Details

Time bar (total: 2.6m)

sample84.0ms

Algorithm
intervals
Results
20.0ms36×body1280valid
18.0ms52×body640valid
14.0ms209×body80nan
11.0ms137×body80valid
4.0ms20×body320valid
2.0ms11×body160valid

simplify39.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize31.0ms

Local error

Found 3 expressions with local error:

2.9b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))

rewrite100.0ms

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
46.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
15.0ms
(/ 1 (sqrt (+ x 1)))
9.0ms
(/ 1 (sqrt x))

series174.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
88.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
56.0ms
(/ 1 (sqrt x))
30.0ms
(/ 1 (sqrt (+ x 1)))

simplify2.0m

Counts
1442 → 781
Calls
1442 calls:
Slowest
442.0ms
(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)))))))
407.0ms
(* (* (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
362.0ms
(fma (/ 1 (sqrt 1)) (/ 1 (sqrt x)) (- (* (sqrt (- x 1)) (/ 1 (sqrt (- (* x x) (* 1 1)))))))
360.0ms
(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)))))))
351.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (cbrt 1) (cbrt (sqrt x))) (- (* (/ 1 (cbrt (sqrt (+ x 1)))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))

prune4.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.8b

localize14.0ms

Local error

Found 3 expressions with local error:

3.0b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))

rewrite106.0ms

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
56.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
33.0ms
(- (sqrt (+ x 1)) (sqrt x))
15.0ms
(* (sqrt x) (sqrt (+ x 1)))

series253.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
147.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
57.0ms
(- (sqrt (+ x 1)) (sqrt x))
50.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify7.5s

Counts
222 → 159
Calls
222 calls:
Slowest
247.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (+ (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
244.0ms
(/ (sqrt x) (* (sqrt x) (sqrt (+ x 1))))
219.0ms
(* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1))))
201.0ms
(* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x)))
187.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))

prune851.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
122×*-un-lft-identity
78×times-frac
59×sqrt-prod
49×add-sqr-sqrt
46×distribute-lft-out
41×add-cube-cbrt
32×add-exp-log
27×associate-/l*
20×add-cbrt-cube
14×div-exp
9×pow1
8×associate-/r/
7×cbrt-undiv associate-/r* fma-def associate-*r*
6×flip3-+ associate-*l* flip-+ add-log-exp
5×prod-exp
4×expm1-log1p-u sqrt-div associate-*r/ insert-posit16 log1p-expm1-u div-inv unswap-sqr
3×rec-exp 1-exp pow-prod-down cbrt-unprod
2×clear-num frac-2neg sqrt-pow1 pow1/2
1×+-commutative sum-log sqrt-unprod *-commutative pow-flip inv-pow associate-/l/
Counts
4 → 185
Calls
4 calls:
Slowest
46.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
24.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
19.0ms
(+ (sqrt (+ x 1)) (sqrt x))
15.0ms
(* (sqrt x) (sqrt (+ x 1)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
63.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
51.0ms
(* (sqrt x) (sqrt (+ x 1)))
45.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify11.5s

Counts
237 → 197
Calls
237 calls:
Slowest
300.0ms
(/ (/ 1 (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (sqrt x))
279.0ms
(* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
265.0ms
(/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
262.0ms
(+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
218.0ms
(* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1 (fma (sqrt x) (sqrt (+ x 1)) x))
0.1b
(/ (/ 1 (fma (sqrt x) (sqrt (+ x 1)) x)) (sqrt (+ x 1)))
0.0b
(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)

series316.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
158.0ms
(/ (/ 1 (fma (sqrt x) (sqrt (+ x 1)) x)) (sqrt (+ x 1)))
90.0ms
(/ 1 (fma (sqrt x) (sqrt (+ x 1)) x))
68.0ms
(fma (sqrt x) (sqrt (+ x 1)) x)

simplify9.1s

Counts
288 → 187
Calls
288 calls:
Slowest
407.0ms
(* (* (fma (sqrt x) (sqrt (+ x 1)) x) (fma (sqrt x) (sqrt (+ x 1)) x)) (fma (sqrt x) (sqrt (+ x 1)) x))
352.0ms
(/ (/ (* (* 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))))
283.0ms
(/ (* (* (/ 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))))
247.0ms
(/ (/ (* (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)))))
142.0ms
(/ (/ 1 (fma (sqrt x) (sqrt (+ x 1)) x)) (sqrt (+ (pow x 3) (pow 1 3))))

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes33.0ms

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
519.0ms4125×body80valid
494.0ms7809×body80nan
477.0ms1862×body640valid
335.0ms1080×body1280valid
122.0ms629×body320valid
33.0ms304×body160valid