Details

Time bar (total: 36.4s)

sample48.0ms

Algorithm
intervals
Results
24.0ms258×body80valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5000
42165
3512
2154
162
029

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z)
0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
3.0b
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
20.8b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
104×add-sqr-sqrt *-un-lft-identity
72×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×add-cbrt-cube add-exp-log associate-/r/
6×div-inv associate-/l*
5×flip3-- flip--
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef
Counts
4 → 163
Calls
4 calls:
0.0ms
(fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z)
0.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
19.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
13.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

series684.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z)
47.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
122.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
387.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

simplify2.4s

Counts
175 → 175
Iterations
IterNodes
done5000
23550
1700
0293

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.1b
(fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z)
0.1b
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (- x 2.0)))
20.8b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
690×times-frac
376×add-sqr-sqrt *-un-lft-identity
292×add-cube-cbrt
42×distribute-lft-out-- difference-of-squares
38×div-inv
29×associate-/r/
28×add-exp-log
24×associate-/r*
18×add-cbrt-cube
17×div-exp
16×associate-/l*
14×flip3-- flip--
9×cbrt-undiv
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
2×rec-exp clear-num frac-2neg 1-exp fma-udef
1×associate-/l/
Counts
4 → 382
Calls
4 calls:
0.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.0ms
(fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z)
21.0ms
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (- x 2.0)))
4.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))

series1.0s

Counts
4 → 12
Calls
4 calls:
33.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
131.0ms
(fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z)
443.0ms
(/ (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (- x 2.0)))
395.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))

simplify2.3s

Counts
394 → 394
Iterations
IterNodes
done5001
12031
0642

prune3.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize101.0ms

Local error

Found 4 expressions with local error:

7.7b
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
7.7b
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
11.7b
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
17.1b
(* (/ 1 (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
475×times-frac
406×add-sqr-sqrt
261×*-un-lft-identity
175×add-cube-cbrt
123×sqrt-prod
114×add-exp-log
113×associate-*r*
71×associate-*l*
67×div-exp
44×unswap-sqr
42×add-cbrt-cube
30×prod-exp
25×distribute-lft-out-- difference-of-squares
19×cbrt-undiv
18×1-exp
10×associate-/r/
9×rec-exp cbrt-unprod div-inv
8×pow1
6×associate-/l*
5×associate-/r*
4×expm1-log1p-u flip3-- log1p-expm1-u flip-- add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 368
Calls
4 calls:
2.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
2.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
22.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
176.0ms
(* (/ 1 (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
155.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
142.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
267.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
485.0ms
(* (/ 1 (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))))

simplify2.3s

Counts
380 → 380
Iterations
IterNodes
done5001
11945
0551

prune3.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize74.0ms

Local error

Found 4 expressions with local error:

7.7b
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
11.7b
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
11.9b
(/ (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
18.4b
(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
2196×times-frac
1202×add-sqr-sqrt
1201×*-un-lft-identity
911×add-cube-cbrt
711×sqrt-prod
145×distribute-lft-out-- difference-of-squares
63×div-inv
49×associate-/r/
47×associate-/r*
31×associate-/l*
24×flip3-- flip--
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 985
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
17.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
78.0ms
(/ (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
9.0ms
(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

series1.4s

Counts
4 → 12
Calls
4 calls:
151.0ms
(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
218.0ms
(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
475.0ms
(/ (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
560.0ms
(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify4.0s

Counts
997 → 997
Iterations
IterNodes
done5000
14054
01103

prune7.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes377.0ms

Accuracy

95.6% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 25.1b

bsearch281.0ms

Steps
ItersRangePoint
9
488997712.5877659
631776370996477.2
620615997107907.6
3
-6.376815652518718e+28
-5.267362834597857e+28
-6.307474851398664e+28

simplify10.0ms

Iterations
IterNodes
done38
138
033

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.6s8010×body80valid