Details

Time bar (total: 10.2s)

sample35.0ms

Algorithm
intervals
Results
18.0ms256×body80valid

simplify539.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02937
16230
215330
338330
4125130
done500030

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.0b
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
28.1b
(/ (* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log add-cbrt-cube
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-/r* fma-udef
2×cbrt-undiv associate-*r/ div-exp associate-/l/
1×flip3-- frac-2neg prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l*
Counts
4 → 55
Calls
4 calls:
0.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
11.0ms
(/ (* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

series464.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
96.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
282.0ms
(/ (* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

simplify479.0ms

Counts
67 → 67
Iterations

Useful iterations: done (476.0ms)

IterNodesCost
01401552
13241522
210321272
done50001268

prune348.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
2.8b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
26.1b
(/ (fma (fma (fma (fma 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)))

rewrite27.0ms

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-exp-log associate-/r/ add-cbrt-cube
6×div-inv associate-/l*
5×flip3-- flip--
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef
Counts
4 → 163
Calls
4 calls:
0.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
6.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
10.0ms
(/ (fma (fma (fma (fma 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)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
90.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
279.0ms
(/ (fma (fma (fma (fma 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)))

simplify910.0ms

Counts
175 → 175
Iterations

Useful iterations: 2 (242.0ms)

IterNodesCost
02937015
16326860
223856552
done50006552

prune807.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.0b
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
26.1b
(/ (fma (fma (fma (fma 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))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 59
Calls
4 calls:
0.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
2.0ms
(/ (fma (fma (fma (fma 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))

series433.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
99.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
247.0ms
(/ (fma (fma (fma (fma 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))

simplify1.1s

Counts
71 → 71
Iterations

Useful iterations: 3 (325.0ms)

IterNodesCost
01291747
12491718
26511542
324041538
done50001538

prune344.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

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))
16.5b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
16.7b
(* (/ (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))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
22.8b
(/ (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)))

rewrite61.0ms

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-*r*
22×associate-*l*
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))
12.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
36.0ms
(* (/ (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))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
3.0ms
(/ (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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
294.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
155.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
296.0ms
(* (/ (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))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
375.0ms
(/ (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)))

simplify861.0ms

Counts
213 → 213
Iterations

Useful iterations: done (850.0ms)

IterNodesCost
02998963
17818490
224657595
done50017520

prune832.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes250.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 25.6b

bsearch192.0ms

Steps
ItersRangePoint
8
6.217793645765005e+41
3.9777289923527025e+45
3.6379943132031436e+44
6
-1.134609644762367e+48
-1.5785591069619822e+47
-3.224942267140988e+47

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03458
13949
done3949

end0.0ms

sample761.0ms

Algorithm
intervals
Results
584.0ms8005×body80valid