Details

Time bar (total: 8.2s)

sample59.0ms

Algorithm
intervals
Results
42.0ms256×body80valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06211
115411
250311
3184011
4500311

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.5b

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 (+ x 43.3400022514) x 263.505074721) x 313.399215894)
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)))
20.8b
(/ (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:
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
11.0ms
(/ (- 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)))
2.0ms
(/ (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))

series507.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
34.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
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)))
167.0ms
(/ (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))

simplify85.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06742773
126182640
250012638

prune770.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.1b
(* (/ (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)) (+ x 2.0))
13.3b
(/ (- (* x x) (* 2.0 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)) (+ x 2.0)))
20.8b
(/ (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))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity
23×times-frac
22×add-cube-cbrt
20×add-exp-log add-cbrt-cube
13×associate-*l*
7×associate-/l*
6×pow1 cbrt-undiv div-exp
5×associate-/r/
4×expm1-log1p-u frac-times flip3-+ associate-*r/ associate-*r* prod-exp associate-/r* cbrt-unprod flip-+ log1p-expm1-u add-log-exp
3×div-inv
2×frac-2neg associate-*l/ clear-num associate-/l/ difference-of-squares unswap-sqr
1×distribute-rgt-in flip3-- distribute-lft-in div-sub pow-prod-down *-commutative flip-- fma-udef distribute-lft-out
Counts
4 → 115
Calls
4 calls:
0.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
14.0ms
(* (/ (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)) (+ x 2.0))
12.0ms
(/ (- (* x x) (* 2.0 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)) (+ x 2.0)))
2.0ms
(/ (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))

series730.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
193.0ms
(* (/ (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)) (+ x 2.0))
326.0ms
(/ (- (* x x) (* 2.0 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)) (+ x 2.0)))
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))

simplify82.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06441821
130181579
250021577

prune614.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
1.3b
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
20.8b
(* (/ (- 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))

rewrite31.0ms

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:
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
12.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
15.0ms
(* (/ (- 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))

series433.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
40.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
90.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
278.0ms
(* (/ (- 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))

simplify53.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04651204
116861090
250011088

prune506.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

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))
13.3b
(/ (- (* x x) (* 2.0 2.0)) (* (/ (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) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (+ x 2.0)))
13.9b
(/ (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) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
18.1b
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
280×times-frac
160×add-sqr-sqrt
159×add-cube-cbrt *-un-lft-identity
147×sqrt-prod
29×associate-/r*
25×add-exp-log add-cbrt-cube
13×associate-/l*
11×cbrt-undiv div-exp
10×div-inv
6×associate-/r/
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg prod-exp clear-num cbrt-unprod
2×frac-times flip3-+ associate-*r/ flip-+ associate-/l/ difference-of-squares
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 div-sub associate-*l/ flip--
Counts
4 → 270
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
23.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (/ (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) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (+ x 2.0)))
9.0ms
(/ (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) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
3.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

series975.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
331.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (/ (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) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (+ x 2.0)))
176.0ms
(/ (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) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
367.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify109.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010167347
150016666

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

regimes223.0ms

Accuracy

96.8% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 25.2b

bsearch221.0ms

Steps
ItersRangePoint
6
8.582000441022086e+45
6.570892709053075e+46
1.1768636815843567e+46
8
-3.8039615204101026e+57
-3.0816857366909946e+53
-1.2270580557324376e+54

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04626
14626

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.2s8013×body80valid