Details

sample43.0ms

Algorithm

intervals

Results

8.0ms	62×	body	640	valid
6.0ms	39×	body	1280	valid
6.0ms	211×	body	80	nan
4.0ms	132×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	7×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize57.0ms

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))
2.1b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite456.0ms

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` `insert-posit16` `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 → 762

Calls

4 calls:

11.0ms	(sqrt (+ x 1.0))
26.0ms	(/ 1.0 (sqrt (+ x 1.0)))
17.0ms	(/ 1.0 (sqrt x))
185.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ x 1.0))
101.0ms	(/ 1.0 (sqrt (+ x 1.0)))
59.0ms	(/ 1.0 (sqrt x))
208.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify5.1s

Counts

774 → 774

Iterations

Iter	Nodes
done	5000
2	3569
1	1591
0	706

prune5.5s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 18.0b

localize201.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
0.3b	(/ 1.0 (sqrt (sqrt x)))
0.4b	(/ (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt x)))
10.0b	(- (/ (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt x))) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))

rewrite491.0ms

Algorithm

rewrite-expression-head

Rules

870×	`sqrt-prod`
591×	`add-sqr-sqrt`
546×	`times-frac`
344×	`*-un-lft-identity`
240×	`add-cube-cbrt`
150×	`swap-sqr`
66×	`associate-r` `associate-l`
49×	`unswap-sqr`
44×	`distribute-lft-out`
32×	`add-exp-log`
27×	`add-cbrt-cube`
18×	`associate-/r*`
16×	`sqrt-div`
13×	`fma-neg` `prod-diff`
12×	`div-exp`
11×	`pow1`
9×	`cbrt-undiv`
8×	`prod-exp` `associate-/r/` `div-inv`
6×	`cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-undiv` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-*r/` `frac-sub`
2×	`frac-times` `clear-num` `frac-2neg` `1-exp` `associate-*l/`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `sqrt-unprod` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `difference-of-squares` `associate-/l/`

Counts

4 → 500

Calls

4 calls:

235.0ms	(* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
11.0ms	(/ 1.0 (sqrt (sqrt x)))
33.0ms	(/ (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt x)))
78.0ms	(- (/ (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt x))) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))

series851.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
275.0ms	(/ 1.0 (sqrt (sqrt x)))
61.0ms	(/ (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt x)))
325.0ms	(- (/ (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt x))) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))

simplify7.1s

Counts

512 → 512

Iterations

Iter	Nodes
done	5000
2	4631
1	1626
0	533

prune4.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.0b

localize422.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
0.3b	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
0.3b	(/ 1.0 (sqrt (sqrt x)))
2.1b	(- (* (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (sqrt 1.0))))

rewrite597.0ms

Algorithm

rewrite-expression-head

Rules

872×	`sqrt-prod`
600×	`add-sqr-sqrt`
519×	`times-frac`
338×	`*-un-lft-identity`
232×	`add-cube-cbrt`
150×	`swap-sqr`
76×	`associate-r`
75×	`associate-l`
58×	`unswap-sqr`
45×	`distribute-lft-out`
28×	`sqrt-div`
20×	`add-cbrt-cube` `add-exp-log`
17×	`pow1`
13×	`associate-*r/`
9×	`associate-/r*`
8×	`sqrt-pow1` `associate-/r/`
7×	`flip3-+` `associate-*l/` `flip-+`
6×	`pow-prod-down` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `frac-sub` `cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `sqrt-undiv` `pow1/2` `insert-posit16` `log1p-expm1-u`
3×	`frac-times` `associate-/l*`
2×	`sqrt-unprod` `*-commutative`
1×	`pow2` `clear-num` `sub-neg` `rem-square-sqrt` `frac-2neg` `pow-plus` `flip3--` `fma-neg` `diff-log` `prod-diff` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 485

Calls

4 calls:

245.0ms	(* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
76.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
11.0ms	(/ 1.0 (sqrt (sqrt x)))
138.0ms	(- (* (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (sqrt 1.0))))

series1.6s

Counts

4 → 12

Calls

4 calls:

219.0ms	(* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
229.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
300.0ms	(/ 1.0 (sqrt (sqrt x)))
832.0ms	(- (* (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (sqrt 1.0))))

simplify4.1s

Counts

497 → 497

Iterations

Iter	Nodes
done	5004
1	1875
0	605

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.7b

localize283.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt (sqrt x)))
0.3b	(/ 1.0 (sqrt (sqrt x)))
2.1b	(- (* (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (sqrt 1.0))))
2.1b	(- (* (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (sqrt 1.0))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
54×	`times-frac`
48×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
20×	`associate-*r/`
18×	`associate-/r*`
16×	`sqrt-div`
12×	`associate-*l/`
10×	`frac-sub`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`associate-/l*`
4×	`expm1-log1p-u` `frac-times` `pow1` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `fma-neg` `diff-log` `div-exp` `prod-diff` `div-inv` `flip--`

Counts

4 → 152

Calls

4 calls:

10.0ms	(/ 1.0 (sqrt (sqrt x)))
10.0ms	(/ 1.0 (sqrt (sqrt x)))
86.0ms	(- (* (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (sqrt 1.0))))
87.0ms	(- (* (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (sqrt 1.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ 1.0 (sqrt (sqrt x)))
214.0ms	(/ 1.0 (sqrt (sqrt x)))
554.0ms	(- (* (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (sqrt 1.0))))
552.0ms	(- (* (* 1 (/ 1.0 (sqrt (sqrt x)))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (* (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))) (sqrt 1.0))))

simplify3.3s

Counts

164 → 164

Iterations

Iter	Nodes
done	5004
2	2544
1	790
0	299

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.7b

regimes185.0ms

Accuracy

89.3% (0.3b remaining)

Error of 17.3b against oracle of 16.9b and baseline of 20.2b

bsearch88.0ms

Steps

Iters	Range		Point
9	0.17679972651571432	94859.26993337883	83896.2390210144

simplify28.0ms

Iterations

Iter	Nodes
done	67
2	67
1	60
0	43

end0.0ms

sample1.8s

Algorithm

intervals

Results

468.0ms	4064×	body	80	valid
428.0ms	7974×	body	80	nan
272.0ms	1873×	body	640	valid
185.0ms	1119×	body	1280	valid
87.0ms	619×	body	320	valid
21.0ms	325×	body	160	valid