Details

Time bar (total: 2.7m)

sample93.0ms

Algorithm
intervals
Results
24.0ms67×body640valid
22.0ms274×body80nan
16.0ms31×body1280valid
11.0ms128×body80valid
6.0ms21×body320valid
2.0ms9×body160valid

simplify37.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize20.0ms

Local error

Found 3 expressions with local error:

2.4b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
1063×times-frac
897×*-un-lft-identity
782×add-sqr-sqrt
712×add-cube-cbrt
594×prod-diff
576×sqrt-prod
73×distribute-lft-out
56×div-inv
46×sqrt-div associate-/r/
25×difference-of-squares
23×flip3-+ flip-+
22×fma-neg
13×associate-/r* distribute-lft-out--
11×add-exp-log
7×pow1 add-cbrt-cube
6×pow-flip associate-/l*
5×add-log-exp
4×div-exp
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp inv-pow
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
3 → 772
Calls
3 calls:
Slowest
35.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
25.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))

series178.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
100.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
41.0ms
(/ 1 (sqrt x))
36.0ms
(/ 1 (sqrt (+ x 1)))

simplify2.0m

Counts
1442 → 781
Calls
1442 calls:
Slowest
491.0ms
(fma (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt x)) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
453.0ms
(* (* (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
410.0ms
(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)))))))
410.0ms
(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)))))))
391.0ms
(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)))))))

prune4.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.5b

localize14.0ms

Local error

Found 3 expressions with local error:

2.4b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
84×sqrt-prod
74×*-un-lft-identity
69×add-sqr-sqrt
42×prod-diff
37×add-cube-cbrt
12×difference-of-squares
11×distribute-lft-out
10×times-frac add-cbrt-cube add-exp-log associate-/l*
9×distribute-lft-out--
7×pow1 fma-neg associate-*r*
6×associate-*l*
5×add-log-exp
4×sqrt-div associate-*r/ unswap-sqr
3×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u
2×cbrt-undiv sqrt-pow1 flip3-+ flip3-- pow1/2 div-exp prod-exp associate-/r/ cbrt-unprod flip-+ flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Counts
3 → 150
Calls
3 calls:
Slowest
58.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
27.0ms
(- (sqrt (+ x 1)) (sqrt x))
19.0ms
(* (sqrt x) (sqrt (+ x 1)))

series254.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
145.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
56.0ms
(* (sqrt x) (sqrt (+ x 1)))
52.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify7.6s

Counts
222 → 159
Calls
222 calls:
Slowest
347.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
258.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (+ (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
225.0ms
(* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1))))
223.0ms
(* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x)))
190.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))

prune848.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
110×*-un-lft-identity
78×times-frac
51×sqrt-prod
46×add-sqr-sqrt
41×distribute-lft-out
38×add-cube-cbrt
31×add-exp-log
27×associate-/l*
19×add-cbrt-cube
14×div-exp
8×pow1 associate-/r/
7×cbrt-undiv associate-/r* associate-*r*
6×associate-*l*
5×flip3-+ prod-exp flip-+
4×sqrt-div associate-*r/ div-inv unswap-sqr
3×expm1-log1p-u rec-exp 1-exp pow-prod-down cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg sqrt-pow1 pow1/2
1×sqrt-unprod *-commutative pow-flip inv-pow associate-/l/
Counts
3 → 161
Calls
3 calls:
Slowest
44.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
25.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
17.0ms
(* (sqrt x) (sqrt (+ x 1)))

series286.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
173.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
63.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
49.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify11.4s

Counts
216 → 170
Calls
216 calls:
Slowest
309.0ms
(/ (/ 1 (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (sqrt x))
271.0ms
(/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
239.0ms
(/ (* (sqrt x) (sqrt (+ x 1))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
239.0ms
(/ (* (sqrt x) (sqrt (+ x 1))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
238.0ms
(/ (* (sqrt x) (sqrt (+ x 1))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

prune920.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
172×times-frac
123×*-un-lft-identity
95×add-sqr-sqrt add-cube-cbrt
56×sqrt-prod
16×add-exp-log associate-/l*
14×distribute-lft-out
10×associate-/r* add-cbrt-cube div-inv
8×div-exp
4×pow1 cbrt-undiv
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rec-exp clear-num frac-2neg sqrt-div 1-exp associate-/r/
1×flip3-+ flip-+ fma-udef pow-flip inv-pow associate-/l/
Counts
3 → 178
Calls
3 calls:
Slowest
11.0ms
(/ (/ 1 (fma (sqrt x) (sqrt (+ x 1)) x)) (sqrt (+ x 1)))
4.0ms
(/ 1 (fma (sqrt x) (sqrt (+ x 1)) x))
0.0ms
(fma (sqrt x) (sqrt (+ x 1)) x)

series328.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
165.0ms
(/ (/ 1 (fma (sqrt x) (sqrt (+ x 1)) x)) (sqrt (+ x 1)))
93.0ms
(/ 1 (fma (sqrt x) (sqrt (+ x 1)) x))
71.0ms
(fma (sqrt x) (sqrt (+ x 1)) x)

simplify9.6s

Counts
288 → 187
Calls
288 calls:
Slowest
425.0ms
(/ (/ (* (* 1 1) 1) (* (* (fma (sqrt x) (sqrt (+ x 1)) x) (fma (sqrt x) (sqrt (+ x 1)) x)) (fma (sqrt x) (sqrt (+ x 1)) x))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
422.0ms
(* (* (fma (sqrt x) (sqrt (+ x 1)) x) (fma (sqrt x) (sqrt (+ x 1)) x)) (fma (sqrt x) (sqrt (+ x 1)) x))
293.0ms
(/ (* (* (/ 1 (fma (sqrt x) (sqrt (+ x 1)) x)) (/ 1 (fma (sqrt x) (sqrt (+ x 1)) x))) (/ 1 (fma (sqrt x) (sqrt (+ x 1)) x))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
270.0ms
(/ (/ 1 (fma (sqrt x) (sqrt (+ x 1)) x)) (sqrt (+ x 1)))
249.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (fma (sqrt x) (sqrt (+ x 1)) x)) (cbrt (fma (sqrt x) (sqrt (+ x 1)) x)))) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.3b remaining)

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

bsearch1.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
749.0ms8167×body80nan
443.0ms1796×body640valid
383.0ms1094×body1280valid
235.0ms4178×body80valid
139.0ms636×body320valid
32.0ms296×body160valid