Details

Time bar (total: 18.2s)

sample66.0ms

Algorithm
intervals
Results
31.0ms256×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
02937
16230
215430
350230
4176630
done500030

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
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)))
23.2b
(/ (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))

rewrite42.0ms

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 (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
29.0ms
(/ (- 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)))
6.0ms
(/ (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))

series726.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
40.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
391.0ms
(/ (- 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)))
234.0ms
(/ (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))

simplify1.4s

Counts
164 → 164
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02637109
16606981
221376631
done50006626

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.0b
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
1.0b
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
23.5b
(* (/ (- 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))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
38×*-un-lft-identity
31×times-frac
24×add-cube-cbrt
19×associate-*l*
11×add-exp-log add-cbrt-cube
7×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-/l*
4×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
3×associate-*r* associate-/r*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub pow-prod-down associate-*l/ clear-num *-commutative flip--
Counts
4 → 102
Calls
4 calls:
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
1.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
19.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
50.0ms
(* (/ (- 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))

series647.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
70.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
113.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
429.0ms
(* (/ (- 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))

simplify1.4s

Counts
114 → 114
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01973079
14623040
213832742
done50002738

prune792.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.0b
(/ 1 (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))
0.9b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
23.5b
(* (/ 1 (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
186×add-sqr-sqrt
174×*-un-lft-identity
122×add-cube-cbrt
68×associate-*l*
36×add-exp-log
26×associate-/r*
25×distribute-lft-out-- difference-of-squares
20×add-cbrt-cube
18×associate-/r/
15×div-exp
10×div-inv
8×flip3-- flip--
7×pow1 cbrt-undiv prod-exp
6×associate-/l*
5×unswap-sqr
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×associate-*r* cbrt-unprod fma-udef
2×frac-2neg clear-num
1×distribute-rgt-in pow-flip distribute-lft-in pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 259
Calls
4 calls:
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
22.0ms
(/ 1 (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))
14.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
64.0ms
(* (/ 1 (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series787.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
153.0ms
(/ 1 (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))
146.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
443.0ms
(* (/ 1 (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify1.6s

Counts
271 → 271
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03778568
18587958
221817343
done50017290

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b
(* (/ (- (* x x) (* 2.0 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (+ x 2.0)))
22.6b
(/ (- (* x x) (* 2.0 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
23.5b
(* (* (/ (- (* x x) (* 2.0 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (+ x 2.0))) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
60×add-exp-log
47×add-sqr-sqrt
43×times-frac
38×*-un-lft-identity
36×add-cbrt-cube
30×add-cube-cbrt
25×prod-exp
21×associate-*r*
17×div-exp associate-*l*
13×cbrt-unprod
11×pow1
9×cbrt-undiv
7×difference-of-squares
6×associate-*l/ unswap-sqr
4×expm1-log1p-u rec-exp 1-exp pow-prod-down log1p-expm1-u associate-/l* add-log-exp
3×associate-/r* fma-udef div-inv distribute-lft-out
2×frac-times associate-*r/ associate-/r/ un-div-inv *-commutative associate-/l/
1×distribute-rgt-in flip3-- frac-2neg distribute-lft-in flip3-+ div-sub clear-num flip-- flip-+
Counts
4 → 149
Calls
4 calls:
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
66.0ms
(* (/ (- (* x x) (* 2.0 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (+ x 2.0)))
40.0ms
(/ (- (* x x) (* 2.0 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
111.0ms
(* (* (/ (- (* x x) (* 2.0 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (+ x 2.0))) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series806.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
145.0ms
(* (/ (- (* x x) (* 2.0 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (+ x 2.0)))
105.0ms
(/ (- (* x x) (* 2.0 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
500.0ms
(* (* (/ (- (* x x) (* 2.0 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (+ x 2.0))) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify2.2s

Counts
161 → 161
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02925600
17865319
226154432
done50024045

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes284.0ms

Accuracy

96.2% (0.9b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 24.8b

bsearch397.0ms

Steps
ItersRangePoint
9
30646363810.07727
1.5508478278740396e+18
1.5220683705628803e+18
10
-1.8872343870183804e+52
-5.721293794858056e+41
-9.990458313923675e+47

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
04068
14959
done4959

end0.0ms

sample1.1s

Algorithm
intervals
Results
728.0ms8009×body80valid