Details

sample74.0ms

Algorithm

intervals

Results

38.0ms

256×

body

valid

simplify636.0ms

Counts: 1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
0.1b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
23.2b	(/ (* (- 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))

rewrite389.0ms

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×	`frac-times` `prod-exp` `cbrt-unprod` `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 → 91

Calls

4 calls:

83.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
60.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
27.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
213.0ms	(/ (* (- 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))

series609.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
63.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
103.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
373.0ms	(/ (* (- 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))

simplify1.4s

Counts: 103 → 103

prune855.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

8.2b	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
11.8b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
12.0b	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))) (/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))))
19.7b	(/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
108×	`times-frac`
95×	`*-un-lft-identity`
69×	`add-cube-cbrt`
63×	`sqrt-prod`
61×	`associate-*l/`
60×	`frac-add`
42×	`associate-l`
40×	`sqrt-div`
32×	`associate-/r/`
30×	`associate-r`
21×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
9×	`unswap-sqr`
8×	`associate-/l*`
7×	`pow1`
6×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `-commutative` `flip--`

Counts

4 → 235

Calls

4 calls:

113.0ms	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
136.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
681.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))) (/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))))
264.0ms	(/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))

series992.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
130.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
340.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))) (/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))))
444.0ms	(/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))

simplify878.0ms

Counts: 247 → 247

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

11.7b	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
11.7b	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
11.8b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
17.9b	(* (/ (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))) (/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

795×	`times-frac`
656×	`sqrt-prod`
622×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
390×	`associate-l`
326×	`add-cube-cbrt`
169×	`associate-*l/`
168×	`frac-add`
144×	`sqrt-div`
96×	`associate-/r/`
61×	`distribute-lft-out--` `difference-of-squares`
56×	`flip3-+` `flip-+`
40×	`unswap-sqr`
39×	`associate-r`
27×	`add-exp-log` `add-cbrt-cube`
12×	`div-inv`
10×	`pow1` `cbrt-undiv` `div-exp`
8×	`sqrt-pow1`
6×	`prod-exp` `associate-/r*` `cbrt-unprod`
5×	`associate-/l*`
4×	`rem-sqrt-square` `pow1/2` `add-log-exp`
2×	`associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

4 → 611

Calls

4 calls:

110.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
104.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
117.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
1.0s	(* (/ (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))) (/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))))

series897.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
189.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
177.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
373.0ms	(* (/ (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))) (/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))))

simplify2.1s

Counts: 623 → 623

prune6.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize109.0ms

Local error

Found 4 expressions with local error:

15.6b	(cbrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
15.6b	(cbrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
15.6b	(cbrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
19.7b	(/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))

rewrite465.0ms

Algorithm

rewrite-expression-head

Rules

48×	`associate-*l/` `frac-add`
24×	`cbrt-div`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
17×	`flip3-+` `flip-+`
12×	`sqrt-prod`
9×	`cbrt-prod`
8×	`sqrt-div` `associate-/r/`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/l*`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 106

Calls

4 calls:

63.0ms	(cbrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
95.0ms	(cbrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
61.0ms	(cbrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
236.0ms	(/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))

series965.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
171.0ms	(cbrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
170.0ms	(cbrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
477.0ms	(/ (+ (* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))

simplify1.2s

Counts: 118 → 118

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes542.0ms

Accuracy

95.6% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 24.4b

bsearch483.0ms

Steps

Iters	Range		Point
7	1.7856564911545559e+27	1.2079217355322146e+29	1.445684426618435e+28
9	-1.6853749013735252e+30	-5.452804783141298e+22	-2.2521013600981868e+24

simplify954.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.7s

8005×

body

valid