Details

Time bar (total: 24.9s)

sample74.0ms

Algorithm
intervals
Results
40.0ms256×body80valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5000
41857
3505
2152
162
029

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.0b

localize57.0ms

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)
3.9b
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
23.1b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
38×*-un-lft-identity
31×times-frac
24×add-cube-cbrt
19×associate-*r*
11×add-cbrt-cube add-exp-log
7×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod fma-udef div-inv unswap-sqr associate-/l/
1×clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 104
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)
25.0ms
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
40.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

series519.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
28.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
99.0ms
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
349.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify1.9s

Counts
116 → 116
Iterations
IterNodes
done5000
21532
1462
0200

prune862.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize88.0ms

Local error

Found 4 expressions with local error:

7.1b
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
14.8b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
14.9b
(* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
18.8b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
94×add-sqr-sqrt
83×*-un-lft-identity
82×times-frac
56×associate-*r*
55×add-cube-cbrt
50×add-exp-log
47×sqrt-prod
32×add-cbrt-cube
22×prod-exp
13×distribute-lft-out-- difference-of-squares
12×pow1 div-exp cbrt-unprod
7×cbrt-undiv
6×associate-/r*
5×associate-/l* unswap-sqr
4×expm1-log1p-u associate-*l* pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp un-div-inv div-inv
2×frac-times associate-*l/ *-commutative associate-/l/
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 div-sub flip--
Counts
4 → 194
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
20.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
88.0ms
(* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
31.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

series1.2s

Counts
4 → 12
Calls
4 calls:
140.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
213.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
423.0ms
(* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
447.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

simplify2.8s

Counts
206 → 206
Iterations
IterNodes
done5000
22833
1888
0320

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.1b
(* x (fma 4.16438922228 x 78.6994924154))
3.9b
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
23.1b
(* (fma x (fma x (+ (* x (fma 4.16438922228 x 78.6994924154)) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×*-un-lft-identity
31×times-frac
26×add-cube-cbrt
22×associate-*r*
13×add-cbrt-cube add-exp-log
8×pow1
7×distribute-lft-out-- difference-of-squares
6×associate-*l*
5×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* prod-exp cbrt-unprod fma-udef unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv associate-/l/
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in flip3-- div-sub associate-*r/ flip--
Counts
4 → 116
Calls
4 calls:
0.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
7.0ms
(* x (fma 4.16438922228 x 78.6994924154))
16.0ms
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
58.0ms
(* (fma x (fma x (+ (* x (fma 4.16438922228 x 78.6994924154)) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

series701.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
105.0ms
(* x (fma 4.16438922228 x 78.6994924154))
127.0ms
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
425.0ms
(* (fma x (fma x (+ (* x (fma 4.16438922228 x 78.6994924154)) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify2.0s

Counts
128 → 128
Iterations
IterNodes
done5001
21721
1517
0219

prune974.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

7.1b
(sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))
7.1b
(sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))
14.8b
(/ (- x 2.0) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)))
23.1b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (/ (- x 2.0) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
424×times-frac
309×add-sqr-sqrt
283×*-un-lft-identity
221×sqrt-prod
208×associate-*r*
197×add-cube-cbrt
43×distribute-lft-out-- difference-of-squares
15×add-cbrt-cube add-exp-log
8×pow1 div-inv
7×unswap-sqr
6×associate-/r*
5×associate-/l*
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 328
Calls
4 calls:
1.0ms
(sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))
1.0ms
(sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))
19.0ms
(/ (- x 2.0) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)))
131.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (/ (- x 2.0) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))))

series967.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))
128.0ms
(sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))
240.0ms
(/ (- x 2.0) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)))
452.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (/ (- x 2.0) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))))

simplify3.1s

Counts
340 → 340
Iterations
IterNodes
done5001
23924
11235
0452

prune2.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes357.0ms

Accuracy

97% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 23.7b

bsearch478.0ms

Steps
ItersRangePoint
9
1.5718858767320834e+57
3.8209299420369884e+64
9.776865012149899e+58
10
-1.5590323174545235e+78
-1.4985113408838331e+65
-2.447941498404213e+65

simplify44.0ms

Iterations
IterNodes
done48
148
040

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.9s8006×body80valid