Details

Time bar (total: 1.1m)

sample98.0ms

Algorithm
intervals
Results
22.0ms64×body640valid
19.0ms40×body1280valid
18.0ms243×body80nan
11.0ms123×body80valid
6.0ms10×body160valid
6.0ms19×body320valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
315
215
111
08

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1))
0.2b
(/ 1 (sqrt (+ x 1)))
0.3b
(/ 1 (sqrt x))
2.4b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
1063×times-frac
902×*-un-lft-identity
788×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
580×sqrt-prod
74×distribute-lft-out
56×div-inv
48×sqrt-div
46×associate-/r/
25×difference-of-squares
24×flip3-+ flip-+
22×fma-neg
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube
6×pow-flip associate-/l* add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp hypot-def inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 793
Calls
4 calls:
10.0ms
(sqrt (+ x 1))
19.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))
75.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series214.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(sqrt (+ x 1))
29.0ms
(/ 1 (sqrt (+ x 1)))
45.0ms
(/ 1 (sqrt x))
116.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify3.2s

Counts
805 → 805
Iterations
IterNodes
22418
11414
0651

prune8.8s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 19.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))))
0.3b
(/ 1 (sqrt x))
0.3b
(/ 1 (sqrt x))
2.5b
(- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1)))))

rewrite492.0ms

Algorithm
rewrite-expression-head
Rules
6052×sqrt-prod
3399×times-frac
3032×*-un-lft-identity
2647×add-sqr-sqrt
2453×add-cube-cbrt
2250×prod-diff
752×distribute-rgt-in distribute-lft-in
248×distribute-lft-out
180×div-inv
168×sqrt-div
150×associate-/r/
79×flip3-+ flip-+
72×difference-of-squares
53×associate-*r*
28×distribute-lft-out--
25×fma-neg
17×associate-*l*
14×add-exp-log
12×associate-/r*
10×pow1 add-cbrt-cube
9×frac-times
6×pow-flip associate-/l* add-log-exp
5×flip3-- frac-sub flip--
4×expm1-log1p-u div-exp frac-add insert-posit16 log1p-expm1-u
3×sub-neg associate-*l/ associate-*r/
2×cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp inv-pow
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 2541
Calls
4 calls:
245.0ms
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))))
10.0ms
(/ 1 (sqrt x))
9.0ms
(/ 1 (sqrt x))
37.0ms
(- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1)))))

series543.0ms

Counts
4 → 12
Calls
4 calls:
323.0ms
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))))
48.0ms
(/ 1 (sqrt x))
36.0ms
(/ 1 (sqrt x))
135.0ms
(- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1)))))

simplify7.9s

Counts
2553 → 2553
Iterations
IterNodes
16692
01871

prune29.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (sqrt x))
0.3b
(/ 1 (sqrt x))
0.3b
(/ 1 (sqrt x))
2.4b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
1078×times-frac
904×*-un-lft-identity
797×add-sqr-sqrt
727×add-cube-cbrt
594×prod-diff
584×sqrt-prod
69×distribute-lft-out
57×div-inv
44×sqrt-div associate-/r/
25×difference-of-squares
22×flip3-+ fma-neg flip-+
18×associate-/r*
16×add-exp-log
13×distribute-lft-out--
10×pow1 add-cbrt-cube
9×pow-flip associate-/l*
6×div-exp add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp inv-pow
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 814
Calls
4 calls:
5.0ms
(/ 1 (sqrt x))
5.0ms
(/ 1 (sqrt x))
5.0ms
(/ 1 (sqrt x))
30.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series149.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ 1 (sqrt x))
27.0ms
(/ 1 (sqrt x))
27.0ms
(/ 1 (sqrt x))
66.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.5s

Counts
826 → 826
Iterations
IterNodes
22242
11358
0622

prune7.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1))
0.2b
(/ 1 (sqrt (+ x 1)))
10.6b
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
236×*-un-lft-identity
209×add-sqr-sqrt
189×prod-diff
180×times-frac
174×add-cube-cbrt
110×sqrt-prod
89×unpow-prod-down
33×sqr-pow
26×distribute-lft-out
18×sqrt-div
16×associate-/r/
15×difference-of-squares
9×flip3-+ flip-+ div-inv
7×associate-/r* fma-neg add-exp-log
6×pow1
5×add-cbrt-cube add-log-exp
3×expm1-log1p-u insert-posit16 log1p-expm1-u pow-flip associate-/l*
2×sqrt-pow1 pow1/2 div-exp hypot-def distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp clear-num sub-neg frac-2neg flip3-- diff-log 1-exp flip-- inv-pow
Counts
3 → 303
Calls
3 calls:
4.0ms
(sqrt (+ x 1))
8.0ms
(/ 1 (sqrt (+ x 1)))
21.0ms
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series110.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(sqrt (+ x 1))
27.0ms
(/ 1 (sqrt (+ x 1)))
56.0ms
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify1.8s

Counts
312 → 312
Iterations
IterNodes
33597
21677
1930
0401

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.4b

regimes105.0ms

Accuracy

99.7% (0.1b remaining)

Error of 10.8b against oracle of 10.8b and baseline of 29.4b

bsearch62.0ms

Steps
ItersRangePoint
9
3862.7483140020904
25612678030.77693
7517.51302646943

simplify7.0ms

Iterations
IterNodes
247
147
037

end0.0ms

sample2.2s

Algorithm
intervals
Results
669.0ms7976×body80nan
505.0ms1901×body640valid
377.0ms1148×body1280valid
320.0ms4067×body80valid
111.0ms581×body320valid
34.0ms303×body160valid