Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	82×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`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×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `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` `hypot-def` `div-inv`

Counts

3 → 71

Calls

3 calls:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
17.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series227.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(+ 1.0 (sqrt (+ x 1.0)))
30.0ms	(sqrt (+ x 1.0))
148.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify613.0ms

Counts

80 → 80

Iterations

Useful iterations: done (611.0ms)

Iter	Nodes	Cost
0	146	959
1	342	886
2	1244	819
done	5001	812

prune152.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
2.7b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.6b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite112.0ms

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×	`expm1-log1p-u` `sum-cubes` `log1p-expm1-u` `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` `fma-neg` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 194

Calls

4 calls:

23.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms	(pow (sqrt (+ x 1.0)) 3)
14.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
60.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
79.0ms	(pow (sqrt (+ x 1.0)) 3)
66.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
196.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify2.0s

Counts

206 → 206

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	326	4145
1	817	2999
2	3828	2729
done	5001	2725

prune447.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
2.7b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
2.7b	(- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-div`
49×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
35×	`flip3-+` `flip-+`
32×	`associate-*r/`
26×	`sqrt-prod`
23×	`add-cube-cbrt`
20×	`frac-sub`
19×	`pow1`
12×	`frac-times` `times-frac` `distribute-lft-out`
11×	`swap-sqr` `add-log-exp`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-*l/` `add-cbrt-cube`
7×	`associate-r` `associate-l`
5×	`fma-neg` `prod-diff` `pow-prod-up`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`diff-log` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`sub-neg` `flip3--` `distribute-rgt-out--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `associate--l+` `clear-num` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 165

Calls

4 calls:

17.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
21.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
13.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
26.0ms	(- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
68.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
67.0ms	(- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0))))

simplify1.1s

Counts

177 → 177

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	306	3750
1	749	2794
2	2751	2496
done	5001	2494

prune469.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
52×	`times-frac`
40×	`add-cube-cbrt`
39×	`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×	`expm1-log1p-u` `flip3-+` `associate-/r*` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def`
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` `hypot-def`

Counts

4 → 144

Calls

4 calls:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
18.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
50.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ 1.0 (sqrt (+ x 1.0)))
30.0ms	(sqrt (+ x 1.0))
312.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
143.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify730.0ms

Counts

156 → 156

Iterations

Useful iterations: done (725.0ms)

Iter	Nodes	Cost
0	224	2373
1	562	2097
2	2207	1913
done	5000	1902

prune286.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	45
1	25	45
done	25	45

end0.0ms

sample304.0ms

Algorithm

intervals

Results

151.0ms	7997×	body	80	valid
43.0ms	2656×	body	80	nan
0.0ms	3×	body	1280	valid