Details

Time bar (total: 19.4s)

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

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: 28.5b

Counts
2 → 2

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)
0.1b
(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)))
27.6b
(/ (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))

rewrite23.0ms

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)
3.0ms
(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))

series536.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
25.0ms
(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)))
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))

simplify91.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06772773
126212640
250012638

prune737.0ms

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: 0.0b

Counts
166 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

24.8b
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))
24.8b
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))
24.8b
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))
27.6b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (* (* (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)) (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))) (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))) x z))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×cbrt-prod times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-/r* associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 68
Calls
4 calls:
1.0ms
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))
1.0ms
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))
1.0ms
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))
3.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (* (* (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)) (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))) (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))) x z))

series886.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))
238.0ms
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))
237.0ms
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))
176.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (* (* (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)) (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))) (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))) x z))

simplify78.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
02311375
15931263
224261171
350021085

prune442.0ms

Filtered
80 candidates to 68 candidates (85.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New79180
Fresh077
Picked011
Done000
Total79988

Merged error: 0b

Counts
88 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

6.3b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
20.9b
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (/ (fma (pow (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)) 3) x z) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) 2)) 2))
23.2b
(/ (fma (pow (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)) 3) x z) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) 2))
24.8b
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))

rewrite489.0ms

Algorithm
rewrite-expression-head
Rules
5451×times-frac
2324×add-sqr-sqrt
2323×add-cube-cbrt *-un-lft-identity
1260×sqrt-prod
239×associate-/r*
97×div-inv
23×add-exp-log associate-/r/ add-cbrt-cube
13×cbrt-undiv div-exp
9×associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 1682
Calls
4 calls:
2.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
64.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (/ (fma (pow (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)) 3) x z) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) 2)) 2))
8.0ms
(/ (fma (pow (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)) 3) x z) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) 2))
2.0ms
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))

series1.7s

Counts
4 → 12
Calls
4 calls:
99.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
872.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (/ (fma (pow (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)) 3) x z) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) 2)) 2))
514.0ms
(/ (fma (pow (cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)) 3) x z) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) 2))
232.0ms
(cbrt (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y))

simplify777.0ms

Algorithm
egg-herbie
Counts
1694 → 1694
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
0500169190

prune10.2s

Filtered
1694 candidates to 1203 candidates (71.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New169401694
Fresh077
Picked011
Done011
Total169491703

Merged error: 0b

Counts
1703 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (cbrt (/ (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))) (cbrt (/ (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))))
27.6b
(/ (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))
27.6b
(/ (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))
27.6b
(/ (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
84×add-sqr-sqrt
69×times-frac
64×cbrt-prod
60×add-cube-cbrt *-un-lft-identity
16×swap-sqr associate-*r* associate-*l*
12×add-exp-log
11×pow1
10×add-cbrt-cube
9×associate-/r* associate-/l* unswap-sqr
7×div-inv
6×pow1/3
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×cbrt-undiv frac-2neg div-exp clear-num
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 167
Calls
4 calls:
12.0ms
(* (cbrt (/ (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))) (cbrt (/ (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))
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))

series846.0ms

Counts
4 → 12
Calls
4 calls:
350.0ms
(* (cbrt (/ (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))) (cbrt (/ (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))))
165.0ms
(/ (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))
165.0ms
(/ (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))
166.0ms
(/ (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))

simplify71.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03243547
111123346
250013165

prune893.0ms

Filtered
179 candidates to 136 candidates (76.0%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1790179
Fresh066
Picked011
Done022
Total1799188

Merged error: 0b

Counts
188 → 9

regimes364.0ms

Accuracy

94.8% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 24.9b

bsearch251.0ms

Steps
ItersRangePoint
10
0.000608309806168642
2529654550.545884
2485685511.02154
8
-1.2390142263488878e+49
-4.7622933319838e+46
-1.3288448495506195e+48

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06022
16022

end0.0ms

sample772.0ms

Algorithm
intervals
Results
589.0ms8010×body80valid