Details

Time bar (total: 9.5s)

sample22.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
2.0ms80×body80nan

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 61
Calls
3 calls:
21.0ms
(+ 1.0 (sqrt (+ x 1.0)))
7.0ms
(sqrt (+ x 1.0))
33.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series257.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ 1.0 (sqrt (+ x 1.0)))
43.0ms
(sqrt (+ x 1.0))
161.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify781.0ms

Counts
70 → 70
Iterations

Useful iterations: 2 (218.0ms)

IterNodesCost
0140917
1326848
21523785
done5001785

prune220.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.1b
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×add-sqr-sqrt
26×times-frac
23×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×flip3-+ div-exp prod-exp associate-/r* sqrt-prod associate-/r/ flip-+
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 106
Calls
4 calls:
20.0ms
(+ 1.0 (sqrt (+ x 1.0)))
14.0ms
(sqrt (+ x 1.0))
112.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
46.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series439.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ 1.0 (sqrt (+ x 1.0)))
34.0ms
(sqrt (+ x 1.0))
183.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
164.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify1.5s

Counts
118 → 118
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01861578
14761385
224831210
done50001208

prune250.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sqrt (+ x 1.0)) 3)
0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.9b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
5.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
62×sqrt-div
43×add-sqr-sqrt
34×sqrt-prod
32×flip3-+ flip-+
31×add-cube-cbrt
28×associate-*r/ distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
16×frac-sub
12×frac-times
11×swap-sqr
9×add-exp-log sqrt-pow1 pow1/2 associate-/r* add-cbrt-cube
8×associate-*l/
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×sum-cubes sub-div unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div associate-/r/
1×cbrt-undiv pow2 cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- frac-2neg pow-plus sqrt-unprod diff-log unpow3 div-exp pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 184
Calls
4 calls:
17.0ms
(pow (sqrt (+ x 1.0)) 3)
49.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
139.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
51.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

series438.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(pow (sqrt (+ x 1.0)) 3)
25.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
239.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
86.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

simplify689.0ms

Counts
196 → 196
Iterations

Useful iterations: done (678.0ms)

IterNodesCost
03134015
18952975
done50002738

prune620.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ x (+ (- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0)))) (* 1.0 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.9b
(- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0))))

rewrite614.0ms

Algorithm
rewrite-expression-head
Rules
109×*-un-lft-identity
105×times-frac
76×add-sqr-sqrt
64×sqrt-div
63×add-cube-cbrt
40×flip3-+ flip-+
32×associate-*r/
26×sqrt-prod
22×distribute-lft-out
20×frac-sub
19×pow1
15×associate-/l*
12×frac-times associate-/r/
11×add-exp-log swap-sqr add-cbrt-cube add-log-exp
8×sqrt-pow1 pow1/2 associate-*l/
7×associate-*r* associate-*l*
6×div-inv
5×pow-prod-up
4×associate-/r* sub-div unswap-sqr
3×cbrt-undiv diff-log div-exp pow-prod-down pow-sqr
2×sub-neg flip3-- distribute-rgt-out-- flip--
1×pow2 frac-2neg pow-plus sqrt-unprod prod-exp associate--l+ clear-num sum-log rem-square-sqrt *-commutative cbrt-unprod associate-/l/
Counts
4 → 210
Calls
4 calls:
399.0ms
(/ (/ x (+ (- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0)))) (* 1.0 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
52.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
58.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
81.0ms
(- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0))))

series844.0ms

Counts
4 → 12
Calls
4 calls:
636.0ms
(/ (/ x (+ (- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0)))) (* 1.0 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
17.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
105.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
85.0ms
(- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0))))

simplify661.0ms

Counts
222 → 222
Iterations

Useful iterations: done (651.0ms)

IterNodesCost
04397303
112156317
done50005677

prune835.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01544
12144
done2144

end0.0ms

sample703.0ms

Algorithm
intervals
Results
350.0ms7997×body80valid
117.0ms2687×body80nan
0.0ms3×body1280valid