Details

Time bar (total: 20.9s)

sample72.0ms

Algorithm
intervals
Results
40.0ms256×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02937
15537
213837
344837
4153737
done500037

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
24.3b
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite502.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
10×pow1
9×associate-*r* associate-*l*
8×associate-*l/ associate-/l/
7×flip3-+ flip-+
4×frac-times prod-exp cbrt-unprod add-log-exp
3×flip3-- times-frac pow-prod-down associate-/r* *-commutative flip-- unswap-sqr
2×cbrt-undiv associate-*r/ div-exp associate-/r/
1×frac-2neg clear-num div-inv associate-/l*
Counts
4 → 91
Calls
4 calls:
121.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
38.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
92.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
246.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series632.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
92.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
47.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
384.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify1.8s

Counts
103 → 103
Iterations

Useful iterations: 2 (610.0ms)

IterNodesCost
02282606
16702570
228962212
done50002212

prune689.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.3b
(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
22.5b
(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite446.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
110×add-sqr-sqrt
106×*-un-lft-identity
74×add-cube-cbrt
18×associate-/r*
16×distribute-lft-out-- difference-of-squares
15×add-exp-log associate-/r/ add-cbrt-cube
10×flip3-+ flip-+
8×pow1 div-inv associate-/l*
6×associate-*r* associate-*l*
4×cbrt-undiv div-exp associate-*l/ associate-/l/ add-log-exp
2×frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
1×flip3-- div-sub flip--
Counts
4 → 184
Calls
4 calls:
46.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
68.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
161.0ms
(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
157.0ms
(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series691.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
43.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
329.0ms
(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
214.0ms
(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify2.6s

Counts
196 → 196
Iterations

Useful iterations: done (2.6s)

IterNodesCost
03469817
19589681
234999229
done50009219

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
2.1b
(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
22.5b
(* (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite597.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
42×*-un-lft-identity
31×times-frac
28×add-cube-cbrt
27×associate-*l*
15×add-exp-log add-cbrt-cube
10×pow1
9×associate-*r*
7×distribute-lft-out-- difference-of-squares
6×flip3-+ flip-+
5×associate-*l/ associate-/l*
4×prod-exp associate-/r/ cbrt-unprod add-log-exp unswap-sqr
3×pow-prod-down associate-/r* *-commutative
2×cbrt-undiv frac-times associate-*r/ div-exp div-inv associate-/l/
1×distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub clear-num flip--
Counts
4 → 126
Calls
4 calls:
30.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
46.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
63.0ms
(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
452.0ms
(* (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series502.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
47.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
76.0ms
(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
274.0ms
(* (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify1.9s

Counts
138 → 138
Iterations

Useful iterations: 2 (693.0ms)

IterNodesCost
02734110
18594074
230593688
done50003688

prune680.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
4.7b
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.6b
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
19.9b
(* (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))

rewrite848.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
52×*-un-lft-identity
48×times-frac
45×add-exp-log
38×add-cube-cbrt
33×sqrt-prod
27×add-cbrt-cube
24×associate-*l*
20×prod-exp
11×pow1 div-exp
10×cbrt-unprod
9×frac-times associate-*r/
8×flip3-+ sqrt-div flip-+
7×distribute-lft-out-- difference-of-squares
6×cbrt-undiv associate-/r*
5×associate-/l*
4×distribute-rgt-in distribute-lft-in associate-/r/ add-log-exp
3×rec-exp 1-exp pow-prod-down associate-*l/
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv associate-/l/
1×flip3-- frac-2neg div-sub associate-*r* clear-num *-commutative flip--
Counts
4 → 156
Calls
4 calls:
48.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
44.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
63.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
683.0ms
(* (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))

series676.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
86.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
158.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
334.0ms
(* (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))

simplify2.0s

Counts
168 → 168
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03168128
18547585
231586073
done50005911

prune910.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes342.0ms

Accuracy

97.3% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 24.9b

bsearch401.0ms

Steps
ItersRangePoint
9
1.8328795043569038e+44
2.838659756671984e+50
2.2879431708269804e+47
10
-3.976749929960267e+79
-5.528985092060166e+69
-1.1327766250267256e+70

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
04267
16157
done6157

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.7s8005×body80valid