Details

Time bar (total: 15.0s)

sample52.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
12.0ms245×body80nan

simplify162.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01114
12114
24113
37013
49913
512813
614113
714313
done14313

prune12.0ms

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))
0.1b
(/ 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))
20.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
25.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series218.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
79.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
97.0ms
(/ 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
16313490
230383298
done50013288

prune743.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
426×times-frac
380×add-sqr-sqrt
310×*-un-lft-identity
290×sqrt-prod
186×add-cube-cbrt
96×difference-of-squares
66×associate-/r*
48×distribute-lft-out--
14×distribute-lft-out
11×add-exp-log add-cbrt-cube
9×associate-/r/
8×associate-/l*
6×pow1 div-inv
4×cbrt-undiv expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
1×flip3-+ flip-+
Counts
4 → 347
Calls
4 calls:
47.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
3.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
3.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
65.0ms
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
559.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
102.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
101.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
391.0ms
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0))))

simplify616.0ms

Counts
359 → 359
Iterations

Useful iterations: done (598.0ms)

IterNodesCost
042910566
111219670
done50019389

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
622×sqrt-prod
584×times-frac
525×add-sqr-sqrt
507×*-un-lft-identity
251×add-cube-cbrt
96×difference-of-squares
72×distribute-lft-out
65×swap-sqr
60×associate-/r*
48×distribute-lft-out--
37×associate-*r* associate-*l*
21×pow1
16×unswap-sqr
11×add-exp-log add-cbrt-cube
10×sqrt-pow1 pow1/2
9×associate-/r/ div-inv
5×pow-prod-up
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp pow-prod-down pow-sqr associate-/l*
2×rem-sqrt-square
1×pow2 frac-times frac-2neg pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 475
Calls
4 calls:
1.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
1.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
168.0ms
(* (sqrt (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))) (sqrt (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
31.0ms
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0))))

series766.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
99.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
284.0ms
(* (sqrt (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))) (sqrt (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
314.0ms
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0))))

simplify720.0ms

Counts
487 → 487
Iterations

Useful iterations: done (699.0ms)

IterNodesCost
054817531
1131513574
done500013121

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))
0.3b
(/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0)))
0.3b
(/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.6b
(* (/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))))

rewrite333.0ms

Algorithm
rewrite-expression-head
Rules
1002×times-frac
762×add-sqr-sqrt
614×*-un-lft-identity
563×sqrt-prod
444×add-cube-cbrt
221×associate-*r*
85×distribute-lft-out-- difference-of-squares
47×associate-/r*
40×associate-*l*
35×unswap-sqr
34×add-exp-log add-cbrt-cube
30×associate-/r/
18×div-inv associate-/l*
14×cbrt-undiv flip3-- div-exp flip--
6×pow1 prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times sqrt-undiv associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 717
Calls
4 calls:
15.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))
23.0ms
(/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0)))
8.0ms
(/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
231.0ms
(* (/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))))

series707.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))
213.0ms
(/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0)))
164.0ms
(/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
154.0ms
(* (/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))))

simplify1.4s

Counts
729 → 729
Iterations

Useful iterations: done (1.3s)

IterNodesCost
068323023
1230521120
done500020432

prune2.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes55.0ms

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

sample1.3s

Algorithm
intervals
Results
543.0ms8000×body80valid
433.0ms7921×body80nan