add-exp-log add-cbrt-cube
37×associate-/r/
35×div-inv
32×associate-*r/
28×associate-/r*
21×cbrt-undiv div-exp
18×flip3-+ prod-exp cbrt-unprod flip-+
14×associate-/l*
4×pow1 frac-2neg clear-num add-log-exp
2×sqrt-div
1×frac-add associate-/l/
Counts
4 → 258
Calls
4 calls:
28.0ms
(/ 1.0 (sqrt (+ x 1.0)))
15.0ms
(/ 1.0 (sqrt x))
44.0ms
(/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0)))
204.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series881.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ 1.0 (sqrt (+ x 1.0)))
39.0ms
(/ 1.0 (sqrt x))
48.0ms
(/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0)))
675.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify935.0ms

Counts
270 → 270
Iterations

Useful iterations: done (925.0ms)

IterNodesCost
04507240
113076316
done50025834

prune844.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01525
12025
done2025

end0.0ms

sample2.4s

Algorithm
intervals
Results
783.0ms4116×body80valid
475.0ms1844×body640valid
356.0ms8189×body80nan
299.0ms1132×body1280valid
83.0ms602×body320valid
29.0ms306×body160valid