Details

Time bar (total: 55.1s)

sample67.0ms

Algorithm
intervals
Results
33.0ms256×body80valid

simplify1.7s

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
2.1b
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
23.1b
(/ (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)))

rewrite42.0ms

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 (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
0.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
18.0ms
(/ (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) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
41.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
99.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
309.0ms
(/ (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)))

simplify2.2s

Counts
175 → 175
Iterations
IterNodes
done5001
23541
1702
0293

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0))))
3.0b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (+ x 2.0))
19.3b
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0)))
20.1b
(* (/ 1 (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0)))) (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (+ x 2.0)))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
245×times-frac
157×add-sqr-sqrt
142×*-un-lft-identity
124×add-cube-cbrt
64×add-exp-log
59×associate-*l*
34×add-cbrt-cube
30×div-exp
26×associate-/r*
25×difference-of-squares
22×associate-/r/
18×associate-*r*
14×cbrt-undiv prod-exp
12×div-inv
10×unswap-sqr
9×associate-/l*
8×flip3-- flip--
7×pow1 distribute-lft-out
6×rec-exp 1-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×flip3-+ flip-+
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative pow-flip inv-pow
Counts
4 → 289
Calls
4 calls:
17.0ms
(/ 1 (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0))))
17.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (+ x 2.0))
11.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0)))
109.0ms
(* (/ 1 (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0)))) (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (+ x 2.0)))

series829.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ 1 (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0))))
154.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (+ x 2.0))
115.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0)))
460.0ms
(* (/ 1 (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- (* x x) (* 2.0 2.0)))) (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (+ x 2.0)))

simplify1.6s

Counts
301 → 301
Iterations
IterNodes
done5000
11369
0441

prune2.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize60.0ms

Local error

Found 4 expressions with local error:

7.0b
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
14.3b
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
14.4b
(/ (/ (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)))
20.2b
(/ (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))

rewrite437.0ms

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))
91.0ms
(/ (/ (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)))
10.0ms
(/ (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:
138.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
171.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
318.0ms
(/ (/ (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)))
487.0ms
(/ (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))

simplify5.2s

Counts
2884 → 2884
Iterations
IterNodes
done5000
03077

prune23.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize105.0ms

Local error

Found 4 expressions with local error:

14.3b
(* (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- (* x (* x x)) (* 2.0 (* 2.0 2.0)))) (+ (* x x) (+ (* 2.0 2.0) (* x 2.0))))
14.4b
(/ (/ (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 (* x x)) (* 2.0 (* 2.0 2.0)))) (+ (* x x) (+ (* 2.0 2.0) (* x 2.0)))))
20.2b
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- (* x (* x x)) (* 2.0 (* 2.0 2.0))))
20.2b
(/ (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))

rewrite386.0ms

Algorithm
rewrite-expression-head
Rules
499×times-frac
244×add-sqr-sqrt
236×*-un-lft-identity add-cube-cbrt
118×sqrt-prod
80×associate-/l*
66×add-exp-log
52×add-cbrt-cube
38×div-exp
30×associate-*l*
27×associate-/r*
26×cbrt-undiv cube-unmult
16×div-inv
13×difference-cubes
12×associate-/r/
10×prod-exp
8×cbrt-unprod
6×pow1
4×expm1-log1p-u frac-times flip3-+ 1-exp associate-*r/ flip-+ log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r* unswap-sqr
2×flip3-- associate-*l/ flip--
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/
Counts
4 → 399
Calls
4 calls:
189.0ms
(* (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- (* x (* x x)) (* 2.0 (* 2.0 2.0)))) (+ (* x x) (+ (* 2.0 2.0) (* x 2.0))))
90.0ms
(/ (/ (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 (* x x)) (* 2.0 (* 2.0 2.0)))) (+ (* x x) (+ (* 2.0 2.0) (* x 2.0)))))
61.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- (* x (* x x)) (* 2.0 (* 2.0 2.0))))
17.0ms
(/ (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))

series1.5s

Counts
4 → 12
Calls
4 calls:
225.0ms
(* (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- (* x (* x x)) (* 2.0 (* 2.0 2.0)))) (+ (* x x) (+ (* 2.0 2.0) (* x 2.0))))
583.0ms
(/ (/ (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 (* x x)) (* 2.0 (* 2.0 2.0)))) (+ (* x x) (+ (* 2.0 2.0) (* x 2.0)))))
178.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- (* x (* x x)) (* 2.0 (* 2.0 2.0))))
481.0ms
(/ (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))

simplify2.6s

Counts
411 → 411
Iterations
IterNodes
done5002
12145
0634

prune5.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

regimes624.0ms

Accuracy

97.3% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 24.4b

bsearch292.0ms

Steps
ItersRangePoint
6
2.915474134638951e+52
3.0455316621450604e+53
1.8497151307659583e+53
7
-3.5539660008838154e+52
-7.123290046831777e+50
-1.486655794493064e+52

simplify15.0ms

Iterations
IterNodes
done46
146
038

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.8s8007×body80valid