Details

Time bar (total: 29.4s)

sample111.0ms

Algorithm
intervals
Results
27.0ms278×body80nan
25.0ms56×body640valid
19.0ms33×body1280valid
16.0ms142×body80valid
7.0ms20×body320valid
1.0ms5×body160valid

simplify61.0ms

Calls
1 calls:
Slowest
60.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize30.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
24×prod-diff
23×*-un-lft-identity
22×add-sqr-sqrt
19×add-cube-cbrt
17×div-inv
12×sqrt-div
10×associate-/r/
9×associate-/r*
6×pow1 flip3-+ add-exp-log sqrt-prod flip-+ add-log-exp
4×expm1-log1p-u add-cbrt-cube fma-neg insert-posit16 log1p-expm1-u pow-flip distribute-lft-out--
3×pow1/2
2×rec-exp clear-num frac-2neg inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip-- difference-of-squares
Calls
4 calls:
Slowest
17.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
3.0ms
(/ 1 (sqrt (+ x 1)))
2.0ms
(/ 1 (sqrt x))
1.0ms
(sqrt (+ x 1))

series82.0ms

Calls
4 calls:
Slowest
41.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
16.0ms
(/ 1 (sqrt (+ x 1)))
14.0ms
(/ 1 (sqrt x))
10.0ms
(sqrt (+ x 1))

simplify5.1s

Calls
92 calls:
Slowest
208.0ms
(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))))))
200.0ms
(fma 1 (/ 1 (sqrt x)) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
186.0ms
(fma (* (cbrt (/ 1 (sqrt x))) (cbrt (/ 1 (sqrt x)))) (cbrt (/ 1 (sqrt x))) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
182.0ms
(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))))))
179.0ms
(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))))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.1b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
0.4b
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
0.3b
(/ 1 (sqrt x))
0.3b
(/ 1 (sqrt x))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
16×frac-sub
14×add-exp-log pow-flip
9×frac-times associate-*l/ associate-*r/ un-div-inv
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt inv-pow
6×rec-exp associate-/r* add-cbrt-cube pow1/2 pow-prod-up add-log-exp
4×expm1-log1p-u associate-*r* associate-*l* pow-prod-down prod-exp insert-posit16 log1p-expm1-u div-inv
2×clear-num frac-2neg
1×pow2 sub-neg pow-plus flip3-- fma-neg diff-log prod-diff *-commutative cbrt-unprod flip-- difference-of-squares
Calls
4 calls:
Slowest
10.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
6.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
1.0ms
(/ 1 (sqrt x))
1.0ms
(/ 1 (sqrt x))

series62.0ms

Calls
4 calls:
Slowest
18.0ms
(/ 1 (sqrt x))
17.0ms
(/ 1 (sqrt x))
16.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
10.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))

simplify4.3s

Calls
94 calls:
Slowest
264.0ms
(- (* (* 1 (/ 1 (sqrt x))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (sqrt x) (* 1 1)))
259.0ms
(/ (exp (* (/ 1 (sqrt x)) (/ 1 (sqrt x)))) (exp (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))))
213.0ms
(- (* (* (/ 1 (sqrt x)) 1) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (sqrt x) (* 1 1)))
195.0ms
(- (* (* (/ 1 (sqrt x)) 1) (sqrt (+ x 1))) (* (sqrt x) (* (/ 1 (sqrt (+ x 1))) 1)))
195.0ms
(- (* (/ 1 (sqrt x)) (sqrt (+ x 1))) (* (sqrt x) (* 1 (/ 1 (sqrt (+ x 1))))))

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.6b

localize17.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.1b
(/ 1 (fma x x x))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
32×div-inv
28×times-frac
21×add-sqr-sqrt add-cube-cbrt
20×distribute-lft-out
19×associate-/r*
11×add-exp-log
7×pow1
6×add-cbrt-cube
5×associate-/r/ pow-flip
4×expm1-log1p-u rec-exp clear-num frac-2neg insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×sqrt-prod inv-pow
2×flip3-+ pow1/2 sqrt-div div-exp flip-+
1×cbrt-undiv frac-add associate-/l/
Calls
4 calls:
Slowest
27.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
3.0ms
(/ 1 (sqrt (+ x 1)))
2.0ms
(/ 1 (fma x x x))
2.0ms
(/ 1 (sqrt x))

series111.0ms

Calls
4 calls:
Slowest
71.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
15.0ms
(/ 1 (fma x x x))
13.0ms
(/ 1 (sqrt x))
12.0ms
(/ 1 (sqrt (+ x 1)))

simplify7.3s

Calls
102 calls:
Slowest
411.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
406.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
397.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
383.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
381.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
15×flip3-+ flip-+
13×associate-/r/
12×frac-times
11×*-un-lft-identity
10×associate-/r*
9×add-sqr-sqrt pow1 add-exp-log add-cube-cbrt
6×add-cbrt-cube frac-add associate-*r/
5×associate-*r* div-inv
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l* sqrt-prod
2×rec-exp sqrt-div pow-prod-down prod-exp pow-flip distribute-lft-out
1×distribute-rgt-in distribute-lft-in *-commutative cbrt-unprod inv-pow
Calls
4 calls:
Slowest
15.0ms
(* (+ x 1) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1)))))
11.0ms
(/ 1 (* (+ x 1) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1))))))
1.0ms
(/ x (sqrt (+ x 1)))
1.0ms
(/ x (sqrt x))

series176.0ms

Calls
4 calls:
Slowest
75.0ms
(/ 1 (* (+ x 1) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1))))))
54.0ms
(* (+ x 1) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1)))))
25.0ms
(/ x (sqrt x))
22.0ms
(/ x (sqrt (+ x 1)))

simplify5.4s

Calls
66 calls:
Slowest
374.0ms
(* (+ (* x x) (- (* 1 1) (* x 1))) (* (sqrt x) (sqrt (+ x 1))))
372.0ms
(* (+ (* x x) (- (* 1 1) (* x 1))) (* (sqrt x) (sqrt (+ x 1))))
369.0ms
(+ (* (/ x (sqrt x)) (/ x (sqrt x))) (- (* (/ x (sqrt (+ x 1))) (/ x (sqrt (+ x 1)))) (* (/ x (sqrt x)) (/ x (sqrt (+ x 1))))))
314.0ms
(* (+ (pow x 3) (pow 1 3)) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1)))))
308.0ms
(* (- (* x x) (* 1 1)) (+ (pow (/ x (sqrt x)) 3) (pow (/ x (sqrt (+ x 1))) 3)))

prune711.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
824.0ms8167×body80nan
575.0ms1796×body640valid
421.0ms1180×body1280valid
273.0ms4121×body80valid
113.0ms621×body320valid
33.0ms282×body160valid