Details

Time bar (total: 23.9s)

sample89.0ms

Algorithm
intervals
Results
46.0ms256×body80valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
02937
16230
215430
351330
4220730
done500130

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.3b
(/ (- x 2.0) (/ (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)))
26.1b
(/ (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))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
96×add-sqr-sqrt *-un-lft-identity
68×add-cube-cbrt
16×associate-/r*
14×distribute-lft-out-- difference-of-squares
11×add-exp-log add-cbrt-cube
8×div-inv associate-/l*
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef associate-/l/
1×flip3-- div-sub associate-/r/ flip--
Counts
4 → 152
Calls
4 calls:
1.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
38.0ms
(/ (- x 2.0) (/ (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)))
5.0ms
(/ (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))

series828.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
37.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
464.0ms
(/ (- x 2.0) (/ (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)))
276.0ms
(/ (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))

simplify1.9s

Counts
164 → 164
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02667066
17316960
234076604
done50016599

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.1b
(fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416))
0.3b
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z)))
26.1b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
96×add-sqr-sqrt *-un-lft-identity
68×add-cube-cbrt
16×associate-/r*
14×distribute-lft-out-- difference-of-squares
11×add-exp-log add-cbrt-cube
8×div-inv associate-/l*
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef associate-/l/
1×flip3-- div-sub associate-/r/ flip--
Counts
4 → 152
Calls
4 calls:
0.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0ms
(fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416))
22.0ms
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z)))
5.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z))

series646.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
34.0ms
(fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416))
345.0ms
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z)))
205.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z))

simplify1.5s

Counts
164 → 164
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02667513
17337407
234927023
done50016592

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.3b
(/ (- x 2.0) (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) x y) x z))))
0.3b
(/ 1 (fma (fma (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) x y) x z))
26.1b
(* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) x y) x z)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
32×add-exp-log
27×*-un-lft-identity
25×times-frac
22×add-cube-cbrt
20×add-cbrt-cube
13×associate-*r*
11×div-exp
8×prod-exp associate-/l*
7×pow1
6×cbrt-undiv
4×expm1-log1p-u associate-/r* cbrt-unprod log1p-expm1-u add-log-exp
3×rec-exp 1-exp associate-*l* div-inv unswap-sqr
2×frac-2neg associate-*r/ clear-num associate-/r/ un-div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×flip3-- pow-flip div-sub pow-prod-down *-commutative flip-- fma-udef inv-pow
Counts
4 → 117
Calls
4 calls:
1.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
52.0ms
(/ (- x 2.0) (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) x y) x z))))
9.0ms
(/ 1 (fma (fma (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) x y) x z))
25.0ms
(* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) x y) x z)))

series730.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
334.0ms
(/ (- x 2.0) (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) x y) x z))))
124.0ms
(/ 1 (fma (fma (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) x y) x z))
239.0ms
(* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) x y) x z)))

simplify1.2s

Counts
129 → 129
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01913747
14483516
220063016
done50003009

prune921.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

8.0b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
16.9b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
17.0b
(/ (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z)))
26.1b
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z))

rewrite282.0ms

Algorithm
rewrite-expression-head
Rules
2116×times-frac
1176×add-sqr-sqrt
1175×*-un-lft-identity
885×add-cube-cbrt
693×sqrt-prod
145×distribute-lft-out-- difference-of-squares
61×div-inv
45×associate-/l*
31×associate-/r*
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg div-sub clear-num associate-/l/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip--
Counts
4 → 941
Calls
4 calls:
3.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
39.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
74.0ms
(/ (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z)))
7.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z))

series1.1s

Counts
4 → 12
Calls
4 calls:
123.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
179.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
402.0ms
(/ (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z)))
367.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma 4.16438922228 (* x x) (fma 78.6994924154 x 137.519416416)) x y) x z))

simplify2.1s

Counts
953 → 953
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0102183474
1381678763
done500277823

prune4.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes424.0ms

Accuracy

96.5% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 24.4b

bsearch386.0ms

Steps
ItersRangePoint
9
8.375463895322616e+20
3.7617724825378538e+28
3.712486315822509e+28
8
-2.2452448923255262e+32
-2.408385263222486e+28
-2.2489554391470123e+30

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03560
13951
done3951

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.7s8007×body80valid