Details

sample17.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
1.0ms	80×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
done	8	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

16.0ms	(+ 1.0 (sqrt (+ x 1.0)))
31.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series185.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
144.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.6s

Counts

51 → 51

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	117	739
1	277	693
2	831	636
3	3565	630
done	5000	628

prune99.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

38.0ms	(/ x (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
14.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
16.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
14.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

series4.7s

Counts

4 → 12

Calls

4 calls:

4.0s	(/ x (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
246.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
242.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
230.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

simplify888.0ms

Counts

83 → 83

Iterations

Useful iterations: done (885.0ms)

Iter	Nodes	Cost
0	224	2052
1	591	1888
2	2078	1654
done	5001	1559

prune231.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.4b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.1b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`sum-cubes` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

10.0ms	(pow (sqrt (+ x 1.0)) 3)
39.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
29.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
88.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(pow (sqrt (+ x 1.0)) 3)
19.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
67.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
198.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify1.4s

Counts

196 → 196

Iterations

Useful iterations: 2 (462.0ms)

Iter	Nodes	Cost
0	313	4015
1	746	2931
2	2736	2700
done	5001	2700

prune424.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.4b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.1b	(/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) x)

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `associate-/l*`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`sum-cubes` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `associate-/r*` `pow-sqr`
2×	`cube-div` `associate-/l/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

10.0ms	(pow (sqrt (+ x 1.0)) 3)
39.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
27.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
137.0ms	(/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) x)

series277.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (sqrt (+ x 1.0)) 3)
18.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
67.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
124.0ms	(/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) x)

simplify1.4s

Counts

196 → 196

Iterations

Useful iterations: 2 (426.0ms)

Iter	Nodes	Cost
0	301	3995
1	715	2957
2	2537	2721
done	5001	2721

prune425.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

99.2% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.9b

bsearch32.0ms

Steps

Iters	Range		Point
8	1126179.5725289274	335341194.4438158	28329089.96762624

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	49
1	29	49
done	29	49

end0.0ms

sample354.0ms

Algorithm

intervals

Results

156.0ms	7994×	body	80	valid
42.0ms	2681×	body	80	nan
1.0ms	6×	body	1280	valid