Details

Time bar (total: 13.6s)

sample43.0ms

Algorithm
intervals
Results
12.0ms334×body80nan
11.0ms256×body80valid

simplify172.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01114
12114
24113
36913
49413
511813
613113
713313
done13313

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (sqrt x) 4.0 (+ x 1.0))
0.0b
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
0.0b
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
103×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×associate-/r/
10×add-exp-log add-cbrt-cube
6×div-inv associate-/l*
5×flip3-- flip--
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×fma-udef
Counts
3 → 153
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
17.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
27.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series220.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
87.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
86.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify1.3s

Counts
162 → 162
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02503612
15483468
218733294
done50003288

prune530.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 6.0 (- x 1.0))
0.0b
(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.1b
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
18×prod-diff
11×distribute-rgt-in distribute-lft-in
10×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 associate-*r*
4×fma-def associate-*r/
3×expm1-log1p-u times-frac associate-*l* associate-/r* sum-log log1p-expm1-u
2×cbrt-undiv sub-neg flip3-- flip3-+ div-exp prod-exp associate-/r/ flip-- cbrt-unprod flip-+ associate-/l/
1×+-commutative associate-+l+ frac-2neg pow-prod-down clear-num *-commutative div-inv distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 92
Calls
3 calls:
39.0ms
(* 6.0 (- x 1.0))
45.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
80.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series192.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(* 6.0 (- x 1.0))
50.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
81.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify1.2s

Counts
101 → 101
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01871534
14661342
214161067
done50001040

prune238.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (sqrt x) 4.0 (+ x 1.0))
0.1b
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0))))
0.1b
(* (+ (sqrt x) (sqrt 1.0)) (/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))))
0.2b
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
417×times-frac
387×add-sqr-sqrt
282×*-un-lft-identity
178×add-cube-cbrt
152×sqrt-prod
104×associate-*r*
100×difference-of-squares
50×distribute-lft-out--
42×associate-/r*
20×add-exp-log add-cbrt-cube
18×associate-/r/
10×div-inv
8×flip3-- flip--
7×cbrt-undiv div-exp
6×pow1 associate-/l*
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×prod-exp cbrt-unprod unswap-sqr
2×frac-times frac-2neg flip3-+ associate-*l/ clear-num flip-+ distribute-lft-out
1×associate-*r/ pow-prod-down *-commutative fma-udef
Counts
4 → 351
Calls
4 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
43.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0))))
154.0ms
(* (+ (sqrt x) (sqrt 1.0)) (/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))))
28.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
46.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
210.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0))))
461.0ms
(* (+ (sqrt x) (sqrt 1.0)) (/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))))
332.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))

simplify2.4s

Counts
363 → 363
Iterations

Useful iterations: done (2.4s)

IterNodesCost
04799964
112339364
249058788
done50008785

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* 4.0 (sqrt x)) (* 4.0 (sqrt x)))
4.9b
(/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)))
8.4b
(+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x)))))
17.6b
(* (/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3))) (+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x))))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
48×frac-add
45×pow1
42×frac-times
41×flip3-+ flip-+
32×associate-*r/
30×add-exp-log add-cbrt-cube
25×flip3-- flip--
18×pow-prod-down
15×*-un-lft-identity
13×associate-*l/ prod-exp cbrt-unprod
12×associate-*l*
11×add-sqr-sqrt
10×times-frac
9×add-cube-cbrt add-log-exp
5×associate-/r*
4×cbrt-undiv expm1-log1p-u div-exp associate-*r* associate-/r/ pow-sqr pow-prod-up log1p-expm1-u
3×associate-+r+ sum-cubes distribute-lft-out
2×distribute-rgt-in associate-+l+ distribute-lft-in pow-plus sum-log *-commutative div-inv associate-/l/
1×+-commutative pow2 associate-+r- sub-neg fma-def frac-2neg diff-log swap-sqr prod-diff clear-num associate-/l* unswap-sqr
Counts
4 → 175
Calls
4 calls:
61.0ms
(* (* 4.0 (sqrt x)) (* 4.0 (sqrt x)))
126.0ms
(/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)))
155.0ms
(+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x)))))
824.0ms
(* (/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3))) (+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x))))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (* 4.0 (sqrt x)) (* 4.0 (sqrt x)))
118.0ms
(/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)))
84.0ms
(+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x)))))
182.0ms
(* (/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3))) (+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x))))))

simplify917.0ms

Counts
187 → 187
Iterations

Useful iterations: done (908.0ms)

IterNodesCost
036211069
115538523
done50007714

prune957.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11113
done1113

end0.0ms

sample993.0ms

Algorithm
intervals
Results
337.0ms8000×body80valid
302.0ms8104×body80nan