Details

Time bar (total: 16.6s)

sample48.0ms

Algorithm
intervals
Results
9.0ms55×body640valid
8.0ms245×body80nan
7.0ms151×body80valid
4.0ms22×body1280valid
2.0ms18×body320valid
1.0ms10×body160valid

simplify9.0ms

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: 18.6b

localize22.0ms

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))
3.6b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite258.0ms

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))
21.0ms
(/ 1.0 (sqrt (+ x 1.0)))
11.0ms
(/ 1.0 (sqrt x))
118.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series363.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ x 1.0))
107.0ms
(/ 1.0 (sqrt (+ x 1.0)))
56.0ms
(/ 1.0 (sqrt x))
157.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.3s

Counts
770 → 770
Iterations

Useful iterations: done (2.3s)

IterNodesCost
070140764
1153135216
2301226244
done500120672

prune1.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (sqrt x) (sqrt 1.0))
0.1b
(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
0.2b
(/ 1.0 (sqrt x))
3.8b
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
490×times-frac
384×add-sqr-sqrt
373×*-un-lft-identity
365×add-cube-cbrt
286×prod-diff
140×sqrt-prod
40×div-inv
22×fma-neg
9×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp difference-of-squares
5×distribute-lft-out--
4×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg hypot-udef flip3-- diff-log frac-sub flip--
Counts
4 → 414
Calls
4 calls:
0.0ms
(hypot (sqrt x) (sqrt 1.0))
5.0ms
(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
8.0ms
(/ 1.0 (sqrt x))
91.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

series1.9s

Counts
4 → 12
Calls
4 calls:
300.0ms
(hypot (sqrt x) (sqrt 1.0))
608.0ms
(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
46.0ms
(/ 1.0 (sqrt x))
938.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

simplify2.3s

Counts
426 → 426
Iterations

Useful iterations: done (2.3s)

IterNodesCost
054422119
1125519048
2285314444
done500012362

prune715.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

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))
51.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
33.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
18.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series507.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(sqrt (+ x 1.0))
296.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
70.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
107.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.4s

Counts
110 → 110
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02041790
15571653
218681321
done50001277

prune407.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 17.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.9b
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
22×add-sqr-sqrt
18×times-frac
16×*-un-lft-identity
14×add-cube-cbrt
12×cbrt-undiv div-exp associate-/l*
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-+
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 → 128
Calls
4 calls:
91.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
103.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
27.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
40.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

series795.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
564.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
68.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
3.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

simplify1.6s

Counts
140 → 140
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02893978
18403760
238292747
done50002704

prune694.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

regimes49.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01019
11419
done1419

end0.0ms

sample1.5s

Algorithm
intervals
Results
380.0ms7863×body80nan
372.0ms1848×body640valid
215.0ms1090×body1280valid
180.0ms4094×body80valid
59.0ms614×body320valid
23.0ms354×body160valid