Details

Time bar (total: 17.8s)

sample66.0ms

Algorithm
intervals
Results
17.0ms123×body80valid
12.0ms312×body80nan
12.0ms67×body640valid
6.0ms30×body1280valid
3.0ms28×body320valid
1.0ms8×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done14
214
111
08

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.4b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
879×*-un-lft-identity
747×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
566×sqrt-prod
74×distribute-lft-out
54×div-inv
48×sqrt-div
46×associate-/r/
24×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-cbrt-cube add-exp-log
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log frac-sub hypot-def flip--
Counts
4 → 758
Calls
4 calls:
13.0ms
(sqrt (+ x 1.0))
17.0ms
(/ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ 1.0 (sqrt x))
119.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series414.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(sqrt (+ x 1.0))
101.0ms
(/ 1.0 (sqrt (+ x 1.0)))
57.0ms
(/ 1.0 (sqrt x))
204.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.5s

Counts
770 → 770
Iterations
IterNodes
done5000
23579
11587
0702

prune4.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 22.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.4b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×*-un-lft-identity sqrt-prod
11×add-cbrt-cube add-exp-log add-cube-cbrt
9×pow1
7×associate-*r*
6×sqrt-div associate-*l* add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u unswap-sqr
3×sqrt-pow1 flip3-+ times-frac pow1/2 pow-prod-down flip-+ associate-/l*
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod flip-- distribute-lft-out associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg fma-neg sqrt-unprod diff-log div-sub prod-diff *-commutative hypot-def div-inv
Counts
4 → 98
Calls
4 calls:
6.0ms
(sqrt (+ x 1.0))
50.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
21.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
25.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series627.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(sqrt (+ x 1.0))
385.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
69.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
140.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.8s

Counts
110 → 110
Iterations
IterNodes
done5005
22181
1591
0206

prune724.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 22.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
0.5b
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
1.7b
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
37×pow-prod-down
30×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
16×add-sqr-sqrt associate-*r/
14×sqrt-div
11×sqrt-prod
10×*-un-lft-identity
9×associate-*r*
8×associate-*l* pow-sqr pow-prod-up add-cube-cbrt
7×flip3-+ flip-+
6×add-log-exp
4×expm1-log1p-u frac-times pow-plus log1p-expm1-u unswap-sqr
3×*-commutative
2×pow2 sqrt-pow1 pow1/2 swap-sqr associate-*l/
1×sub-neg flip3-- fma-neg sqrt-unprod diff-log prod-diff flip-- distribute-lft-out difference-of-squares
Counts
4 → 132
Calls
4 calls:
81.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
20.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
46.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
76.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

series181.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
79.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
28.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
21.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

simplify1.4s

Counts
144 → 144
Iterations
IterNodes
done5001
21569
1496
0183

prune530.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
0.2b
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt times-frac
35×*-un-lft-identity
31×add-cube-cbrt
20×add-cbrt-cube add-exp-log
18×associate-/l*
15×sqrt-prod
9×pow1
8×associate-/r/
7×cbrt-undiv div-exp associate-*r*
6×flip3-+ sqrt-div associate-*l* flip-+
4×expm1-log1p-u associate-/r* associate-*r/ log1p-expm1-u div-inv add-log-exp unswap-sqr
3×sqrt-pow1 pow1/2 pow-prod-down prod-exp cbrt-unprod
2×clear-num frac-2neg distribute-lft-out
1×rem-sqrt-square sqrt-unprod *-commutative hypot-def associate-/l/
Counts
4 → 139
Calls
4 calls:
6.0ms
(sqrt (+ x 1.0))
19.0ms
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
42.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series856.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(sqrt (+ x 1.0))
184.0ms
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
572.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
67.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.6s

Counts
151 → 151
Iterations
IterNodes
done5019
22829
1804
0290

prune578.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes85.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done17
117
013

end0.0ms

sample1.6s

Algorithm
intervals
Results
390.0ms669×body320valid
301.0ms7998×body80nan
293.0ms1817×body640valid
240.0ms1102×body1280valid
167.0ms4129×body80valid
20.0ms283×body160valid