Details

sample42.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify38.0ms

Counts: 1 → 1

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize43.0ms

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) 137.519416416) x) y) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
24.2b	(/ (* (- 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))

rewrite498.0ms

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:

79.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
153.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
45.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
217.0ms	(/ (* (- 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))

series583.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
93.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
89.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
350.0ms	(/ (* (- 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))

simplify93.0ms

Counts: 103 → 103

prune897.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x)
0.1b	(* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x)
0.3b	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ 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)))
22.5b	(/ (+ (* (+ (* (+ (* (+ 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))

rewrite742.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 191

Calls

4 calls:

156.0ms	(* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x)
75.0ms	(* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x)
238.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ 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)))
260.0ms	(/ (+ (* (+ (* (+ (* (+ 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))

series731.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (+ (* (+ (* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x) (/ 604816789577447.0 4398046511104.0)) x) y) x)
90.0ms	(* (+ (* x (/ 4688685437421479.0 1125899906842624.0)) (/ 5537984448691291.0 70368744177664.0)) x)
381.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ 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)))
176.0ms	(/ (+ (* (+ (* (+ (* (+ 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))

simplify187.0ms

Counts: 203 → 203

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
7.5b	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
13.9b	(* (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))) (/ (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)))
22.4b	(/ (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))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

68×	`associate-*l/`
60×	`frac-add`
54×	`add-sqr-sqrt`
40×	`times-frac` `sqrt-div`
36×	`add-cube-cbrt` `*-un-lft-identity`
35×	`sqrt-prod`
24×	`associate-r`
22×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `frac-times` `associate-/l/`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`associate-/r/` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 157

Calls

4 calls:

105.0ms	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
100.0ms	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
710.0ms	(* (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))) (/ (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)))
239.0ms	(/ (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))

series703.0ms

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)))
101.0ms	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
187.0ms	(* (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))) (/ (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)))
338.0ms	(/ (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))

simplify138.0ms

Counts: 169 → 169

prune2.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
13.1b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
13.3b	(* (/ (- 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)))))
19.8b	(/ (+ (* (+ (* (+ (* (+ (* 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))))

rewrite1.1s

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:

115.0ms	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
138.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
659.0ms	(* (/ (- 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)))))
216.0ms	(/ (+ (* (+ (* (+ (* (+ (* 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))))

series1.0s

Counts

4 → 12

Calls

4 calls:

98.0ms	(sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0)))
160.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x (/ 6099563062176297.0 140737488355328.0)) x) (/ 1158907574534893.0 4398046511104.0)) x) (/ 172293041005667.0 549755813888.0)) x) (/ 6624073998258585.0 140737488355328.0))))
327.0ms	(* (/ (- 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)))))
443.0ms	(/ (+ (* (+ (* (+ (* (+ (* 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))))

simplify129.0ms

Counts: 247 → 247

prune2.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes380.0ms

Accuracy

97.5% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 25.2b

bsearch512.0ms

Steps

Iters	Range		Point
10	2.6969245666033035e+35	4.264445276026206e+51	4.185814178876574e+51
9	-5.504247016617868e+37	-3.1641101034949086e+31	-4.1468195884167556e+37

simplify34.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.3s

8011×

body

valid