Details

Time bar (total: 6.5s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms76×body80nan

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
068
188
done88

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt times-frac
5×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×fma-def associate-/l*
2×pow1 expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 52
Calls
2 calls:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
16.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series192.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(+ 1.0 (sqrt (+ x 1.0)))
146.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify388.0ms

Counts
58 → 58
Iterations

Useful iterations: done (386.0ms)

IterNodesCost
0121771
1296722
21109665
done5000660

prune115.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ x (pow (+ 1.0 (sqrt (+ x 1.0))) 1))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
24×times-frac
20×add-sqr-sqrt add-cube-cbrt
16×unpow-prod-down
8×associate-/r*
7×add-exp-log
5×distribute-lft-out
4×add-cbrt-cube add-log-exp sqr-pow
3×fma-def div-exp associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u
1×cbrt-undiv +-commutative pow-to-exp frac-2neg flip3-+ pow-exp clear-num sum-log flip-+ div-inv
Counts
2 → 68
Calls
2 calls:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
34.0ms
(/ x (pow (+ 1.0 (sqrt (+ x 1.0))) 1))

series185.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
143.0ms
(/ x (pow (+ 1.0 (sqrt (+ x 1.0))) 1))

simplify559.0ms

Counts
74 → 74
Iterations

Useful iterations: done (557.0ms)

IterNodesCost
01551216
1355993
21479885
done5000881

prune121.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

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)
3.2b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.3b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite106.0ms

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×expm1-log1p-u sum-cubes log1p-expm1-u 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 fma-neg sqrt-unprod diff-log unpow3 div-exp prod-diff pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 194
Calls
4 calls:
23.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms
(pow (sqrt (+ x 1.0)) 3)
13.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
55.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
67.0ms
(pow (sqrt (+ x 1.0)) 3)
65.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
193.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify2.1s

Counts
206 → 206
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03264145
18172999
238282729
done50012725

prune437.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
54×add-sqr-sqrt
52×times-frac
38×add-cube-cbrt
35×sqrt-prod
30×associate-*r*
14×distribute-lft-out
10×add-exp-log add-cbrt-cube
6×associate-*l* associate-/l* unswap-sqr
5×pow1 add-log-exp
4×associate-/r* associate-/r/
3×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
3 → 125
Calls
3 calls:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
17.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
46.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series484.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(+ 1.0 (sqrt (+ x 1.0)))
299.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
142.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify729.0ms

Counts
134 → 134
Iterations

Useful iterations: done (725.0ms)

IterNodesCost
01992185
15161933
220761759
done50011750

prune237.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes13.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
0810
1128
done128

end0.0ms

sample310.0ms

Algorithm
intervals
Results
155.0ms7998×body80valid
43.0ms2640×body80nan
0.0ms2×body1280valid