Details

Time bar (total: 2.4m)

sample125.0ms

Algorithm
intervals
Results
29.0ms65×body640valid
29.0ms298×body80nan
25.0ms29×body1280valid
16.0ms136×body80valid
5.0ms14×body320valid
3.0ms12×body160valid

simplify39.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
39.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize52.0ms

Local error

Found 3 expressions with local error:

3.2b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.2b
(/ 1 (sqrt (+ x 1)))

rewrite124.0ms

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
60.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
9.0ms
(/ 1 (sqrt (+ x 1)))
8.0ms
(/ 1 (sqrt x))

series195.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
109.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
51.0ms
(/ 1 (sqrt x))
35.0ms
(/ 1 (sqrt (+ x 1)))

simplify2.0m

Counts
1401 → 781
Calls
1401 calls:
Slowest
495.0ms
(fma (- (sqrt (- x 1))) (/ 1 (sqrt (- (* x x) (* 1 1)))) (* (sqrt (- x 1)) (/ 1 (sqrt (- (* x x) (* 1 1))))))
446.0ms
(fma (- (/ (sqrt 1) (cbrt (sqrt (+ x 1))))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
444.0ms
(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))))))))
408.0ms
(fma (* (cbrt (/ 1 (sqrt x))) (cbrt (/ 1 (sqrt x)))) (cbrt (/ 1 (sqrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
358.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt x) (cbrt x)))) (/ (cbrt 1) (sqrt (cbrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))

prune4.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.4b

localize16.0ms

Local error

Found 3 expressions with local error:

3.2b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))

rewrite105.0ms

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
57.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
28.0ms
(- (sqrt (+ x 1)) (sqrt x))
17.0ms
(* (sqrt x) (sqrt (+ x 1)))

series244.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
140.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
53.0ms
(* (sqrt x) (sqrt (+ x 1)))
51.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify4.7s

Counts
180 → 159
Calls
180 calls:
Slowest
175.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
155.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
124.0ms
(/ (* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x))) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))))
122.0ms
(/ (* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x))) (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))))
117.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
31×*-un-lft-identity
23×sqrt-prod
21×add-sqr-sqrt
20×add-cbrt-cube
19×pow1
18×associate-*r/
14×flip3-+ sqrt-div flip-+
13×associate-*r* prod-exp add-cube-cbrt
10×distribute-lft-out
9×pow-prod-down
8×frac-times associate-/r/
7×fma-def associate-*l* cbrt-unprod
6×div-exp add-log-exp
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u unswap-sqr
3×cbrt-undiv rec-exp times-frac 1-exp pow-flip associate-/l*
2×sqrt-pow1 pow1/2 *-commutative
1×distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in sqrt-unprod div-inv inv-pow
Counts
4 → 138
Calls
4 calls:
Slowest
83.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
65.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms
(+ (sqrt (+ x 1)) (sqrt x))
15.0ms
(* (sqrt x) (sqrt (+ x 1)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
175.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
155.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
49.0ms
(* (sqrt x) (sqrt (+ x 1)))
47.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify5.2s

Counts
109 → 150
Calls
109 calls:
Slowest
273.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
270.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
254.0ms
(/ (* (* 1 1) 1) (* (* (* (* (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 1)) (sqrt x)))))
247.0ms
(/ (* (* 1 1) 1) (* (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))
231.0ms
(* (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))

prune815.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
117×*-un-lft-identity
78×times-frac
59×sqrt-prod
46×distribute-lft-out
44×add-sqr-sqrt
36×add-exp-log add-cube-cbrt
20×add-cbrt-cube
18×sqrt-div associate-*r/ associate-/r/
15×div-exp
13×pow1
12×associate-/l*
11×flip3-+ flip-+
9×div-inv
7×cbrt-undiv associate-/r* fma-def associate-*r* prod-exp
6×associate-*l* pow-prod-down add-log-exp
4×expm1-log1p-u rec-exp sqrt-pow1 pow1/2 1-exp insert-posit16 log1p-expm1-u pow-flip unswap-sqr
3×cbrt-unprod
2×clear-num frac-2neg
1×+-commutative sum-log sqrt-unprod *-commutative inv-pow associate-/l/
Counts
4 → 190
Calls
4 calls:
Slowest
42.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
19.0ms
(+ (sqrt (+ x 1)) (sqrt x))
18.0ms
(* (sqrt x) (sqrt (+ x 1)))
18.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
56.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
51.0ms
(* (sqrt x) (sqrt (+ x 1)))
46.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify6.8s

Counts
207 → 202
Calls
207 calls:
Slowest
184.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3))))) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
175.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
172.0ms
(/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))))
163.0ms
(/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))))
152.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3))))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
738.0ms1782×body640valid
471.0ms8141×body80nan
348.0ms1161×body1280valid
268.0ms4099×body80valid
120.0ms647×body320valid
34.0ms311×body160valid