Details

Time bar (total: 8.7s)

sample34.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.2b

localize20.0ms

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 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)))
23.4b
(/ (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 43.3400022514) x 263.505074721) x 313.399215894)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
13.0ms
(/ (- 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))

series556.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
27.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
305.0ms
(/ (- 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)))
186.0ms
(/ (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))

simplify101.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06742773
126182640
250012638

prune776.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

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))
15.0b
(/ (- (* 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)))
23.4b
(/ (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)
18.0ms
(* (/ (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))
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 (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))

series764.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
204.0ms
(* (/ (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))
347.0ms
(/ (- (* 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)))
186.0ms
(/ (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
127 → 127
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06371806
129921563
250021561

prune610.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
14.9b
(* (/ (- (* 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)) (+ (pow x 3) (pow 2.0 3)))) (+ (* x x) (- (* 2.0 2.0) (* x 2.0))))
20.8b
(/ (- (* 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)) (+ (pow x 3) (pow 2.0 3))))
23.4b
(/ (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))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log add-cbrt-cube
19×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*l*
10×associate-/r/
9×cbrt-undiv div-exp
8×prod-exp cbrt-unprod
7×associate-/l*
6×pow1 frac-times flip3-+ associate-*r/ flip-+
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×associate-*r* associate-*l/ div-inv difference-of-squares
2×frac-2neg clear-num associate-/l/
1×distribute-rgt-in flip3-- distribute-lft-in div-sub pow-prod-down *-commutative flip-- fma-udef unswap-sqr
Counts
4 → 117
Calls
4 calls:
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
99.0ms
(* (/ (- (* 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)) (+ (pow x 3) (pow 2.0 3)))) (+ (* x x) (- (* 2.0 2.0) (* x 2.0))))
22.0ms
(/ (- (* 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)) (+ (pow x 3) (pow 2.0 3))))
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))

series1.2s

Counts
4 → 12
Calls
4 calls:
27.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
424.0ms
(* (/ (- (* 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)) (+ (pow x 3) (pow 2.0 3)))) (+ (* x x) (- (* 2.0 2.0) (* x 2.0))))
559.0ms
(/ (- (* 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)) (+ (pow x 3) (pow 2.0 3))))
189.0ms
(/ (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))

simplify60.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
08812527
150012078

prune783.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
14.9b
(* (/ (- (* x x) (* 2.0 2.0)) (* (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (+ (pow x 3) (pow 2.0 3)))) (+ (* x x) (- (* 2.0 2.0) (* x 2.0))))
20.8b
(/ (- (* x x) (* 2.0 2.0)) (* (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (+ (pow x 3) (pow 2.0 3))))
23.4b
(* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
69×add-exp-log
45×add-cbrt-cube
34×add-sqr-sqrt
29×prod-exp
28×times-frac
26×*-un-lft-identity
25×add-cube-cbrt
20×div-exp
19×associate-*l*
17×cbrt-unprod
16×associate-*r* associate-/r/
13×associate-*r/
12×cbrt-undiv
10×frac-times
9×pow1
8×flip3-+ flip-+
7×un-div-inv associate-/l*
5×associate-*l/
4×expm1-log1p-u rec-exp 1-exp associate-/r* log1p-expm1-u div-inv add-log-exp unswap-sqr
3×difference-of-squares
2×frac-2neg pow-prod-down clear-num *-commutative associate-/l/
1×distribute-rgt-in flip3-- pow-flip distribute-lft-in div-sub flip-- inv-pow
Counts
4 → 163
Calls
4 calls:
2.0ms
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
134.0ms
(* (/ (- (* x x) (* 2.0 2.0)) (* (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (+ (pow x 3) (pow 2.0 3)))) (+ (* x x) (- (* 2.0 2.0) (* x 2.0))))
32.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (+ (pow x 3) (pow 2.0 3))))
11.0ms
(* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

series1.1s

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
414.0ms
(* (/ (- (* x x) (* 2.0 2.0)) (* (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (+ (pow x 3) (pow 2.0 3)))) (+ (* x x) (- (* 2.0 2.0) (* x 2.0))))
366.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (+ (pow x 3) (pow 2.0 3))))
177.0ms
(* (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

simplify69.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010643238
150012624

prune915.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes233.0ms

Accuracy

98.1% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 25.0b

bsearch251.0ms

Steps
ItersRangePoint
9
2.6709615057091654e+53
2.2231678681159593e+61
1.3215559728644913e+55
9
-7.372830968500035e+71
-3.094580694806651e+64
-4.2640939686692966e+68

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04419
14419

end0.0ms

sample683.0ms

Algorithm
intervals
Results
502.0ms8005×body80valid