Details

Time bar (total: 13.3s)

sample20.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
2.0ms104×body80nan

simplify21.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
12×times-frac
10×add-sqr-sqrt add-cube-cbrt
4×associate-/r* distribute-lft-out
3×add-exp-log add-cbrt-cube associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv add-log-exp
Counts
1 → 33
Calls
1 calls:
41.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series177.0ms

Counts
1 → 3
Calls
1 calls:
177.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify446.0ms

Counts
36 → 36

prune80.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b
(pow (sqrt (+ x 1.0)) 3)
3.8b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.8b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite281.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
62×sqrt-div
43×add-sqr-sqrt
34×sqrt-prod
32×flip3-+ flip-+
31×add-cube-cbrt
28×associate-*r/ distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
16×frac-sub
12×frac-times
11×swap-sqr
9×add-exp-log sqrt-pow1 pow1/2 associate-/r* add-cbrt-cube
8×associate-*l/
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×sum-cubes sub-div unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div associate-/r/
1×cbrt-undiv pow2 cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- frac-2neg pow-plus sqrt-unprod diff-log unpow3 div-exp pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 184
Calls
4 calls:
59.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
10.0ms
(pow (sqrt (+ x 1.0)) 3)
55.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
146.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
111.0ms
(pow (sqrt (+ x 1.0)) 3)
92.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
274.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify2.3s

Counts
196 → 196

prune628.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.1b
(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.8b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
132×times-frac
127×*-un-lft-identity
96×sqrt-div
76×add-sqr-sqrt
70×flip3-+ flip-+
66×associate-*r/
65×associate-*l*
63×associate-*l/
59×add-cube-cbrt
58×associate-/r/
52×frac-sub
36×add-exp-log
33×distribute-lft-out
29×add-cbrt-cube
26×sqrt-prod
21×pow1
14×frac-times div-exp
13×associate-/l*
11×swap-sqr div-inv
10×cbrt-undiv flip3-- associate-*r* prod-exp flip--
8×sqrt-pow1 pow1/2
7×cbrt-unprod
6×add-log-exp unswap-sqr
5×pow-prod-up
4×pow-prod-down associate-/r* sub-div
3×pow-sqr
2×1-exp *-commutative
1×pow2 distribute-rgt-in sub-neg distribute-rgt-out-- frac-2neg distribute-lft-in pow-plus sqrt-unprod diff-log clear-num rem-square-sqrt associate-/l/
Counts
4 → 272
Calls
4 calls:
948.0ms
(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
349.0ms
(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
52.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
53.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
394.0ms
(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
754.0ms
(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
32.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
103.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

simplify945.0ms

Counts
284 → 284

prune1.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
360×times-frac
280×*-un-lft-identity
186×sqrt-prod
182×add-sqr-sqrt add-cube-cbrt
49×distribute-lft-out
34×associate-/r*
10×associate-/l*
9×add-exp-log add-cbrt-cube div-inv
4×cbrt-undiv div-exp
2×pow1 frac-2neg clear-num associate-/l/ add-log-exp
1×flip3-+ associate-/r/ flip-+
Counts
2 → 265
Calls
2 calls:
61.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
65.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

series334.0ms

Counts
2 → 6
Calls
2 calls:
157.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
177.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

simplify1.5s

Counts
271 → 271

prune619.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes72.0ms

Accuracy

-46.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify578.0ms

end0.0ms

sample689.0ms

Algorithm
intervals
Results
308.0ms7995×body80valid
134.0ms2704×body80nan
1.0ms5×body1280valid