Details

Time bar (total: 33.1s)

sample52.0ms

Algorithm
intervals
Results
13.0ms53×body1280valid
10.0ms209×body80nan
7.0ms36×body640valid
7.0ms137×body80valid
3.0ms19×body320valid
1.0ms11×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize12.0ms

Local error

Found 1 expressions with local error:

3.0b
(- (sqrt (+ x 1)) (sqrt x))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
57×sqrt-prod
50×*-un-lft-identity
42×prod-diff
37×add-sqr-sqrt
29×add-cube-cbrt
8×distribute-lft-out
7×fma-neg
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u flip--
Counts
1 → 71
Calls
1 calls:
Slowest
61.0ms
(- (sqrt (+ x 1)) (sqrt x))

series490.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
490.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify6.3s

Counts
122 → 74
Calls
122 calls:
Slowest
298.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
279.0ms
(* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x)))
219.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
205.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
192.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune675.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
15×add-sqr-sqrt add-cube-cbrt
7×fma-def
6×associate-/r* add-exp-log
4×add-cbrt-cube add-log-exp
3×pow1 associate-/l*
2×expm1-log1p-u flip3-+ div-exp associate-/r/ flip-+ insert-posit16 log1p-expm1-u
1×cbrt-undiv +-commutative rec-exp clear-num sum-log frac-2neg 1-exp div-inv pow-flip inv-pow
Counts
2 → 72
Calls
2 calls:
Slowest
60.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
44.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series163.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
91.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
72.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify3.2s

Counts
90 → 78
Calls
90 calls:
Slowest
474.0ms
(* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
461.0ms
(/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
422.0ms
(+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
214.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
206.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))

prune714.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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
32.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
6.0ms
(cbrt (+ x 1))
3.0ms
(cbrt (+ x 1))
3.0ms
(cbrt (+ x 1))

series202.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
63.0ms
(cbrt (+ x 1))
49.0ms
(cbrt (+ x 1))
46.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
44.0ms
(cbrt (+ x 1))

simplify6.7s

Counts
149 → 119
Calls
149 calls:
Slowest
282.0ms
(* (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (+ x 1)) (cbrt (+ x 1))))
266.0ms
(- (+ (* 2/3 (pow (/ 1 x) 1/3)) (pow (/ -1 x) -2/3)) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))
254.0ms
(* (cbrt (- (* x x) (* 1 1))) (cbrt (+ (pow x 3) (pow 1 3))))
252.0ms
(* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (- (* x x) (* 1 1))))
234.0ms
(- (+ (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))))

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
66×cbrt-prod
43×add-sqr-sqrt
41×*-un-lft-identity
36×sqrt-prod
21×add-cube-cbrt
18×cbrt-div
16×sqrt-div
14×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×flip3-+ pow1/3 flip-+ distribute-lft-out unswap-sqr
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 129
Calls
4 calls:
Slowest
28.0ms
(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))
7.0ms
(cbrt (sqrt (+ x 1)))
5.0ms
(cbrt (+ x 1))
4.0ms
(cbrt (sqrt (+ x 1)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
62.0ms
(cbrt (sqrt (+ x 1)))
60.0ms
(cbrt (sqrt (+ x 1)))
51.0ms
(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))
43.0ms
(cbrt (+ x 1))

simplify7.8s

Counts
187 → 141
Calls
187 calls:
Slowest
322.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
314.0ms
(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))
268.0ms
(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))
259.0ms
(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
251.0ms
(- (+ (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))))

prune2.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
940.0ms1648×body1280valid
416.0ms7809×body80nan
376.0ms1291×body640valid
292.0ms4129×body80valid
128.0ms622×body320valid
70.0ms310×body160valid