Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
4.0ms	93×	body	80	nan

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

26.0ms	(sqrt (+ x 1.0))
29.0ms	(+ 1.0 (sqrt (+ x 1.0)))
81.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series1.0s

Counts

3 → 9

Calls

3 calls:

51.0ms	(sqrt (+ x 1.0))
72.0ms	(+ 1.0 (sqrt (+ x 1.0)))
884.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	1095
1	326
0	140

prune480.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x)))))
0.1b	(* (+ 1.0 x) (sqrt (+ 1.0 x)))
0.2b	(/ x (+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))))
6.7b	(cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
14×	`flip3-+` `flip-+`
12×	`times-frac` `sqrt-div`
9×	`pow1`
8×	`add-exp-log` `frac-times` `cbrt-div` `add-cbrt-cube`
7×	`associate-r` `distribute-lft-out`
6×	`add-log-exp`
5×	`sqrt-prod`
4×	`associate-r/` `associate-l` `associate-l/` `associate-/r*`
3×	`associate-/l*`
2×	`pow3` `associate-/r/` `pow-prod-up` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `cbrt-prod` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `div-inv`

Counts

4 → 98

Calls

4 calls:

12.0ms	(+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x)))))
71.0ms	(* (+ 1.0 x) (sqrt (+ 1.0 x)))
27.0ms	(/ x (+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))))
30.0ms	(cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x)))))
107.0ms	(* (+ 1.0 x) (sqrt (+ 1.0 x)))
256.0ms	(/ x (+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))))
66.0ms	(cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))

simplify3.4s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1616
1	467
0	203

prune2.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))
0.2b	(/ x (cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
6.7b	(cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

88×	`frac-times`
87×	`flip3-+` `flip-+`
52×	`cbrt-div`
44×	`associate-*l/`
34×	`*-un-lft-identity`
30×	`pow1`
26×	`associate-*r/` `associate-/r/`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
13×	`add-exp-log`
12×	`times-frac` `add-cbrt-cube`
8×	`associate-r`
7×	`pow-plus` `pow-prod-up` `distribute-lft-out`
6×	`swap-sqr`
5×	`cbrt-prod` `associate-l`
4×	`pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
3×	`pow2` `pow-sqr` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `pow1/3` `div-exp` `clear-num` `rem-cbrt-cube` `div-inv`

Counts

4 → 190

Calls

4 calls:

724.0ms	(* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))
22.0ms	(/ x (cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))))
310.0ms	(* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
401.0ms	(cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

449.0ms	(* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))
471.0ms	(/ x (cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))))
190.0ms	(* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
417.0ms	(cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0)))))

simplify7.8s

Counts

202 → 202

Iterations

Iter	Nodes
done	5001
2	3359
1	888
0	310

prune2.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
39×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 132

Calls

4 calls:

19.0ms	(sqrt (+ x 1.0))
32.0ms	(+ 1.0 (sqrt (+ x 1.0)))
68.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
1.3s	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (+ x 1.0))
71.0ms	(+ 1.0 (sqrt (+ x 1.0)))
650.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
330.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify4.5s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1880
1	557
0	216

prune1.9s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes54.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 6.9b

bsearch264.0ms

Steps

Iters	Range		Point
8	87.84726908649233	263824.51516633737	1614.0612239232446

simplify38.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end3.0ms

sample2.7s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
664.0ms	2661×	body	80	nan