Details

Time bar (total: 16.8s)

sample71.0ms

Algorithm
intervals
Results
24.0ms252×body80nan
11.0ms56×body640valid
9.0ms42×body1280valid
6.0ms123×body80valid
3.0ms21×body320valid
1.0ms14×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.5b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
879×*-un-lft-identity
747×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
566×sqrt-prod
74×distribute-lft-out
54×div-inv
48×sqrt-div
46×associate-/r/
24×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip-- hypot-def
Counts
4 → 758
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
15.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
93.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series758.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(sqrt (+ x 1.0))
109.0ms
(/ 1.0 (sqrt (+ x 1.0)))
72.0ms
(/ 1.0 (sqrt x))
534.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.9s

Counts
770 → 770
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
070140764
1158535304
2497827512
done500027512

prune1.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 20.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
3.6b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×*-un-lft-identity sqrt-prod
11×add-exp-log add-cube-cbrt add-cbrt-cube
9×pow1
7×associate-*r*
6×sqrt-div associate-*l* add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u unswap-sqr
3×sqrt-pow1 flip3-+ times-frac pow1/2 pow-prod-down flip-+ associate-/l*
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ flip-- cbrt-unprod associate-/l/ distribute-lft-out
1×sub-neg rem-sqrt-square frac-2neg fma-neg sqrt-unprod diff-log div-sub prod-diff clear-num associate-/r* *-commutative hypot-def div-inv
Counts
4 → 98
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
63.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
40.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
32.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series656.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ x 1.0))
409.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
84.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
124.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.8s

Counts
110 → 110
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02041790
15871665
228051364
done50011356

prune446.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
0.1b
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.4b
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
22×add-sqr-sqrt times-frac
16×*-un-lft-identity
14×add-cube-cbrt associate-/l*
12×cbrt-undiv div-exp
11×sqrt-prod
10×associate-*r/
8×pow1 associate-/r/
7×associate-*r* prod-exp cbrt-unprod
6×associate-*l* add-log-exp
5×flip3-+ flip-+ distribute-lft-out--
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv unswap-sqr
3×div-sub pow-prod-down associate-/l/
2×flip3-- frac-2neg sqrt-pow1 pow1/2 associate--l+ clear-num associate-/r* flip--
1×distribute-rgt-in sub-neg distribute-lft-in fma-neg sqrt-unprod diff-log prod-diff *-commutative distribute-lft-out
Counts
4 → 133
Calls
4 calls:
97.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
96.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
32.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
56.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

series936.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
690.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
61.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
5.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

simplify572.0ms

Counts
145 → 145
Iterations

Useful iterations: done (565.0ms)

IterNodesCost
02954063
19103406
done50012860

prune527.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
25×*-un-lft-identity
24×add-sqr-sqrt
18×times-frac sqrt-prod
16×add-cube-cbrt
12×cbrt-undiv div-exp associate-/l*
10×associate-*r/
8×pow1 associate-/r/
7×associate-*r* prod-exp cbrt-unprod
6×fma-def flip3-+ associate-*l* flip-+ add-log-exp
5×distribute-lft-out
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r*
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 128
Calls
4 calls:
24.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
25.0ms
(/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
56.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
26.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series937.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
147.0ms
(/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
625.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
71.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify2.0s

Counts
140 → 140
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02672572
17572246
243801891
done50001888

prune492.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes76.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01229
11629
done1629

end0.0ms

sample1.9s

Algorithm
intervals
Results
454.0ms4060×body80valid
412.0ms8028×body80nan
334.0ms1838×body640valid
278.0ms1157×body1280valid
65.0ms603×body320valid
57.0ms342×body160valid