Details

Time bar (total: 11.5s)

sample39.0ms

Algorithm
intervals
Results
19.0ms256×body80valid

simplify475.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02937
16230
215330
339030
4127230
done500030

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.0b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
23.2b
(/ (* (- 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))

rewrite119.0ms

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×expm1-log1p-u frac-times prod-exp cbrt-unprod log1p-expm1-u 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 → 99
Calls
4 calls:
32.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
20.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
10.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
54.0ms
(/ (* (- 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))

series409.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
44.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
66.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
233.0ms
(/ (* (- 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))

simplify1.1s

Counts
111 → 111
Iterations

Useful iterations: 2 (206.0ms)

IterNodesCost
02352812
16982272
230932012
done50002012

prune551.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

6.1b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.8b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
15.0b
(* (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
19.3b
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
108×times-frac
95×*-un-lft-identity
69×add-cube-cbrt
63×sqrt-prod
34×associate-*l*
22×associate-*r*
20×add-exp-log add-cbrt-cube
13×distribute-lft-out-- difference-of-squares
12×associate-/r*
9×unswap-sqr
8×associate-/l*
7×pow1
6×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
2×frac-2neg clear-num associate-/l/
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 201
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
9.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
35.0ms
(* (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
5.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

series886.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
156.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
279.0ms
(* (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
352.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify980.0ms

Counts
213 → 213
Iterations

Useful iterations: done (969.0ms)

IterNodesCost
02988973
17828576
230747625
done50007550

prune853.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b
(/ 1 (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
23.4b
(* (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (/ 1 (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
27×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
22×add-cbrt-cube
19×associate-*r*
18×times-frac
16×frac-times associate-*l/
14×pow1 prod-exp
8×flip3-+ cbrt-unprod flip-+
7×associate-*l*
6×flip3-- div-exp flip--
5×associate-*r/ pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp 1-exp associate-/r* *-commutative associate-/l*
2×div-inv unswap-sqr
1×pow-flip frac-2neg clear-num un-div-inv inv-pow
Counts
4 → 133
Calls
4 calls:
20.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
10.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
2.0ms
(/ 1 (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
110.0ms
(* (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (/ 1 (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
67.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
77.0ms
(/ 1 (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
259.0ms
(* (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (/ 1 (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify1.4s

Counts
145 → 145
Iterations

Useful iterations: 2 (291.0ms)

IterNodesCost
02874247
18483642
238103186
done50003186

prune608.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.0b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
23.7b
(/ (* (- (* x x) (* 2.0 2.0)) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (+ x 2.0)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×associate-*r* associate-*l*
8×associate-*l/ associate-/l/
7×flip3-+ prod-exp cbrt-unprod flip-+
4×cbrt-undiv expm1-log1p-u frac-times associate-*r/ div-exp log1p-expm1-u add-log-exp
3×flip3-- pow-prod-down *-commutative flip-- unswap-sqr
2×associate-/r/
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 99
Calls
4 calls:
32.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
20.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
11.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
40.0ms
(/ (* (- (* x x) (* 2.0 2.0)) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (+ x 2.0)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
39.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
65.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
307.0ms
(/ (* (- (* x x) (* 2.0 2.0)) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (+ x 2.0)))

simplify1.0s

Counts
111 → 111
Iterations

Useful iterations: 2 (251.0ms)

IterNodesCost
02373125
17632683
237822214
done50012214

prune588.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes194.0ms

Accuracy

96.8% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 24.5b

bsearch293.0ms

Steps
ItersRangePoint
10
3.1558492924628487e+21
2.0877402634697386e+37
1.1453649274389147e+36
6
-5.080993971428125e+22
-4.398643727244591e+21
-3.55588684135671e+22

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
05298
17489
done7489

end0.0ms

sample668.0ms

Algorithm
intervals
Results
490.0ms8009×body80valid