Details

sample80.0ms

Algorithm

intervals

Results

18.0ms	68×	body	640	valid
14.0ms	256×	body	80	nan
10.0ms	30×	body	1280	valid
8.0ms	123×	body	80	valid
5.0ms	26×	body	320	valid
1.0ms	9×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
3.0b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite464.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--` `hypot-def`

Counts

4 → 758

Calls

4 calls:

15.0ms	(sqrt (+ x 1.0))
26.0ms	(/ 1.0 (sqrt (+ x 1.0)))
13.0ms	(/ 1.0 (sqrt x))
216.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

216.0ms	(sqrt (+ x 1.0))
191.0ms	(/ 1.0 (sqrt (+ x 1.0)))
205.0ms	(/ 1.0 (sqrt x))
534.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify8.5s

Counts

770 → 770

Iterations

Iter	Nodes
done	5000
2	3590
1	1585
0	701

prune6.1s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 22.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
3.1b	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `sqrt-prod`
11×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
9×	`pow1`
7×	`associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `times-frac` `pow1/2` `pow-prod-down` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `fma-neg` `sqrt-unprod` `diff-log` `div-sub` `prod-diff` `clear-num` `associate-/r` `-commutative` `hypot-def` `div-inv`

Counts

4 → 98

Calls

4 calls:

16.0ms	(sqrt (+ x 1.0))
93.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
62.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
39.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series813.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ x 1.0))
485.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
105.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
173.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify2.9s

Counts

110 → 110

Iterations

Iter	Nodes
done	5034
2	2174
1	586
0	204

prune1.1s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 22.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
0.3b	(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
0.5b	(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
2.4b	(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

86×	`pow1`
37×	`pow-prod-down`
30×	`add-exp-log` `add-cbrt-cube`
17×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt` `associate-*r/`
14×	`sqrt-div`
11×	`sqrt-prod`
10×	`*-un-lft-identity`
9×	`associate-r`
8×	`add-cube-cbrt` `associate-l` `pow-sqr` `pow-prod-up`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`expm1-log1p-u` `frac-times` `pow-plus` `log1p-expm1-u` `unswap-sqr`
3×	`*-commutative`
2×	`pow2` `sqrt-pow1` `pow1/2` `swap-sqr` `associate-*l/`
1×	`sub-neg` `flip3--` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

4 → 132

Calls

4 calls:

54.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
126.0ms	(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
81.0ms	(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
200.0ms	(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
74.0ms	(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
54.0ms	(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
34.0ms	(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

simplify3.2s

Counts

144 → 144

Iterations

Iter	Nodes
done	5003
2	1528
1	502
0	185

prune999.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
0.2b	(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
0.6b	(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

rewrite402.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
18×	`associate-*r/`
14×	`flip3-+` `sqrt-div` `flip-+`
13×	`pow1` `*-un-lft-identity`
11×	`add-cube-cbrt` `sqrt-prod`
10×	`associate-r`
8×	`frac-times` `associate-/r/`
7×	`associate-l` `prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `unswap-sqr`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `*-commutative`
1×	`+-commutative` `distribute-rgt-in` `fma-def` `frac-2neg` `distribute-lft-in` `sqrt-unprod` `clear-num` `associate-/r*` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 112

Calls

4 calls:

32.0ms	(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
172.0ms	(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
55.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
133.0ms	(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

series1.9s

Counts

4 → 12

Calls

4 calls:

199.0ms	(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
521.0ms	(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
97.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.1s	(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

simplify5.2s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	3362
1	853
0	273

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes177.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	12

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	1828×	body	640	valid
730.0ms	1098×	body	1280	valid
496.0ms	7895×	body	80	nan
311.0ms	4133×	body	80	valid
257.0ms	621×	body	320	valid
57.0ms	320×	body	160	valid