Details

Time bar (total: 10.3s)

sample33.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify46.0ms

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: 21.9b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
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)))
21.2b
(/ (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))

rewrite21.0ms

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 4.16438922228 78.6994924154) x 137.519416416)
1.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
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))

series569.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
94.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
276.0ms
(/ (- 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)))
173.0ms
(/ (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 (58.0ms)

IterNodesCost
06732789
126382653
250022650

prune706.0ms

Filtered
164 candidates to 126 candidates (76.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1568164
Fresh011
Picked101
Done000
Total1579166

Merged error: 0.1b

Counts
166 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

4.4b
(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)))
15.3b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
21.3b
(/ (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))

rewrite129.0ms

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))
29.0ms
(/ (/ (- 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))

series798.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
273.0ms
(/ (/ (- 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)))
148.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
280.0ms
(/ (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))

simplify426.0ms

Algorithm
egg-herbie
Counts
953 → 953
Iterations

Useful iterations: 1 (59.0ms)

IterNodesCost
0310433066
1500232245

prune2.6s

Filtered
953 candidates to 426 candidates (44.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New9530953
Fresh088
Picked011
Done000
Total9539962

Merged error: 0.1b

Counts
962 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (/ (- 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))))
21.2b
(/ (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))
21.2b
(/ (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))
21.2b
(/ (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))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
137×times-frac
103×add-sqr-sqrt *-un-lft-identity
77×add-cube-cbrt
70×cbrt-prod
13×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
9×associate-/r* div-inv associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv frac-2neg div-exp clear-num
1×cbrt-div pow1/3 associate-/r/
Counts
4 → 168
Calls
4 calls:
8.0ms
(cbrt (/ (- 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))
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))
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))

series896.0ms

Counts
4 → 12
Calls
4 calls:
381.0ms
(cbrt (/ (- 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))))
171.0ms
(/ (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))
170.0ms
(/ (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))
173.0ms
(/ (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))

simplify98.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
06633496
120543350
250023342

prune958.0ms

Filtered
180 candidates to 139 candidates (77.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1800180
Fresh077
Picked011
Done011
Total1809189

Merged error: 0.1b

Counts
189 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

13.5b
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
13.5b
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
13.5b
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
18.7b
(/ (* (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (* (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log
9×cbrt-prod
8×add-cbrt-cube
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow1/3
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 62
Calls
4 calls:
1.0ms
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
1.0ms
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
1.0ms
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
9.0ms
(/ (* (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (* (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))))

series967.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
197.0ms
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
198.0ms
(cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
368.0ms
(/ (* (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (* (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (cbrt (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))))

simplify104.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (91.0ms)

IterNodesCost
03491219
111001000
24699896
35001884

prune461.0ms

Filtered
74 candidates to 62 candidates (83.8%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New74074
Fresh066
Picked011
Done022
Total74983

Merged error: 0.1b

Counts
83 → 9

regimes329.0ms

Accuracy

96.2% (0.9b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 24.7b

bsearch111.0ms

Steps
ItersRangePoint
5
3.0822022890821534e+23
6.596987901191405e+23
6.495781457111713e+23
3
-1.92533204736021e+43
-1.6010517425641268e+43
-1.905064528310455e+43

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04022
14022

end0.0ms

sample707.0ms

Algorithm
intervals
Results
528.0ms8007×body80valid