Details

Time bar (total: 10.8s)

sample42.0ms

Algorithm
intervals
Results
23.0ms257×body80valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06211
115411
250311
3184011
4500311

prune14.0ms

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: 25.4b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.1b
(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)))
24.7b
(/ (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))

rewrite24.0ms

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 (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
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))

series570.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
27.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
297.0ms
(/ (- 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)))
183.0ms
(/ (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))

simplify93.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06772773
126212640
250012638

prune953.0ms

Filtered
164 candidates to 126 candidates (76.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1577164
Fresh011
Picked101
Done000
Total1588166

Merged error: 0b

Counts
166 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 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)))
0.3b
(/ x (/ (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)))
24.7b
(/ (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))
24.7b
(/ (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))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
168×times-frac
104×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×associate-/r*
18×add-exp-log add-cbrt-cube
12×div-inv associate-/l*
8×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×associate-/r/
Counts
4 → 202
Calls
4 calls:
6.0ms
(/ 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
(/ x (/ (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))
4.0ms
(/ (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))

series968.0ms

Counts
4 → 12
Calls
4 calls:
276.0ms
(/ 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)))
328.0ms
(/ x (/ (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)))
180.0ms
(/ (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))
184.0ms
(/ (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))

simplify113.0ms

Algorithm
egg-herbie
Counts
214 → 214
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06743636
129873424
250023422

prune1.0s

Filtered
214 candidates to 176 candidates (82.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2140214
Fresh077
Picked011
Done000
Total2148222

Merged error: 0b

Counts
222 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
2.8b
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
24.8b
(* (/ (- 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))

rewrite25.0ms

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 (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
10.0ms
(/ (- 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))

series487.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
98.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
301.0ms
(* (/ (- 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))

simplify57.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04681204
116891090
250011088

prune480.0ms

Filtered
114 candidates to 87 candidates (76.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1140114
Fresh066
Picked011
Done011
Total1148122

Merged error: 0b

Counts
122 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

7.7b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.9b
(/ (/ (- 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)))
15.7b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
24.6b
(/ (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))

rewrite144.0ms

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:
2.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
30.0ms
(/ (/ (- 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)))
8.0ms
(/ (- 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))

series882.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
308.0ms
(/ (/ (- 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)))
167.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
297.0ms
(/ (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 (58.0ms)

IterNodesCost
0310433066
1500232245

prune2.8s

Filtered
953 candidates to 425 candidates (44.6%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New9530953
Fresh055
Picked011
Done022
Total9538961

Merged error: 0b

Counts
961 → 8

regimes403.0ms

Accuracy

97% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 24.9b

bsearch224.0ms

Steps
ItersRangePoint
9
8.796380387336769e+32
1.6883106978042227e+42
1.6463116780624083e+42
7
-2.6270612343545538e+53
-1.0205942138599043e+52
-1.1713927062611842e+53

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03925
13925

end0.0ms

sample823.0ms

Algorithm
intervals
Results
639.0ms8006×body80valid

Profiling

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