Details

Time bar (total: 46.4s)

sample72.0ms

Algorithm
intervals
Results
41.0ms256×body80valid

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done5000
42165
3512
2154
162
029

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
2.6b
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
23.7b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
104×add-sqr-sqrt *-un-lft-identity
72×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×add-cbrt-cube add-exp-log associate-/r/
6×div-inv associate-/l*
5×flip3-- flip--
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef
Counts
4 → 163
Calls
4 calls:
0.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
14.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
16.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
33.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
109.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
364.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

simplify2.1s

Counts
175 → 175
Iterations
IterNodes
done5000
23509
1701
0296

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
19.9b
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0)))
23.7b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0))) (+ x 2.0)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt *-un-lft-identity times-frac add-cbrt-cube add-exp-log add-cube-cbrt
7×associate-/r/
6×associate-/l*
5×cbrt-undiv associate-/r* div-exp
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp difference-of-squares
2×frac-times clear-num frac-2neg flip3-+ prod-exp associate-*r/ cbrt-unprod flip-+ fma-udef div-inv
1×flip3-- associate-*l/ flip--
Counts
4 → 85
Calls
4 calls:
0.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
16.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0)))
23.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0))) (+ x 2.0)))

series596.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
28.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
95.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0)))
436.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0))) (+ x 2.0)))

simplify2.1s

Counts
97 → 97
Iterations
IterNodes
done5001
22206
1500
0206

prune858.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.1b
(* (* x x) (* x x))
22.6b
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* (* x x) (* x x)) (* (* 2.0 2.0) (* 2.0 2.0))))
23.7b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (* (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* (* x x) (* x x)) (* (* 2.0 2.0) (* 2.0 2.0)))) (+ (* x x) (* 2.0 2.0))) (+ x 2.0)))

rewrite622.0ms

Algorithm
rewrite-expression-head
Rules
115×pow1
36×pow-prod-up
32×add-cbrt-cube add-exp-log
23×pow-prod-down
22×pow-sqr
19×associate-/r/
18×pow-plus
16×frac-times
15×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
13×pow2 prod-exp cbrt-unprod
12×flip3-+ flip-+
8×associate-*l/ associate-*r/
6×cbrt-undiv div-exp associate-/l*
5×associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp difference-of-squares
2×clear-num frac-2neg div-inv
1×flip3-- swap-sqr associate-*r* associate-*l* *-commutative fma-udef flip-- unswap-sqr
Counts
4 → 154
Calls
4 calls:
0.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
35.0ms
(* (* x x) (* x x))
51.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* (* x x) (* x x)) (* (* 2.0 2.0) (* 2.0 2.0))))
526.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (* (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* (* x x) (* x x)) (* (* 2.0 2.0) (* 2.0 2.0)))) (+ (* x x) (* 2.0 2.0))) (+ x 2.0)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
47.0ms
(* (* x x) (* x x))
120.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* (* x x) (* x x)) (* (* 2.0 2.0) (* 2.0 2.0))))
508.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (* (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* (* x x) (* x x)) (* (* 2.0 2.0) (* 2.0 2.0)))) (+ (* x x) (* 2.0 2.0))) (+ x 2.0)))

simplify1.5s

Counts
166 → 166
Iterations
IterNodes
done5000
1882
0281

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
13.4b
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
13.5b
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
20.9b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1))

rewrite600.0ms

Algorithm
rewrite-expression-head
Rules
9324×times-frac
4496×add-sqr-sqrt
4495×*-un-lft-identity
3617×add-cube-cbrt
2136×sqrt-prod
439×distribute-lft-out-- difference-of-squares
227×div-inv
185×associate-/r/
80×associate-/l*
73×flip3-- flip--
63×associate-/r*
41×add-exp-log
32×add-cbrt-cube
28×div-exp
19×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg 1-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 2872
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
10.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
114.0ms
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
14.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1))

series1.1s

Counts
4 → 12
Calls
4 calls:
118.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
175.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
320.0ms
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
483.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1))

simplify4.4s

Counts
2884 → 2884
Iterations
IterNodes
done5000
03077

prune23.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes603.0ms

Accuracy

96% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 24.5b

bsearch393.0ms

Steps
ItersRangePoint
9
6803.12139425764
1528168778729.1204
1498395052788.919
9
-1.8713307606778553e+30
-2.085807323628561e+25
-9.097538303619485e+29

simplify7.0ms

Iterations
IterNodes
done44
144
041

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.7s8010×body80valid