Details

Time bar (total: 14.1s)

sample26.0ms

Algorithm
intervals
Results
12.0ms255×body80valid
3.0ms82×body80nan
0.0ms1×body1280valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done8
18
06

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
13×add-sqr-sqrt
12×times-frac add-cube-cbrt
5×distribute-lft-out
4×associate-/r* add-cbrt-cube add-exp-log sqrt-prod
3×pow1 associate-/l*
2×flip3-+ sqrt-div associate-/r/ flip-+ insert-posit16 add-log-exp
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
2 → 51
Calls
2 calls:
5.0ms
(sqrt (+ x 1.0))
19.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series240.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(sqrt (+ x 1.0))
204.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts
57 → 57
Iterations
IterNodes
done5000
21041
1293
0129

prune254.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
30×add-sqr-sqrt
26×times-frac
22×add-cube-cbrt
18×associate-*r*
16×add-exp-log
10×add-cbrt-cube
8×distribute-lft-out
7×pow1
4×associate-/r* div-exp prod-exp associate-/r/ sqrt-prod
3×flip3-+ associate-*l* flip-+ insert-posit16 associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
3 → 97
Calls
3 calls:
8.0ms
(sqrt (+ x 1.0))
37.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
42.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series342.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(sqrt (+ x 1.0))
107.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
192.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.3s

Counts
106 → 106
Iterations
IterNodes
done5000
21522
1433
0176

prune322.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.5b
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
306×*-un-lft-identity
232×sqrt-prod
192×add-sqr-sqrt
190×add-cube-cbrt
58×distribute-lft-out
30×associate-/l*
24×sqrt-div
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-cbrt-cube add-exp-log
10×div-inv
6×pow1
4×cbrt-undiv div-exp insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 321
Calls
4 calls:
15.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
15.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
22.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
48.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
154.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
169.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
562.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
175.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify2.3s

Counts
333 → 333
Iterations
IterNodes
done5019
22455
1895
0384

prune951.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
2.8b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.5b
(/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

rewrite291.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-div
54×add-sqr-sqrt
44×*-un-lft-identity
34×flip3-+ flip-+
30×associate-*r/ add-cube-cbrt
26×sqrt-prod
25×times-frac associate-*l*
21×pow1
16×frac-sub
14×frac-times
13×add-cbrt-cube add-exp-log
11×swap-sqr
10×associate-*r*
9×associate-*l/
8×sqrt-pow1 pow1/2
7×cube-unmult pow3 sum-cubes
6×distribute-lft-out add-log-exp unswap-sqr
5×pow-prod-up
4×associate-/r* pow-prod-down associate-/r/ insert-posit16 sub-div
3×prod-exp pow-sqr cbrt-unprod associate-/l*
2×cbrt-undiv div-exp *-commutative div-inv
1×pow2 distribute-rgt-in clear-num sub-neg rem-square-sqrt frac-2neg distribute-lft-in pow-plus flip3-- distribute-rgt-out-- sqrt-unprod diff-log flip--
Counts
4 → 175
Calls
4 calls:
192.0ms
(* (/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
26.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
19.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
52.0ms
(/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

series852.0ms

Counts
4 → 12
Calls
4 calls:
507.0ms
(* (/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
24.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
78.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
242.0ms
(/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

simplify2.9s

Counts
187 → 187
Iterations
IterNodes
done5004
24594
11202
0388

prune901.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done13
113
08

end0.0ms

sample657.0ms

Algorithm
intervals
Results
401.0ms7994×body80valid
118.0ms2721×body80nan
1.0ms6×body1280valid