Details

Time bar (total: 18.5s)

sample61.0ms

Algorithm
intervals
Results
21.0ms309×body80nan
19.0ms256×body80valid

simplify225.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01114
12114
24113
36913
49413
511813
613113
713313
done13313

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite41.0ms

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))
12.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
17.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series329.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
133.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
121.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify1.6s

Counts
162 → 162
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02503612
15483468
218733294
done50003288

prune615.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
37×*-un-lft-identity
31×times-frac
23×add-cube-cbrt
19×associate-*r*
10×add-exp-log add-cbrt-cube
7×distribute-lft-out-- difference-of-squares
5×pow1 associate-/l*
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num *-commutative flip-- fma-udef
Counts
3 → 90
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
28.0ms
(* 6.0 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))
27.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

series264.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
120.0ms
(* 6.0 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))
77.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

simplify2.6s

Counts
99 → 99
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01431667
13491615
29561455
330681453
done50011452

prune695.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
149×*-un-lft-identity
135×sqrt-prod
134×add-sqr-sqrt
116×times-frac
69×add-cube-cbrt
34×associate-*r*
28×difference-of-squares
26×distribute-lft-out
14×associate-/l* distribute-lft-out--
13×add-exp-log add-cbrt-cube
12×associate-/r*
7×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×cbrt-undiv div-exp associate-*l* div-inv unswap-sqr
2×frac-2neg prod-exp clear-num cbrt-unprod
1×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 div-sub associate-*r/ pow-prod-down *-commutative flip-- flip-+
Counts
4 → 214
Calls
4 calls:
3.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
85.0ms
(* 6.0 (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
40.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
44.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
368.0ms
(* 6.0 (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
368.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
312.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify1.6s

Counts
226 → 226
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02755516
16785024
217744784
done50004729

prune783.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite474.0ms

Algorithm
rewrite-expression-head
Rules
193×*-un-lft-identity
158×sqrt-prod
147×add-sqr-sqrt
144×times-frac
89×add-cube-cbrt
70×log-pow
68×exp-prod
38×associate-*r* distribute-lft-out
28×difference-of-squares
14×associate-/l* distribute-lft-out--
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×log-prod
8×pow1
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l/ add-log-exp
3×distribute-rgt-in distribute-lft-in associate-*l*
2×cbrt-undiv frac-2neg div-exp clear-num
1×flip3-- flip3-+ div-sub rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 252
Calls
4 calls:
252.0ms
(* 6.0 (log (exp (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))))
65.0ms
(log (exp (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
61.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
83.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
394.0ms
(* 6.0 (log (exp (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))))
347.0ms
(log (exp (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
410.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
371.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify3.6s

Counts
264 → 264
Iterations

Useful iterations: done (3.5s)

IterNodesCost
03216523
16655929
216005639
347005569
done50005567

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11213
done1213

end0.0ms

sample1.4s

Algorithm
intervals
Results
580.0ms8000×body80valid
572.0ms8101×body80nan