Details

Time bar (total: 29.5s)

sample75.0ms

Algorithm
intervals
Results
19.0ms55×body1280valid
17.0ms267×body80nan
11.0ms41×body640valid
9.0ms132×body80valid
4.0ms22×body320valid
1.0ms6×body160valid

simplify38.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
37.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize17.0ms

Local error

Found 2 expressions with local error:

2.1b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
55×*-un-lft-identity
43×add-sqr-sqrt
42×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×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log hypot-def insert-posit16 log1p-expm1-u
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 92
Calls
2 calls:
Slowest
43.0ms
(- (sqrt (+ x 1)) (sqrt x))
5.0ms
(sqrt (+ x 1))

series102.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
73.0ms
(- (sqrt (+ x 1)) (sqrt x))
29.0ms
(sqrt (+ x 1))

simplify6.0s

Counts
120 → 98
Calls
120 calls:
Slowest
248.0ms
(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
215.0ms
(fma 1 (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
211.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
210.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
196.0ms
(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune887.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 28.8b

localize29.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.1b
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
64×sqrt-prod
56×add-sqr-sqrt
34×pow1
32×add-cube-cbrt
26×distribute-lft-out
24×times-frac
19×swap-sqr
16×sqrt-pow1 pow1/2
13×associate-*r* associate-*l*
12×sqrt-div
10×add-cbrt-cube add-exp-log pow-prod-up
8×difference-of-squares unswap-sqr
7×flip3-+ flip-+
6×associate-/r* pow-prod-down pow-sqr add-log-exp
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u associate-/l*
2×pow2 rem-square-sqrt pow-plus flip3-- sqrt-unprod associate-*l/ prod-exp associate-*r/ associate-/r/ *-commutative cbrt-unprod flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
4 → 189
Calls
4 calls:
Slowest
80.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
26.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
25.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
9.0ms
(* (sqrt x) (sqrt x))

series181.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
22.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
19.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
17.0ms
(* (sqrt x) (sqrt x))

simplify7.8s

Counts
214 → 201
Calls
214 calls:
Slowest
800.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
506.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
309.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
262.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
242.0ms
(/ (* (* (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
28×sqrt-prod
22×distribute-lft-out
21×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt
7×fma-def add-exp-log
6×associate-/r*
5×pow1 add-cbrt-cube add-log-exp
3×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u associate-/l*
2×sqrt-div div-exp associate-/r/ hypot-def
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp clear-num sum-log frac-2neg sqrt-pow1 pow1/2 1-exp div-inv pow-flip inv-pow
Counts
3 → 93
Calls
3 calls:
Slowest
49.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
26.0ms
(+ (sqrt (+ x 1)) (sqrt x))
5.0ms
(sqrt (+ x 1))

series231.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
100.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
84.0ms
(+ (sqrt (+ x 1)) (sqrt x))
47.0ms
(sqrt (+ x 1))

simplify1.6s

Counts
81 → 102
Calls
81 calls:
Slowest
265.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
168.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
158.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
59.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
58.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))

prune930.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
0.2b
(* (cbrt (+ x 1)) (cbrt (+ x 1)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 107
Calls
4 calls:
Slowest
55.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
6.0ms
(cbrt (+ x 1))
5.0ms
(cbrt (+ x 1))
5.0ms
(cbrt (+ x 1))

series187.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
62.0ms
(cbrt (+ x 1))
45.0ms
(cbrt (+ x 1))
41.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
39.0ms
(cbrt (+ x 1))

simplify5.4s

Counts
94 → 119
Calls
94 calls:
Slowest
609.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
271.0ms
(* (cbrt (- (* x x) (* 1 1))) (cbrt (+ (pow x 3) (pow 1 3))))
267.0ms
(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))
229.0ms
(* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (- (* x x) (* 1 1))))
229.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
563.0ms1753×body1280valid
503.0ms7847×body80nan
332.0ms4094×body80valid
263.0ms1215×body640valid
165.0ms623×body320valid
36.0ms315×body160valid