Details

Time bar (total: 9.7s)

sample38.0ms

Algorithm
intervals
Results
20.0ms256×body80valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06211
115411
250311
3184011
4500311

prune16.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.4b

Counts
2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.1b
(fma (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)))
23.7b
(/ (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))

rewrite20.0ms

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)
9.0ms
(/ (- 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)))
3.0ms
(/ (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))

series516.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
280.0ms
(/ (- 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)))
174.0ms
(/ (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))

simplify95.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06742773
126182640
250012638

prune712.0ms

Filtered
164 candidates to 126 candidates (76.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1577164
Fresh101
Picked101
Done000
Total1597166

Merged error: 0.0b

Counts
166 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x 2.0) (/ 1 (/ (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))))
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.2b
(/ 1 (/ (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)))
23.7b
(/ (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))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
106×add-sqr-sqrt
94×*-un-lft-identity
90×add-cube-cbrt
44×associate-*r*
36×add-exp-log
20×add-cbrt-cube
16×associate-/r*
15×div-exp
10×div-inv
7×pow1 cbrt-undiv prod-exp
6×associate-/l*
5×associate-*l* unswap-sqr
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×cbrt-unprod
2×frac-times flip3-- frac-2neg associate-*l/ clear-num associate-/r/ flip--
1×pow-flip associate-*r/ pow-prod-down un-div-inv *-commutative fma-udef distribute-lft-out-- inv-pow difference-of-squares
Counts
4 → 198
Calls
4 calls:
18.0ms
(* (- x 2.0) (/ 1 (/ (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))))
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
6.0ms
(/ 1 (/ (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)))
3.0ms
(/ (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))

series737.0ms

Counts
4 → 12
Calls
4 calls:
289.0ms
(* (- x 2.0) (/ 1 (/ (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))))
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
243.0ms
(/ 1 (/ (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)))
178.0ms
(/ (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))

simplify108.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07193155
136332853
250012727

prune714.0ms

Filtered
210 candidates to 134 candidates (63.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2091210
Fresh066
Picked101
Done000
Total2107217

Merged error: 0.0b

Counts
217 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

5.9b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
15.1b
(/ (/ (- 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 (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
16.0b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
23.7b
(/ (sqrt (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))

rewrite139.0ms

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:
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
27.0ms
(/ (/ (- 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 (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
7.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
4.0ms
(/ (sqrt (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))

series845.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
285.0ms
(/ (/ (- 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 (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
157.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
294.0ms
(/ (sqrt (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))

simplify421.0ms

Algorithm
egg-herbie
Counts
953 → 953
Iterations

Useful iterations: 1 (61.0ms)

IterNodesCost
0310433066
1500232245

prune2.7s

Filtered
953 candidates to 426 candidates (44.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New9521953
Fresh156
Picked011
Done000
Total9537960

Merged error: 0.0b

Counts
960 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
2.1b
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
23.8b
(* (/ (- 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))

rewrite20.0ms

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 43.3400022514) x 263.505074721) x 313.399215894)
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
6.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
9.0ms
(* (/ (- 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))

series453.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
32.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
92.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
292.0ms
(* (/ (- 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))

simplify56.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04651204
116861090
250011088

prune435.0ms

Filtered
114 candidates to 87 candidates (76.3%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1131114
Fresh145
Picked011
Done101
Total1156121

Merged error: 0.0b

Counts
121 → 6

regimes388.0ms

Accuracy

95.9% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 24.9b

bsearch232.0ms

Steps
ItersRangePoint
9
2.3444880623575728e+36
1.6006938423459802e+44
9.736086126028101e+41
8
-2.94609198328492e+21
-8.221364080330966e+17
-2.673505848976334e+21

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05123
15123

end0.0ms

sample830.0ms

Algorithm
intervals
Results
643.0ms8003×body80valid