Details

Time bar (total: 3.9m)

sample112.0ms

Algorithm
intervals
Results
29.0ms67×body640valid
25.0ms273×body80nan
18.0ms33×body1280valid
14.0ms130×body80valid
5.0ms16×body320valid
2.0ms10×body160valid

simplify37.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize28.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite93.0ms

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--
Calls
4 calls:
Slowest
33.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
9.0ms
(sqrt (+ x 1))
9.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))

series196.0ms

Calls
4 calls:
Slowest
89.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
45.0ms
(/ 1 (sqrt (+ x 1)))
33.0ms
(sqrt (+ x 1))
28.0ms
(/ 1 (sqrt x))

simplify1.9m

Calls
1414 calls:
Slowest
500.0ms
(fma (- (/ (cbrt 1) (cbrt (sqrt (+ x 1))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
450.0ms
(fma (- (sqrt (+ (* x x) (- (* 1 1) (* x 1))))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))) (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3))))))
371.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (cbrt 1) (cbrt (sqrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
367.0ms
(fma (- (/ (cbrt 1) (cbrt (sqrt (+ x 1))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
352.0ms
(fma (- (/ (cbrt 1) (cbrt (sqrt (+ x 1))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

prune4.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.4b

localize23.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
0.5b
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
0.3b
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(/ 1 (sqrt x))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
296×times-frac
274×*-un-lft-identity
209×add-sqr-sqrt
134×sqrt-prod
127×add-cube-cbrt
80×distribute-lft-out
50×add-exp-log
32×frac-sub
30×swap-sqr
29×pow1
28×div-inv
27×pow-flip
25×unswap-sqr
22×associate-/r* associate-*r* associate-*l*
20×add-cbrt-cube
19×div-exp
18×difference-of-squares associate-/l/
17×frac-times associate-*l/ associate-*r/ un-div-inv
16×prod-exp
9×rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-up inv-pow
7×associate-/l*
6×cbrt-undiv add-log-exp
5×pow-prod-down pow-sqr
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u
3×associate-/r/
2×clear-num frac-2neg flip3-- flip--
1×pow2 sub-neg flip3-+ pow-plus fma-neg diff-log div-sub prod-diff frac-add *-commutative flip-+
Calls
4 calls:
Slowest
68.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
21.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
15.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
5.0ms
(/ 1 (sqrt x))

series208.0ms

Calls
4 calls:
Slowest
116.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
41.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
30.0ms
(/ 1 (sqrt x))
20.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))

simplify36.7s

Calls
479 calls:
Slowest
526.0ms
(/ (sqrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) 1)
506.0ms
(/ (sqrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
494.0ms
(/ (sqrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) (/ 1 (sqrt 1)))
380.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt x) (sqrt x)) (sqrt x))) (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))))
364.0ms
(* (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))) (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))))

prune2.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.2b

localize21.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.1b
(/ 1 (fma x x x))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
661×times-frac
618×*-un-lft-identity
260×add-sqr-sqrt add-cube-cbrt
228×distribute-lft-out
196×sqrt-prod
77×div-inv
32×associate-/r*
25×add-exp-log
22×associate-/l*
15×add-cbrt-cube
12×div-exp
9×pow1
7×pow-flip
6×cbrt-undiv
5×associate-/r/
4×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×inv-pow
2×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
1×frac-add associate-/l/
Calls
4 calls:
Slowest
41.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
8.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))
4.0ms
(/ 1 (fma x x x))

series218.0ms

Calls
4 calls:
Slowest
136.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
31.0ms
(/ 1 (sqrt x))
27.0ms
(/ 1 (sqrt (+ x 1)))
23.0ms
(/ 1 (fma x x x))

simplify32.3s

Calls
600 calls:
Slowest
491.0ms
(+ (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (- (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (* (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))
373.0ms
(/ (/ (cbrt 1) (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
278.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
277.0ms
(/ (/ 1 (fma x x x)) (+ (/ (sqrt 1) (sqrt x)) (/ (sqrt 1) (sqrt (+ x 1)))))
276.0ms
(/ (/ 1 (fma x x x)) (+ (/ (cbrt 1) (sqrt x)) (/ (cbrt 1) (sqrt (+ x 1)))))

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ x (sqrt x))
0.2b
(/ x (sqrt (+ 1 x)))
0.2b
(/ (/ 1 (+ 1 x)) (+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x))))
0.0b
(+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
872×*-un-lft-identity
852×times-frac
332×distribute-lft-out
308×add-sqr-sqrt add-cube-cbrt
280×sqrt-prod
59×div-inv
37×associate-/r/
27×associate-/r* fma-def
24×associate-/l*
19×flip3-+ flip-+
17×add-exp-log
13×add-cbrt-cube
8×div-exp
7×pow1
6×add-log-exp
5×cbrt-undiv
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
2×frac-add pow-div
1×+-commutative rec-exp sum-log sqrt-pow1 pow1/2 1-exp associate-/l/
Calls
4 calls:
Slowest
48.0ms
(/ (/ 1 (+ 1 x)) (+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x))))
29.0ms
(+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x)))
7.0ms
(/ x (sqrt (+ 1 x)))
4.0ms
(/ x (sqrt x))

series330.0ms

Calls
4 calls:
Slowest
139.0ms
(/ (/ 1 (+ 1 x)) (+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x))))
90.0ms
(+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x)))
52.0ms
(/ x (sqrt (+ 1 x)))
50.0ms
(/ x (sqrt x))

simplify39.4s

Calls
706 calls:
Slowest
434.0ms
(/ (/ 1 (+ 1 x)) (+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x))))
404.0ms
(/ (* (* x x) x) (* (* (sqrt x) (sqrt x)) (sqrt x)))
368.0ms
(/ (/ 1 (+ (pow 1 3) (pow x 3))) (/ (* (cbrt x) (cbrt x)) 1))
324.0ms
(/ (/ 1 (+ (pow 1 3) (pow x 3))) (/ (* (cbrt x) (cbrt x)) (sqrt 1)))
321.0ms
(/ (/ 1 (+ (pow 1 3) (pow x 3))) (/ (* (cbrt x) (cbrt x)) (sqrt 1)))

prune2.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
566.0ms4052×body80valid
528.0ms1879×body640valid
420.0ms8046×body80nan
367.0ms1115×body1280valid
101.0ms628×body320valid
56.0ms326×body160valid