Details

Time bar (total: 29.7s)

sample50.0ms

Algorithm
intervals
Results
10.0ms57×body640valid
9.0ms243×body80nan
8.0ms37×body1280valid
6.0ms131×body80valid
3.0ms22×body320valid
1.0ms9×body160valid

simplify22.0ms

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: 20.2b

localize9.0ms

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))
2.3b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite283.0ms

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:
10.0ms
(sqrt (+ x 1.0))
17.0ms
(/ 1.0 (sqrt (+ x 1.0)))
13.0ms
(/ 1.0 (sqrt x))
127.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series366.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(sqrt (+ x 1.0))
109.0ms
(/ 1.0 (sqrt (+ x 1.0)))
55.0ms
(/ 1.0 (sqrt x))
170.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify3.2s

Counts
770 → 770
Iterations

Useful iterations: done (3.1s)

IterNodesCost
070140764
1153135216
2301226244
done500120672

prune1.2s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 19.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
0.3b
(/ 1.0 (sqrt x))
0.3b
(/ 1.0 (sqrt x))
2.3b
(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
5936×sqrt-prod
3335×times-frac
2978×*-un-lft-identity
2551×add-sqr-sqrt
2453×add-cube-cbrt
2250×prod-diff
752×distribute-rgt-in distribute-lft-in
246×distribute-lft-out
174×div-inv
168×sqrt-div
150×associate-/r/
79×flip3-+ flip-+
32×difference-of-squares
31×associate-*r*
25×fma-neg
24×distribute-lft-out--
15×associate-*l*
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×frac-times
6×pow1 associate-/l* add-log-exp
5×flip3-- frac-sub flip--
4×expm1-log1p-u frac-add log1p-expm1-u
3×sub-neg associate-*r/ associate-*l/
2×cbrt-undiv frac-2neg div-exp clear-num
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 2479
Calls
4 calls:
947.0ms
(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
9.0ms
(/ 1.0 (sqrt x))
6.0ms
(/ 1.0 (sqrt x))
133.0ms
(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
75.0ms
(/ 1.0 (sqrt x))
70.0ms
(/ 1.0 (sqrt x))
512.0ms
(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

simplify3.1s

Counts
2491 → 2491
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02051210323
done5000187953

prune10.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt x))
0.5b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
3.2b
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (/ (* 1.0 1.0) (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
15.4b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (/ (* 1.0 1.0) (+ x 1.0)))

rewrite290.0ms

Algorithm
rewrite-expression-head
Rules
312×times-frac
274×*-un-lft-identity
208×add-sqr-sqrt
134×add-cube-cbrt
132×sqrt-prod
85×distribute-lft-out
32×difference-of-squares
28×swap-sqr
22×associate-*r* associate-*l*
20×add-exp-log associate-/r* add-cbrt-cube
19×div-inv
11×pow1
10×prod-diff
9×unswap-sqr
8×associate-/l*
6×cbrt-undiv div-exp frac-sub add-log-exp
5×associate-/r/ associate-/l/
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×frac-times associate-*r/ associate-*l/
2×flip3-- frac-2neg flip3-+ clear-num flip-- flip-+
1×pow2 sub-neg pow-plus fma-neg diff-log div-sub pow-prod-down frac-add pow-sqr *-commutative pow-prod-up
Counts
4 → 290
Calls
4 calls:
7.0ms
(/ 1.0 (sqrt x))
34.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
194.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (/ (* 1.0 1.0) (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
34.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (/ (* 1.0 1.0) (+ x 1.0)))

series513.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ 1.0 (sqrt x))
27.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
371.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (/ (* 1.0 1.0) (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
71.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (/ (* 1.0 1.0) (+ x 1.0)))

simplify2.4s

Counts
302 → 302
Iterations

Useful iterations: done (2.4s)

IterNodesCost
04778462
113397784
247646651
done50006649

prune891.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
2.0b
(- (+ x 1.0) x)

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
319×*-un-lft-identity
296×times-frac
124×sqrt-prod
121×distribute-lft-out
116×add-sqr-sqrt
114×add-cube-cbrt
37×add-exp-log add-cbrt-cube
35×associate-/r/
34×div-inv
30×associate-*r/
27×associate-/r*
17×flip3-+ flip-+
15×cbrt-undiv div-exp
13×associate-/l*
12×prod-diff
9×prod-exp cbrt-unprod add-log-exp
4×pow1 expm1-log1p-u fma-neg log1p-expm1-u
3×frac-2neg clear-num
2×sqrt-div diff-log distribute-lft-out--
1×sub-neg flip3-- frac-add associate--l+ sum-log flip-- associate-/l/ difference-of-squares
Counts
4 → 272
Calls
4 calls:
13.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
149.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
45.0ms
(- (+ x 1.0) x)

series581.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
471.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.0ms
(- (+ x 1.0) x)

simplify692.0ms

Counts
284 → 284
Iterations

Useful iterations: done (682.0ms)

IterNodesCost
04938052
112567393
done50006568

prune526.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

regimes34.0ms

Accuracy

0% (0.3b remaining)

Error of 5.3b against oracle of 5.0b and baseline of 5.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01323
11723
done1723

end0.0ms

sample1.5s

Algorithm
intervals
Results
510.0ms1833×body640valid
288.0ms1123×body1280valid
266.0ms7865×body80nan
171.0ms4161×body80valid
84.0ms602×body320valid
17.0ms281×body160valid