Details

Time bar (total: 13.6s)

sample21.0ms

Algorithm
intervals
Results
6.0ms67×body640valid
4.0ms138×body80valid
2.0ms35×body320valid
1.0ms16×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
199
2129
done129

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
1.7b
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
28×times-frac
27×add-sqr-sqrt
15×add-cube-cbrt
8×distribute-lft-out--
7×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp difference-of-squares
3×div-inv associate-/l*
2×pow1 associate-/r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num frac-sub flip-- flip-+
Counts
2 → 58
Calls
2 calls:
20.0ms
(/ 1.0 (+ x 1.0))
114.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

series132.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(/ 1.0 (+ x 1.0))
91.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

simplify757.0ms

Counts
64 → 64
Iterations

Useful iterations: done (754.0ms)

IterNodesCost
0120810
1285766
21122724
done5000718

prune187.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ 1.0 (+ x 1.0)))
0.0b
(sqrt (/ 1.0 (+ x 1.0)))
0.1b
(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
6.6b
(- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 1.0 x))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
134×sqrt-prod
114×*-un-lft-identity
97×add-sqr-sqrt
93×times-frac
60×add-cube-cbrt
29×swap-sqr
24×distribute-lft-out
21×pow1 associate-*r* associate-*l*
12×associate-/r/
10×sqrt-pow1 pow1/2 sqrt-div
9×unswap-sqr
6×add-exp-log flip3-+ add-cbrt-cube flip-+ div-inv add-log-exp
5×pow-prod-up
4×rem-sqrt-square
3×pow-prod-down pow-sqr frac-sub
2×frac-times associate-*r/ associate-*l/ difference-of-squares
1×pow2 sub-neg flip3-- pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod
Counts
4 → 185
Calls
4 calls:
22.0ms
(sqrt (/ 1.0 (+ x 1.0)))
21.0ms
(sqrt (/ 1.0 (+ x 1.0)))
123.0ms
(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
44.0ms
(- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 1.0 x))

series480.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(sqrt (/ 1.0 (+ x 1.0)))
119.0ms
(sqrt (/ 1.0 (+ x 1.0)))
96.0ms
(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
153.0ms
(- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 1.0 x))

simplify1.7s

Counts
197 → 197
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02403592
15222429
223452299
done50002270

prune575.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))
0.1b
(* (sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x))) (sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x))))
1.7b
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))
1.7b
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

rewrite715.0ms

Algorithm
rewrite-expression-head
Rules
204×*-un-lft-identity
146×add-sqr-sqrt
136×times-frac
97×sqrt-prod
70×distribute-lft-out--
49×add-cube-cbrt
28×swap-sqr difference-of-squares
27×sqrt-div distribute-lft-out
20×pow1
18×associate-*r* associate-*l*
14×div-inv
11×flip3-- frac-sub flip--
9×frac-times sqrt-pow1 pow1/2
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow-prod-up
4×unswap-sqr
3×associate-*r/ pow-prod-down associate-*l/ pow-sqr
2×sub-neg diff-log
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 186
Calls
4 calls:
93.0ms
(sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))
425.0ms
(* (sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x))) (sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x))))
79.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))
89.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

series377.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))
63.0ms
(* (sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x))) (sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x))))
62.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))
72.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

simplify1.4s

Counts
198 → 198
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02224732
14573506
218563308
done50003227

prune540.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1.0 (pow x 4))
0.5b
(/ 1.0 (pow x 3))
0.9b
(/ 1.0 (pow x 2))
10.3b
(- (/ 1.0 (pow x 3)) (+ (/ 1.0 (pow x 4)) (/ 1.0 (pow x 2))))

rewrite421.0ms

Algorithm
rewrite-expression-head
Rules
94×times-frac
79×*-un-lft-identity
78×add-sqr-sqrt
65×add-cube-cbrt
37×unpow-prod-down
27×associate-/r*
19×add-exp-log
13×cube-prod sqr-pow
10×add-cbrt-cube
9×div-exp associate-/l* add-log-exp
6×div-inv distribute-lft-out--
5×distribute-lft-out difference-of-squares
4×pow1 cube-mult unpow3 unpow2
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num frac-sub
2×diff-log
1×sub-neg flip3-- flip3-+ frac-add sum-log flip-- flip-+ associate--r+
Counts
4 → 187
Calls
4 calls:
11.0ms
(/ 1.0 (pow x 4))
9.0ms
(/ 1.0 (pow x 3))
9.0ms
(/ 1.0 (pow x 2))
378.0ms
(- (/ 1.0 (pow x 3)) (+ (/ 1.0 (pow x 4)) (/ 1.0 (pow x 2))))

series246.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ 1.0 (pow x 4))
75.0ms
(/ 1.0 (pow x 3))
32.0ms
(/ 1.0 (pow x 2))
60.0ms
(- (/ 1.0 (pow x 3)) (+ (/ 1.0 (pow x 4)) (/ 1.0 (pow x 2))))

simplify3.7s

Counts
199 → 199
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
02952713
16832404
245792256
done50002256

prune733.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes145.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 26.3b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02475
12959
done2959

end0.0ms

sample1.0s

Algorithm
intervals
Results
395.0ms1948×body640valid
207.0ms4241×body80valid
183.0ms1218×body320valid
44.0ms595×body160valid