Details

Time bar (total: 18.8s)

sample79.0ms

Algorithm
intervals
Results
49.0ms256×body80valid

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02937
15537
213837
344837
4153737
done500037

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
25.3b
(/ (* (- 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))

rewrite347.0ms

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:
88.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
28.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
54.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
173.0ms
(/ (* (- 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))

series465.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
69.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
46.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
259.0ms
(/ (* (- 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))

simplify1.5s

Counts
103 → 103
Iterations

Useful iterations: 2 (489.0ms)

IterNodesCost
02272664
16542592
227782274
done50022274

prune558.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) 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)))
22.0b
(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite465.0ms

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:
43.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
73.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
152.0ms
(/ (- 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)))
183.0ms
(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series689.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
54.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
335.0ms
(/ (- 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)))
195.0ms
(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify1.9s

Counts
196 → 196
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03469875
19519725
234519291
done50029281

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
2.8b
(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
22.0b
(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite660.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
42×*-un-lft-identity
31×times-frac
28×add-cube-cbrt
27×associate-*r*
15×add-exp-log add-cbrt-cube
10×pow1
9×associate-*l*
7×distribute-lft-out-- difference-of-squares
6×flip3-+ associate-*l/ flip-+
5×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 div-exp div-inv associate-/l/
1×flip3-- frac-2neg div-sub associate-*r/ clear-num flip--
Counts
4 → 124
Calls
4 calls:
30.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
83.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
97.0ms
(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
445.0ms
(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
43.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
76.0ms
(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
312.0ms
(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify1.7s

Counts
136 → 136
Iterations

Useful iterations: 2 (577.0ms)

IterNodesCost
02644056
17113986
227023620
done50003620

prune933.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

7.7b
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
7.7b
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
13.4b
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
22.0b
(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (* (/ 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)))))

rewrite669.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
40×*-un-lft-identity
38×add-exp-log
30×times-frac
26×add-cube-cbrt
24×sqrt-prod add-cbrt-cube
17×prod-exp
11×pow1
9×frac-times div-exp cbrt-unprod
7×flip3-+ flip-+ distribute-lft-out-- difference-of-squares
6×sqrt-div associate-*r/ associate-/r*
5×cbrt-undiv associate-*l/ associate-/l*
4×add-log-exp
3×associate-*l* pow-prod-down
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/r/ associate-/l/
1×flip3-- frac-2neg div-sub associate-*r* clear-num *-commutative flip-- div-inv
Counts
4 → 127
Calls
4 calls:
49.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
56.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
91.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
468.0ms
(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (* (/ 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)))))

series719.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
75.0ms
(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
184.0ms
(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
371.0ms
(* (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (* (/ 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)))))

simplify1.7s

Counts
139 → 139
Iterations

Useful iterations: 2 (547.0ms)

IterNodesCost
02826213
17025759
223684525
done50004525

prune904.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes449.0ms

Accuracy

97.6% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 24.7b

bsearch400.0ms

Steps
ItersRangePoint
11
1.9138944455855922e+68
4.7705286842092256e+92
1.9308694312533926e+69
7
-3.807880116067595e+71
-3.6274401496220754e+69
-9.168391507400123e+69

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
04471
16557
done6557

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.5s8010×body80valid