Details

Time bar (total: 21.5s)

sample40.0ms

Algorithm
intervals
Results
7.0ms265×body80nan
6.0ms45×body1280valid
5.0ms49×body640valid
4.0ms130×body80valid
2.0ms24×body320valid
0.0ms8×body160valid

simplify26.0ms

Counts
1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize7.0ms

Local error

Found 1 expressions with local error:

2.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
1 → 19
Calls
1 calls:
60.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series103.0ms

Counts
1 → 3
Calls
1 calls:
103.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify811.0ms

Counts
22 → 22

prune92.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 55
Calls
2 calls:
60.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
75.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series292.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
209.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify500.0ms

Counts
61 → 61

prune187.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite865.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
80.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
83.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
73.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
558.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.1s

Counts
4 → 12
Calls
4 calls:
224.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
234.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
459.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
189.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.5s

Counts
457 → 457

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1 (sqrt 1)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b
(* (/ (/ 1 (sqrt 1)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite2.8s

Algorithm
rewrite-expression-head
Rules
3737×sqrt-prod
3192×times-frac
2572×*-un-lft-identity
2095×add-sqr-sqrt
1085×add-cube-cbrt
764×distribute-lft-out
402×associate-*r*
270×associate-*l*
220×unswap-sqr
80×add-exp-log
68×sqrt-div
60×associate-/r/
58×associate-/l*
55×div-inv
52×add-cbrt-cube
43×div-exp
33×associate-/r*
30×flip3-+ flip-+
25×cbrt-undiv
15×prod-exp
9×cbrt-unprod
6×pow1
4×rec-exp 1-exp add-log-exp
3×frac-2neg clear-num
2×associate-/l/
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 1756
Calls
4 calls:
89.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
84.0ms
(/ (/ 1 (sqrt 1)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
2.1s
(* (/ (/ 1 (sqrt 1)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
238.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series2.2s

Counts
4 → 12
Calls
4 calls:
518.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
554.0ms
(/ (/ 1 (sqrt 1)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
221.0ms
(* (/ (/ 1 (sqrt 1)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
897.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.7s

Counts
1768 → 1768

prune5.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes54.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify22.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
625.0ms1229×body640valid
281.0ms1734×body1280valid
277.0ms8036×body80nan
151.0ms4056×body80valid
52.0ms659×body320valid
18.0ms322×body160valid