Details

Time bar (total: 2.4m)

sample114.0ms

Algorithm
intervals
Results
31.0ms58×body640valid
26.0ms278×body80nan
17.0ms30×body1280valid
16.0ms139×body80valid
7.0ms21×body320valid
2.0ms8×body160valid

simplify37.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite113.0ms

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--
Counts
4 → 793
Calls
4 calls:
Slowest
54.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
9.0ms
(/ 1 (sqrt (+ x 1)))
6.0ms
(/ 1 (sqrt x))
5.0ms
(sqrt (+ x 1))

series188.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
79.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
40.0ms
(sqrt (+ x 1))
39.0ms
(/ 1 (sqrt x))
31.0ms
(/ 1 (sqrt (+ x 1)))

simplify1.9m

Counts
1414 → 805
Calls
1414 calls:
Slowest
455.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (cbrt 1) (cbrt (sqrt x))) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
372.0ms
(fma (/ (sqrt 1) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (sqrt 1) (cbrt (sqrt x))) (- (* (/ (cbrt 1) (sqrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (+ x 1)))))))
359.0ms
(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))))))))
331.0ms
(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)))))))
322.0ms
(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)))))))

prune4.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.7b

localize16.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.0b
(sqrt (+ x 1))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
88×sqrt-prod
79×*-un-lft-identity
75×add-sqr-sqrt
42×prod-diff
39×add-cube-cbrt
12×distribute-lft-out difference-of-squares
11×add-cbrt-cube add-exp-log
10×times-frac associate-/l*
9×pow1 distribute-lft-out--
7×fma-neg associate-*r*
6×sqrt-div associate-*l* add-log-exp
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod hypot-def flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Counts
4 → 171
Calls
4 calls:
Slowest
55.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
27.0ms
(- (sqrt (+ x 1)) (sqrt x))
14.0ms
(* (sqrt x) (sqrt (+ x 1)))
4.0ms
(sqrt (+ x 1))

series270.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
54.0ms
(* (sqrt x) (sqrt (+ x 1)))
53.0ms
(- (sqrt (+ x 1)) (sqrt x))
22.0ms
(sqrt (+ x 1))

simplify4.9s

Counts
193 → 183
Calls
193 calls:
Slowest
177.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
157.0ms
(- (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 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))))
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)))))
119.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune990.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 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))

rewrite175.0ms

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
79.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
61.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
19.0ms
(+ (sqrt (+ x 1)) (sqrt x))
14.0ms
(* (sqrt x) (sqrt (+ x 1)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
161.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
50.0ms
(+ (sqrt (+ x 1)) (sqrt x))
49.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify5.3s

Counts
109 → 150
Calls
109 calls:
Slowest
281.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
274.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
255.0ms
(/ (* (* 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)))))
251.0ms
(/ (* (* 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)))))
235.0ms
(* (* (* (* (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))))

prune835.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
104×add-exp-log
85×*-un-lft-identity
48×add-sqr-sqrt
44×times-frac prod-exp
39×sqrt-prod
36×div-exp
34×add-cbrt-cube
33×add-cube-cbrt
31×associate-*r*
29×distribute-lft-out
21×pow1
18×rec-exp 1-exp
15×associate-*l*
11×pow-prod-down
10×cbrt-undiv cbrt-unprod
9×pow-flip
8×associate-/r/
7×associate-/r* associate-*r/ unswap-sqr
6×sqrt-div associate-/l*
5×flip3-+ flip-+
4×expm1-log1p-u sqrt-pow1 pow1/2 insert-posit16 log1p-expm1-u div-inv inv-pow add-log-exp
2×clear-num frac-2neg *-commutative
1×frac-times sqrt-unprod associate-*l/ un-div-inv
Counts
4 → 208
Calls
4 calls:
Slowest
97.0ms
(* (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
23.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms
(* (sqrt x) (sqrt (+ x 1)))
16.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))

series583.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
411.0ms
(* (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
66.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
54.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
52.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify8.2s

Counts
194 → 220
Calls
194 calls:
Slowest
281.0ms
(* (/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))) (/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))
210.0ms
(* (/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1))))) (/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))
188.0ms
(+ (- 0 (+ (log (sqrt x)) (log (sqrt (+ x 1))))) (- 0 (log (+ (sqrt (+ x 1)) (sqrt x)))))
188.0ms
(+ (- (log 1) (+ (log (sqrt x)) (log (sqrt (+ x 1))))) (- 0 (log (+ (sqrt (+ x 1)) (sqrt x)))))
180.0ms
(+ (- 0 (log (* (sqrt x) (sqrt (+ x 1))))) (- 0 (log (+ (sqrt (+ x 1)) (sqrt x)))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch1.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
520.0ms4170×body80valid
506.0ms1759×body640valid
475.0ms8344×body80nan
328.0ms1126×body1280valid
119.0ms628×body320valid
36.0ms317×body160valid