Details

Time bar (total: 18.0s)

sample38.0ms

Algorithm
intervals
Results
19.0ms256×body80valid

simplify43.0ms

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: 26.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
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)))
25.6b
(/ (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))

rewrite36.0ms

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 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
24.0ms
(/ (- 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)))
5.0ms
(/ (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))

series549.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
287.0ms
(/ (- 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)))
179.0ms
(/ (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))

simplify87.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06752788
126402653
250012651

prune804.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize23.0ms

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))
0.3b
(/ 1 (/ (/ (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)))
25.6b
(/ (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))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
781×times-frac
468×add-sqr-sqrt *-un-lft-identity
336×add-cube-cbrt
79×associate-/r*
66×distribute-lft-out-- difference-of-squares
33×div-inv
32×add-exp-log
20×add-cbrt-cube
19×div-exp associate-/l*
11×associate-/r/
10×cbrt-undiv
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp frac-2neg 1-exp clear-num
1×pow-flip fma-udef associate-/l/ inv-pow
Counts
4 → 455
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))
34.0ms
(/ 1 (/ (/ (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)))
5.0ms
(/ (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))

series719.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
213.0ms
(/ (/ (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))
292.0ms
(/ 1 (/ (/ (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)))
187.0ms
(/ (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))

simplify141.0ms

Algorithm
egg-herbie
Counts
467 → 467
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0145110296
150019688

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

8.4b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
8.4b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
23.7b
(* (/ (cbrt 1) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt 1))) (/ (cbrt 1) (/ (/ (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)) (- x 2.0))))
25.5b
(/ (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))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
3471×times-frac
2695×add-sqr-sqrt
1534×*-un-lft-identity
1090×cbrt-prod
1013×add-cube-cbrt
701×associate-*r*
579×sqrt-prod
286×unswap-sqr
245×associate-*l*
132×distribute-lft-out-- difference-of-squares
60×add-exp-log
45×div-inv
39×add-cbrt-cube
31×cbrt-undiv div-exp
14×associate-/r/
12×prod-exp cbrt-unprod
8×pow1
6×flip3-- flip-- associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 1341
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
2.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
2.0s
(* (/ (cbrt 1) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt 1))) (/ (cbrt 1) (/ (/ (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)) (- x 2.0))))
7.0ms
(/ (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))

series790.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
100.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
291.0ms
(* (/ (cbrt 1) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt 1))) (/ (cbrt 1) (/ (/ (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)) (- x 2.0))))
299.0ms
(/ (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))

simplify429.0ms

Algorithm
egg-herbie
Counts
1353 → 1353
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0500144491

prune7.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.0b
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b
(* (+ (* x 4.16438922228) 78.6994924154) x)
27.1b
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
10×pow1
9×associate-*r* associate-*l*
8×associate-*l/ associate-/l/
7×flip3-+ flip-+
4×expm1-log1p-u frac-times prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×flip3-- times-frac pow-prod-down associate-/r* *-commutative flip-- unswap-sqr
2×cbrt-undiv associate-*r/ div-exp associate-/r/
1×frac-2neg clear-num div-inv associate-/l*
Counts
4 → 99
Calls
4 calls:
52.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
41.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
26.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
147.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series383.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
35.0ms
(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
65.0ms
(* (+ (* x 4.16438922228) 78.6994924154) x)
240.0ms
(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify86.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06981112
13276939
25001915

prune507.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes308.0ms

Accuracy

96.8% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 24.4b

bsearch197.0ms

Steps
ItersRangePoint
10
3.095505661370574e+39
1.807849191685867e+49
1.421341501142409e+43
5
-5.073855505099906e+33
-1.9049013017617822e+33
-4.892908567716605e+33

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04216
14216

end0.0ms

sample725.0ms

Algorithm
intervals
Results
488.0ms8008×body80valid