Details

sample31.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	79×	body	80	nan

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite71.0ms

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-cbrt-cube` `add-exp-log` `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` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

3 → 71

Calls

3 calls:

6.0ms	(sqrt (+ x 1.0))
19.0ms	(+ 1.0 (sqrt (+ x 1.0)))
44.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series284.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(sqrt (+ x 1.0))
55.0ms	(+ 1.0 (sqrt (+ x 1.0)))
197.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5003
2	1162
1	333
0	143

prune412.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.0b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.8b	(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
45×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`flip3-+` `flip-+`
30×	`associate-*r/`
28×	`add-cube-cbrt`
26×	`sqrt-prod`
21×	`pow1`
20×	`associate-l`
19×	`times-frac`
16×	`frac-sub`
14×	`frac-times`
13×	`add-cbrt-cube` `add-exp-log`
11×	`swap-sqr`
10×	`associate-r`
9×	`associate-*l/`
8×	`sqrt-pow1` `pow1/2`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `sub-div`
3×	`associate-/r` `prod-exp` `pow-sqr` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `div-exp` `*-commutative` `div-inv`
1×	`pow2` `distribute-rgt-in` `clear-num` `sub-neg` `rem-square-sqrt` `frac-2neg` `distribute-lft-in` `pow-plus` `flip3--` `distribute-rgt-out--` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff` `flip--`

Counts

4 → 170

Calls

4 calls:

205.0ms	(* (/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
36.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
51.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.0ms	(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

751.0ms	(* (/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
23.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
74.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
371.0ms	(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

simplify4.2s

Counts

182 → 182

Iterations

Iter	Nodes
done	5000
2	4848
1	1243
0	392

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(/ 1 (/ (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)) x))
3.0b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.8b	(/ (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)) x)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
76×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
60×	`sqrt-div`
30×	`flip3-+` `flip-+`
28×	`associate-*r/`
26×	`sqrt-prod`
20×	`pow1`
19×	`add-exp-log`
16×	`associate-/r*` `frac-sub`
13×	`add-cbrt-cube`
12×	`frac-times`
11×	`swap-sqr`
8×	`sqrt-pow1` `pow1/2` `div-exp` `associate-*l/`
7×	`associate-r` `associate-l`
6×	`div-inv` `distribute-lft-out` `associate-/l*` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `distribute-rgt-out--` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `pow-flip` `flip--` `inv-pow`

Counts

4 → 208

Calls

4 calls:

52.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
8.0ms	(/ 1 (/ (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)) x))
30.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.0ms	(/ (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)) x)

series636.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
337.0ms	(/ 1 (/ (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)) x))
101.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
178.0ms	(/ (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)) x)

simplify2.2s

Counts

220 → 220

Iterations

Iter	Nodes
done	5004
2	3075
1	1015
0	382

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0))
3.0b	(- (sqrt (+ 1.0 x)) 1.0)
6.8b	(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))
10.2b	(/ (* x (* (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0))) (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

rewrite418.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
63×	`prod-diff`
58×	`add-cube-cbrt`
47×	`sqrt-prod`
23×	`distribute-rgt-in` `distribute-lft-in`
17×	`add-cbrt-cube` `add-exp-log`
12×	`times-frac` `sqrt-div` `associate-*r/`
11×	`distribute-lft-out`
8×	`frac-times` `associate-/l/`
7×	`flip3--` `fma-neg` `associate-l` `flip--`
6×	`pow1` `associate-/r` `flip3-+` `associate-r*` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `difference-of-squares`
3×	`sub-neg`
2×	`clear-num` `frac-2neg` `div-inv` `distribute-lft-out--` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 189

Calls

4 calls:

136.0ms	(* (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0))
75.0ms	(- (sqrt (+ 1.0 x)) 1.0)
7.0ms	(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))
192.0ms	(/ (* x (* (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0))) (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0))
57.0ms	(- (sqrt (+ 1.0 x)) 1.0)
348.0ms	(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))
1.1s	(/ (* x (* (sqrt (+ 1.0 x)) (- (sqrt (+ 1.0 x)) 1.0))) (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

simplify3.5s

Counts

201 → 201

Iterations

Iter	Nodes
done	5000
2	4295
1	983
0	367

prune963.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes47.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 7.1b

bsearch44.0ms

Steps

Iters	Range		Point
6	1.711014091985158e-09	1.0117869227030548e-08	2.769909291191283e-09

simplify10.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample730.0ms

Algorithm

intervals

Results

409.0ms	7995×	body	80	valid
86.0ms	2741×	body	80	nan
44.0ms	5×	body	1280	valid