Details

Time bar (total: 12.3s)

sample26.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
7.0ms269×body80nan

simplify77.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
12114
24013
36613
49013
511413
612713
712913
done12913

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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)))

rewrite23.0ms

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))
5.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
10.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series198.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
77.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
83.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify815.0ms

Counts
162 → 162
Iterations

Useful iterations: 2 (199.0ms)

IterNodesCost
02503612
15683468
225243294
done50003294

prune425.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (fma (sqrt x) 4.0 (+ x 1.0))) (cbrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.3b
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
0.3b
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
0.3b
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
6.0ms
(* (cbrt (fma (sqrt x) 4.0 (+ x 1.0))) (cbrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
0.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
1.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))

series601.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (cbrt (fma (sqrt x) 4.0 (+ x 1.0))) (cbrt (fma (sqrt x) 4.0 (+ x 1.0))))
146.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
143.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
147.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))

simplify2.1s

Counts
93 → 93
Iterations

Useful iterations: 3 (491.0ms)

IterNodesCost
01121791
12621652
28921510
335791276
done50001276

prune348.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (fma (sqrt x) 4.0 (+ x 1.0))) (cbrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.3b
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
0.3b
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
0.3b
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
6.0ms
(* (cbrt (fma (sqrt x) 4.0 (+ x 1.0))) (cbrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
0.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
1.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))

series628.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(* (cbrt (fma (sqrt x) 4.0 (+ x 1.0))) (cbrt (fma (sqrt x) 4.0 (+ x 1.0))))
155.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
160.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))
148.0ms
(cbrt (fma (sqrt x) 4.0 (+ x 1.0)))

simplify2.1s

Counts
93 → 93
Iterations

Useful iterations: 3 (489.0ms)

IterNodesCost
01121791
12621652
28921510
335791276
done50001276

prune315.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))
0.3b
(/ (sqrt 6.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0))))
0.3b
(* (sqrt 6.0) (+ (sqrt 1.0) (sqrt x)))
0.7b
(* (* (sqrt 6.0) (+ (sqrt 1.0) (sqrt x))) (/ (sqrt 6.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
774×times-frac
673×add-sqr-sqrt
501×*-un-lft-identity
465×sqrt-prod
325×add-cube-cbrt
208×associate-*r*
172×difference-of-squares
86×distribute-lft-out--
42×associate-/r*
34×add-exp-log add-cbrt-cube
30×associate-/r/
16×div-inv
14×flip3-- flip--
11×pow1
10×cbrt-undiv div-exp prod-exp cbrt-unprod
9×associate-/l*
7×associate-*r/ associate-*l*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×frac-times frac-2neg associate-*l/ clear-num *-commutative distribute-lft-out unswap-sqr
1×distribute-rgt-in distribute-lft-in
Counts
4 → 572
Calls
4 calls:
11.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))
24.0ms
(/ (sqrt 6.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0))))
22.0ms
(* (sqrt 6.0) (+ (sqrt 1.0) (sqrt x)))
92.0ms
(* (* (sqrt 6.0) (+ (sqrt 1.0) (sqrt x))) (/ (sqrt 6.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
339.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))
294.0ms
(/ (sqrt 6.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0))))
92.0ms
(* (sqrt 6.0) (+ (sqrt 1.0) (sqrt x)))
821.0ms
(* (* (sqrt 6.0) (+ (sqrt 1.0) (sqrt x))) (/ (sqrt 6.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- (sqrt x) (sqrt 1.0)))))

simplify688.0ms

Counts
584 → 584
Iterations

Useful iterations: done (662.0ms)

IterNodesCost
063717921
1194316664
done500016500

prune1.4s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes20.0ms

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

sample665.0ms

Algorithm
intervals
Results
258.0ms8000×body80valid
214.0ms8101×body80nan