Details

Time bar (total: 8.6s)

sample35.0ms

Algorithm
intervals
Results
7.0ms66×body640valid
6.0ms42×body1280valid
5.0ms231×body80nan
3.0ms116×body80valid
2.0ms24×body320valid
0.0ms8×body160valid

simplify14.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.2b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite94.0ms

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:
9.0ms
(sqrt (+ x 1.0))
11.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
64.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(sqrt (+ x 1.0))
68.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
119.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify460.0ms

Counts
145 → 145

prune297.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt x))
0.3b
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
0.4b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
3.2b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
234×times-frac
223×add-sqr-sqrt
181×*-un-lft-identity
139×add-cube-cbrt
132×sqrt-prod
67×swap-sqr
49×associate-*r* associate-*l*
30×add-exp-log add-cbrt-cube
18×pow1 distribute-lft-out unswap-sqr
9×cbrt-undiv div-exp frac-sub div-inv
8×frac-times sqrt-div associate-*r/ associate-*l/ prod-exp associate-/r/ cbrt-unprod
6×associate-/r* add-log-exp
4×flip3-+ flip-+
3×associate-/l*
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
1×sub-neg flip3-- frac-2neg diff-log clear-num flip-- difference-of-squares
Counts
4 → 292
Calls
4 calls:
5.0ms
(/ 1.0 (sqrt x))
59.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
31.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
21.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series147.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 1.0 (sqrt x))
24.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
30.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
56.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify430.0ms

Counts
304 → 304

prune617.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.3b
(/ 1.0 (sqrt x))
2.9b
(- (+ x 1.0) x)

rewrite208.0ms

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-*l/
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:
11.0ms
(/ 1.0 (sqrt (+ x 1.0)))
141.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
5.0ms
(/ 1.0 (sqrt x))
32.0ms
(- (+ x 1.0) x)

series557.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ 1.0 (sqrt (+ x 1.0)))
451.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
36.0ms
(/ 1.0 (sqrt x))
1.0ms
(- (+ x 1.0) x)

simplify501.0ms

Counts
260 → 260

prune576.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
5.1b
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite180.0ms

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-*l/
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:
11.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
26.0ms
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
120.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series611.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ 1.0 (sqrt (+ x 1.0)))
35.0ms
(/ 1.0 (sqrt x))
38.0ms
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
466.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify485.0ms

Counts
270 → 270

prune574.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

-1224.4% (5.1b remaining)

Error of 5.2b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify810.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
519.0ms1825×body640valid
334.0ms8124×body80nan
221.0ms1155×body1280valid
146.0ms4066×body80valid
53.0ms628×body320valid
18.0ms326×body160valid