Details

sample57.0ms

Algorithm

intervals

Results

11.0ms	66×	body	640	valid
10.0ms	282×	body	80	nan
10.0ms	42×	body	1280	valid
5.0ms	116×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.1b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite230.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `hypot-def` `flip--`

Counts

4 → 758

Calls

4 calls:

12.0ms	(sqrt (+ x 1.0))
13.0ms	(/ 1.0 (sqrt (+ x 1.0)))
5.0ms	(/ 1.0 (sqrt x))
106.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (+ x 1.0))
105.0ms	(/ 1.0 (sqrt (+ x 1.0)))
52.0ms	(/ 1.0 (sqrt x))
204.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.2s

Counts

770 → 770

Iterations

Iter	Nodes
done	5000
2	4935
1	1587
0	702

prune2.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

9.0ms	(sqrt (+ x 1.0))
66.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt (+ x 1.0)) (sqrt x)))
20.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
14.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series628.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ x 1.0))
345.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt (+ x 1.0)) (sqrt x)))
89.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
153.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.3s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	2941
1	586
0	208

prune495.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ (/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt (+ x 1.0)) (sqrt x))
2.2b	(fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
22×	`add-sqr-sqrt`
18×	`times-frac`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp` `associate-/l*`
11×	`sqrt-prod`
8×	`pow1` `associate-/r/`
7×	`associate-l` `prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-*r/`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `sqrt-div` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down`
2×	`clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`sqrt-unprod` `*-commutative` `fma-udef` `distribute-lft-out` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

24.0ms	(/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
53.0ms	(/ (/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
41.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

296.0ms	(/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
693.0ms	(/ (/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
60.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
72.0ms	(fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0))))

simplify1.5s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	4071
1	739
0	263

prune681.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

28.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
25.0ms	(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
39.0ms	(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
24.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

series842.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
157.0ms	(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
540.0ms	(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
68.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

simplify1.3s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	4350
1	760
0	271

prune533.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	14
1	14
0	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

433.0ms	8079×	body	80	nan
367.0ms	659×	body	320	valid
293.0ms	1837×	body	640	valid
190.0ms	1103×	body	1280	valid
176.0ms	4114×	body	80	valid
20.0ms	287×	body	160	valid