Details

Time bar (total: 7.2s)

sample36.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06211
115411
250311
3184011
4500311

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(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)))
24.2b
(/ (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))

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:
0.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
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)))
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))

series540.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(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)
281.0ms
(/ (- 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))

simplify88.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06772773
126212640
250012638

prune773.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.2b
(* (/ (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)) (+ x 2.0))
15.4b
(/ (- (* 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)))
24.2b
(/ (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))

rewrite36.0ms

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 4.16438922228 78.6994924154) x 137.519416416)
15.0ms
(* (/ (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))

series717.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
198.0ms
(* (/ (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))
320.0ms
(/ (- (* 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)))
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))

simplify83.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06371806
129921563
250021561

prune604.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fma x 4.16438922228 78.6994924154) x)
0.2b
(* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (+ (* (fma x 4.16438922228 78.6994924154) x) 137.519416416) x y) x z)) (+ x 2.0))
15.4b
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (+ (* (fma x 4.16438922228 78.6994924154) x) 137.519416416) x y) x z)) (+ x 2.0)))
24.2b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (+ (* (fma x 4.16438922228 78.6994924154) x) 137.519416416) x y) x z))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
26×*-un-lft-identity
24×add-cube-cbrt
23×times-frac
22×add-exp-log add-cbrt-cube
16×associate-*l*
8×pow1
7×associate-*r* associate-/l*
6×cbrt-undiv div-exp
5×prod-exp associate-/r/ cbrt-unprod
4×expm1-log1p-u frac-times flip3-+ associate-*r/ associate-/r* flip-+ log1p-expm1-u add-log-exp
3×div-inv unswap-sqr
2×frac-2neg pow-prod-down associate-*l/ clear-num *-commutative associate-/l/ difference-of-squares
1×distribute-rgt-in flip3-- distribute-lft-in div-sub flip-- distribute-lft-out
Counts
4 → 125
Calls
4 calls:
3.0ms
(* (fma x 4.16438922228 78.6994924154) x)
14.0ms
(* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (+ (* (fma x 4.16438922228 78.6994924154) x) 137.519416416) x y) x z)) (+ x 2.0))
13.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (+ (* (fma 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 x 4.16438922228 78.6994924154) x) 137.519416416) x y) x z))

series763.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (fma x 4.16438922228 78.6994924154) x)
194.0ms
(* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (+ (* (fma x 4.16438922228 78.6994924154) x) 137.519416416) x y) x z)) (+ x 2.0))
332.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (+ (* (fma x 4.16438922228 78.6994924154) x) 137.519416416) x y) x z)) (+ x 2.0)))
172.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (+ (* (fma x 4.16438922228 78.6994924154) x) 137.519416416) x y) x z))

simplify87.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06741976
131741711
250011707

prune638.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize23.0ms

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))
7.7b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
16.1b
(* (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)))
24.0b
(/ (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))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×times-frac
36×add-cube-cbrt *-un-lft-identity
35×sqrt-prod
22×associate-*r*
11×add-exp-log add-cbrt-cube
8×pow1
6×associate-*l* associate-/l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp prod-exp cbrt-unprod div-inv
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 121
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
13.0ms
(* (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)))
3.0ms
(/ (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))

series681.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
100.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
177.0ms
(* (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)))
288.0ms
(/ (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))

simplify59.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03091938
112191710
250011649

prune543.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes318.0ms

Accuracy

97.6% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 25.2b

bsearch338.0ms

Steps
ItersRangePoint
6
5.1210306950163065e+73
7.803470383043457e+74
7.527015027311277e+73
9
-2.510041587470139e+55
-1.4642350205978134e+49
-1.0074840445932115e+53

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04720
14720

end0.0ms

sample684.0ms

Algorithm
intervals
Results
506.0ms8011×body80valid