Details

Time bar (total: 10.2s)

sample32.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06211
115411
250311
3184011
4500311

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.0b
(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))

rewrite20.0ms

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))

series543.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
31.0ms
(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)))
176.0ms
(/ (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))

simplify295.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06772773
126212640
250012638

prune763.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
16.6b
(/ (- (* 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))

rewrite26.0ms

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:
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
8.0ms
(* (/ (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))
11.0ms
(/ (- (* 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)))
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))

series728.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
202.0ms
(* (/ (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))
329.0ms
(/ (- (* 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)))
173.0ms
(/ (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))

simplify86.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06371806
129921563
250021561

prune615.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

5.8b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
15.7b
(/ (/ (- 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)))
16.5b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
23.5b
(/ (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))

rewrite139.0ms

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:
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
28.0ms
(/ (/ (- 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)))
10.0ms
(/ (- 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))

series839.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
289.0ms
(/ (/ (- 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)))
159.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
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))

simplify414.0ms

Algorithm
egg-herbie
Counts
953 → 953
Iterations

Useful iterations: 1 (52.0ms)

IterNodesCost
0310433067
1500232246

prune3.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

5.8b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
5.8b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
16.5b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
20.8b
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (* (/ (- x 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)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
52×*-un-lft-identity
48×times-frac
45×add-exp-log
38×add-cube-cbrt
33×sqrt-prod
27×add-cbrt-cube
22×associate-*l*
20×prod-exp
11×pow1 div-exp
10×cbrt-unprod
7×distribute-lft-out-- difference-of-squares
6×cbrt-undiv associate-/r*
5×associate-/l*
4×distribute-rgt-in expm1-log1p-u distribute-lft-in fma-udef log1p-expm1-u add-log-exp
3×rec-exp 1-exp pow-prod-down associate-*l/
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv associate-/l/
1×frac-times flip3-- frac-2neg div-sub associate-*r/ associate-*r* clear-num *-commutative flip--
Counts
4 → 148
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))
7.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
15.0ms
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (* (/ (- x 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)))

series634.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
97.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
153.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
283.0ms
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (* (/ (- x 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)))

simplify90.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07132521
132812123
250011946

prune636.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes260.0ms

Accuracy

96.4% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 24.8b

bsearch273.0ms

Steps
ItersRangePoint
9
4.77799814363719e+45
1.0469598397755e+53
9.452827926980448e+52
10
-5.651135004763443e+21
-1608183693.8472729
-5.554983803297941e+21

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04419
14419

end0.0ms

sample652.0ms

Algorithm
intervals
Results
485.0ms8009×body80valid