Details

sample50.0ms

Algorithm

intervals

Results

35.0ms

256×

body

valid

simplify6.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
12	4530
11	2981
10	1941
9	1327
8	935
7	744
6	622
5	489
4	295
3	139
2	62
1	35
0	18

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.3b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.7b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
5×	`flip3-+` `flip-+`
4×	`associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 92

Calls

4 calls:

14.0ms	(* (+ z 6.012459259764103) z)
26.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
50.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
65.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series513.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (+ z 6.012459259764103) z)
121.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
100.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
182.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.9s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
2	2021
1	560
0	196

prune675.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize76.0ms

Local error

Found 4 expressions with local error:

8.3b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`*-un-lft-identity` `add-cube-cbrt`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube` `add-exp-log`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 154

Calls

4 calls:

149.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
13.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
11.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
59.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
111.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
91.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
160.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.9s

Counts

166 → 166

Iterations

Iter	Nodes
done	5001
2	2599
1	748
0	261

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 92

Calls

4 calls:

25.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
23.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
24.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
96.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
110.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
81.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
236.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.8s

Counts

104 → 104

Iterations

Iter	Nodes
done	5002
3	3856
2	1072
1	367
0	157

prune944.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ (* y 0.07512208616047561) z) (/ (* y 0.40462203869992125) (* z z))) (* y 0.0692910599291889))
0.2b	(/ (* y 0.07512208616047561) z)
3.9b	(- (/ (* y 0.07512208616047561) z) (/ (* y 0.40462203869992125) (* z z)))
5.0b	(/ (* y 0.40462203869992125) (* z z))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-cbrt-cube` `add-exp-log`
11×	`add-log-exp`
8×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`cbrt-undiv` `div-exp` `add-cube-cbrt`
5×	`prod-exp` `cbrt-unprod`
4×	`pow1` `associate-/r*` `times-frac` `insert-posit16`
2×	`associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-inv` `associate-/l*`
1×	`+-commutative` `flip3-+` `flip3--` `frac-sub` `associate-+l-` `flip-+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

87.0ms	(+ (- (/ (* y 0.07512208616047561) z) (/ (* y 0.40462203869992125) (* z z))) (* y 0.0692910599291889))
20.0ms	(/ (* y 0.07512208616047561) z)
14.0ms	(- (/ (* y 0.07512208616047561) z) (/ (* y 0.40462203869992125) (* z z)))
12.0ms	(/ (* y 0.40462203869992125) (* z z))

series322.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (- (/ (* y 0.07512208616047561) z) (/ (* y 0.40462203869992125) (* z z))) (* y 0.0692910599291889))
35.0ms	(/ (* y 0.07512208616047561) z)
124.0ms	(- (/ (* y 0.07512208616047561) z) (/ (* y 0.40462203869992125) (* z z)))
50.0ms	(/ (* y 0.40462203869992125) (* z z))

simplify1.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5006
2	1834
1	429
0	151

prune526.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes374.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.1b

bsearch245.0ms

Steps

Iters	Range		Point
8	315.1021581913647	2484744.5477507794	727958.1035308853
5	-670394737327.6124	-271299687514.82303	-273974326636.0899

simplify8.0ms

Iterations

Iter	Nodes
done	52
1	52
0	35

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

8000×

body

valid