Details

Time bar (total: 15.3s)

sample56.0ms

Algorithm
intervals
Results
11.0ms250×body80nan
10.0ms47×body1280valid
6.0ms142×body80valid
6.0ms38×body640valid
2.0ms17×body320valid
1.0ms12×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ hypot-def
Counts
2 → 89
Calls
2 calls:
8.0ms
(sqrt (+ x 1.0))
101.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series140.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(sqrt (+ x 1.0))
98.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify759.0ms

Counts
95 → 95
Iterations

Useful iterations: done (756.0ms)

IterNodesCost
01371993
13161446
210401125
done5000951

prune188.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
28×distribute-lft-out
24×times-frac sqrt-prod
18×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l*
3×pow1 flip3-+ flip-+
2×expm1-log1p-u sqrt-div associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
Counts
2 → 71
Calls
2 calls:
8.0ms
(sqrt (+ x 1.0))
86.0ms
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series291.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(sqrt (+ x 1.0))
236.0ms
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.3s

Counts
77 → 77
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01551205
1389956
21839895
done5002890

prune246.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite488.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 258
Calls
4 calls:
81.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
61.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
52.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
259.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
482.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
210.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
152.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
221.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify2.1s

Counts
270 → 270
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03176276
17344476
233354198
done50024140

prune878.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cbrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
0.2b
(/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
0.2b
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (/ (cbrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))))
0.3b
(* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (/ (cbrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))))

rewrite849.0ms

Algorithm
rewrite-expression-head
Rules
324×sqrt-prod
222×*-un-lft-identity
173×times-frac
154×add-sqr-sqrt
90×add-cube-cbrt
76×distribute-lft-out
65×cbrt-prod
64×associate-*r*
45×associate-*l*
24×sqrt-div unswap-sqr
18×add-exp-log associate-/r*
16×pow1
15×add-cbrt-cube
10×pow-prod-down associate-/r/
7×associate-/l*
6×frac-times associate-*r/
5×sqrt-pow1 flip3-+ pow1/2 prod-exp cbrt-unprod flip-+ div-inv
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×cbrt-undiv sqrt-unprod div-exp
2×frac-2neg clear-num *-commutative
1×swap-sqr
Counts
4 → 301
Calls
4 calls:
50.0ms
(/ (cbrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
49.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
457.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (/ (cbrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))))
273.0ms
(* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (/ (cbrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
608.0ms
(/ (cbrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
612.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
311.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (/ (cbrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))))
486.0ms
(* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (/ (cbrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))))

simplify786.0ms

Counts
313 → 313
Iterations

Useful iterations: done (771.0ms)

IterNodesCost
05319871
112708810
done50018399

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
0911
1129
2139
done139

end0.0ms

sample2.2s

Algorithm
intervals
Results
626.0ms4105×body80valid
425.0ms1754×body1280valid
324.0ms7835×body80nan
257.0ms1236×body640valid
157.0ms627×body320valid
20.0ms278×body160valid