Details

sample54.0ms

Algorithm

intervals

Results

26.0ms

256×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1945
3	460
2	138
1	55
0	29

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
0.1b	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
25.1b	(/ (* (- 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))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
8×	`associate-*l/` `associate-/l/`
7×	`flip3-+` `flip-+`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/r` `times-frac` `flip3--` `pow-prod-down` `-commutative` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-*r/` `associate-/r/`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

64.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
36.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
21.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
118.0ms	(/ (* (- 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))

series480.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
49.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
76.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
294.0ms	(/ (* (- 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))

simplify2.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	4176
1	677
0	225

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.3b	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
23.2b	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite400.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
110×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
74×	`add-cube-cbrt`
18×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
10×	`flip3-+` `flip-+`
8×	`pow1` `div-inv` `associate-/l*`
6×	`associate-r` `associate-l`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 184

Calls

4 calls:

45.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
30.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
157.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
161.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series697.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
112.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
344.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
184.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify2.5s

Counts

196 → 196

Iterations

Iter	Nodes
done	5000
1	1058
0	344

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize137.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
7.0b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
15.1b	(/ (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
20.2b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite451.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
30×	`associate-/r*`
22×	`sqrt-div`
17×	`associate-/r/`
12×	`flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv` `associate-/l*`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 264

Calls

4 calls:

63.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
42.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
209.0ms	(/ (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
121.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series915.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
124.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
195.0ms	(/ (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
494.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify2.8s

Counts

276 → 276

Iterations

Iter	Nodes
done	5000
1	925
0	360

prune2.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

localize97.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.2b	(* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x))
17.2b	(/ (* (- (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (* 263.505074721 263.505074721)) x) (- (* (+ x 43.3400022514) x) 263.505074721))
25.1b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (/ (* (- (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (* 263.505074721 263.505074721)) x) (- (* (+ x 43.3400022514) x) 263.505074721)) 313.399215894) x) 47.066876606))

rewrite609.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
28×	`add-cbrt-cube` `add-exp-log`
20×	`associate-*l/`
18×	`pow-prod-down`
12×	`add-sqr-sqrt`
11×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
10×	`*-un-lft-identity` `add-cube-cbrt` `associate-/l/`
8×	`frac-times`
6×	`associate-/r*` `times-frac`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `associate-*r/` `associate-/r/` `pow-sqr` `pow-prod-up` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-plus` `-commutative` `div-inv` `associate-/l`
1×	`pow2` `swap-sqr` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

21.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
83.0ms	(* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x))
109.0ms	(/ (* (- (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (* 263.505074721 263.505074721)) x) (- (* (+ x 43.3400022514) x) 263.505074721))
390.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (/ (* (- (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (* 263.505074721 263.505074721)) x) (- (* (+ x 43.3400022514) x) 263.505074721)) 313.399215894) x) 47.066876606))

series1.4s

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
33.0ms	(* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x))
136.0ms	(/ (* (- (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (* 263.505074721 263.505074721)) x) (- (* (+ x 43.3400022514) x) 263.505074721))
1.2s	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (/ (* (- (* (* (+ x 43.3400022514) x) (* (+ x 43.3400022514) x)) (* 263.505074721 263.505074721)) x) (- (* (+ x 43.3400022514) x) 263.505074721)) 313.399215894) x) 47.066876606))

simplify1.8s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
1	885
0	277

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

regimes591.0ms

Accuracy

97.7% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 24.4b

bsearch324.0ms

Steps

Iters	Range		Point
6	2.915474134638951e+52	3.0455316621450604e+53	1.8497151307659583e+53
7	-3.5539660008838154e+52	-7.123290046831777e+50	-1.486655794493064e+52

simplify10.0ms

Iterations

Iter	Nodes
done	59
1	59
0	41

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s

8007×

body

valid