Details

Time bar (total: 14.4s)

sample44.0ms

Algorithm
intervals
Results
8.0ms253×body80nan
8.0ms55×body640valid
7.0ms34×body1280valid
5.0ms142×body80valid
1.0ms13×body320valid
1.0ms12×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done14
214
111
08

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize32.0ms

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))
2.6b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite111.0ms

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-cbrt-cube add-exp-log distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
11.0ms
(sqrt (+ x 1.0))
11.0ms
(/ 1.0 (sqrt (+ x 1.0)))
5.0ms
(/ 1.0 (sqrt x))
74.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series444.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ x 1.0))
135.0ms
(/ 1.0 (sqrt (+ x 1.0)))
55.0ms
(/ 1.0 (sqrt x))
211.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify834.0ms

Counts
145 → 145
Iterations
IterNodes
done5001
21655
1462
0216

prune679.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(* (sqrt (+ x 1.0)) (sqrt x))
2.5b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×sqrt-prod
20×*-un-lft-identity
18×add-cbrt-cube add-exp-log
9×pow1 add-cube-cbrt
7×associate-*l*
6×sqrt-div associate-*r* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp associate-*l/ difference-of-squares unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ distribute-lft-out distribute-lft-out--
2×flip3-- associate-*r/ associate-/r/ flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg times-frac sqrt-unprod diff-log *-commutative div-inv associate-/l*
Counts
4 → 93
Calls
4 calls:
12.0ms
(sqrt (+ x 1.0))
70.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
22.0ms
(* (sqrt (+ x 1.0)) (sqrt x))
58.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series591.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ x 1.0))
380.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
76.0ms
(* (sqrt (+ x 1.0)) (sqrt x))
96.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.4s

Counts
105 → 105
Iterations
IterNodes
done5000
23032
1531
0192

prune436.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
107×*-un-lft-identity
43×distribute-lft-out
39×sqrt-prod
31×times-frac
29×add-sqr-sqrt add-cbrt-cube add-exp-log
21×add-cube-cbrt
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×associate-/r* associate-*l* distribute-lft-out--
6×associate-*r* associate-/l* add-log-exp
5×flip3-+ flip-+
4×sqrt-div associate-*l/ associate-/r/ unswap-sqr
3×pow-prod-down associate-/l/
2×clear-num frac-2neg sqrt-pow1 pow1/2 div-inv
1×+-commutative associate-+r- sum-log sqrt-unprod div-sub associate-*r/ *-commutative
Counts
4 → 133
Calls
4 calls:
34.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
93.0ms
(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
44.0ms
(* (sqrt (+ x 1.0)) (sqrt x))
94.0ms
(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
98.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
218.0ms
(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
90.0ms
(* (sqrt (+ x 1.0)) (sqrt x))
743.0ms
(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))

simplify2.2s

Counts
145 → 145
Iterations
IterNodes
done5001
24968
1761
0269

prune608.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
73×times-frac
71×*-un-lft-identity
55×add-cube-cbrt
41×sqrt-prod
33×associate-*l*
25×associate-*r*
22×add-cbrt-cube add-exp-log
15×distribute-lft-out
11×associate-/r*
10×pow1 unswap-sqr
8×associate-/r/
6×cbrt-undiv sqrt-div div-exp associate-/l*
5×flip3-+ prod-exp cbrt-unprod flip-+
4×pow-prod-down div-inv add-log-exp
3×associate-*r/
2×clear-num frac-2neg sqrt-pow1 pow1/2 *-commutative
1×frac-times sqrt-unprod associate-*l/
Counts
4 → 182
Calls
4 calls:
10.0ms
(/ 1.0 (sqrt (+ x 1.0)))
9.0ms
(/ 1.0 (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
63.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (+ x (* (sqrt x) (sqrt (+ x 1.0))))))
27.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series626.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ 1.0 (sqrt (+ x 1.0)))
101.0ms
(/ 1.0 (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
310.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (+ x (* (sqrt x) (sqrt (+ x 1.0))))))
106.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify2.1s

Counts
194 → 194
Iterations
IterNodes
done5000
24807
1859
0302

prune948.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done19
219
118
015

end0.0ms

sample1.5s

Algorithm
intervals
Results
362.0ms1914×body640valid
298.0ms7946×body80nan
295.0ms1154×body1280valid
189.0ms4059×body80valid
100.0ms560×body320valid
22.0ms313×body160valid