Details

sample26.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
3.0ms	80×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite72.0ms

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-+` `insert-posit16` `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 → 74

Calls

3 calls:

11.0ms	(sqrt (+ x 1.0))
20.0ms	(+ 1.0 (sqrt (+ x 1.0)))
40.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series352.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(sqrt (+ x 1.0))
80.0ms	(+ 1.0 (sqrt (+ x 1.0)))
223.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.3s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1180
1	336
0	146

prune309.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
26×	`times-frac`
24×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
8×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `sqrt-prod` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `hypot-def` `pow-flip` `inv-pow`

Counts

4 → 122

Calls

4 calls:

5.0ms	(sqrt (+ x 1.0))
13.0ms	(+ 1.0 (sqrt (+ x 1.0)))
42.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
82.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (+ x 1.0))
73.0ms	(+ 1.0 (sqrt (+ x 1.0)))
140.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
183.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.7s

Counts

134 → 134

Iterations

Iter	Nodes
done	5005
2	1670
1	482
0	195

prune546.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 173

Calls

4 calls:

11.0ms	(sqrt (sqrt (+ x 1.0)))
10.0ms	(sqrt (sqrt (+ x 1.0)))
13.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
35.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt (sqrt (+ x 1.0)))
104.0ms	(sqrt (sqrt (+ x 1.0)))
202.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
62.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify1.6s

Counts

185 → 185

Iterations

Iter	Nodes
done	5002
2	1712
1	560
0	248

prune606.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (/ 1 (/ (fma (+ x 1.0) (sqrt (+ x 1.0)) (* (* 1.0 1.0) 1.0)) (fma 1.0 1.0 (* (- (sqrt (+ x 1.0)) 1.0) (sqrt (+ x 1.0)))))))
0.1b	(* (- (sqrt (+ x 1.0)) 1.0) (sqrt (+ x 1.0)))
4.7b	(- (sqrt (+ x 1.0)) 1.0)
5.6b	(/ (fma (+ x 1.0) (sqrt (+ x 1.0)) (* (* 1.0 1.0) 1.0)) (fma 1.0 1.0 (* (- (sqrt (+ x 1.0)) 1.0) (sqrt (+ x 1.0)))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
81×	`times-frac`
66×	`add-cube-cbrt`
51×	`associate-r`
27×	`add-exp-log`
23×	`sqrt-prod`
21×	`prod-diff`
17×	`add-cbrt-cube`
9×	`associate-l`
8×	`pow1` `div-exp` `prod-exp`
7×	`fma-neg` `unswap-sqr`
6×	`sqrt-div` `add-log-exp`
5×	`div-inv` `distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `cbrt-undiv` `flip3--` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
3×	`associate-/r` `flip3-+` `associate-r/` `flip-+` `associate-/l*`
2×	`rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-/r/` `un-div-inv`

Counts

4 → 189

Calls

4 calls:

23.0ms	(* x (/ 1 (/ (fma (+ x 1.0) (sqrt (+ x 1.0)) (* (* 1.0 1.0) 1.0)) (fma 1.0 1.0 (* (- (sqrt (+ x 1.0)) 1.0) (sqrt (+ x 1.0)))))))
119.0ms	(* (- (sqrt (+ x 1.0)) 1.0) (sqrt (+ x 1.0)))
31.0ms	(- (sqrt (+ x 1.0)) 1.0)
6.0ms	(/ (fma (+ x 1.0) (sqrt (+ x 1.0)) (* (* 1.0 1.0) 1.0)) (fma 1.0 1.0 (* (- (sqrt (+ x 1.0)) 1.0) (sqrt (+ x 1.0)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

851.0ms	(* x (/ 1 (/ (fma (+ x 1.0) (sqrt (+ x 1.0)) (* (* 1.0 1.0) 1.0)) (fma 1.0 1.0 (* (- (sqrt (+ x 1.0)) 1.0) (sqrt (+ x 1.0)))))))
166.0ms	(* (- (sqrt (+ x 1.0)) 1.0) (sqrt (+ x 1.0)))
69.0ms	(- (sqrt (+ x 1.0)) 1.0)
781.0ms	(/ (fma (+ x 1.0) (sqrt (+ x 1.0)) (* (* 1.0 1.0) 1.0)) (fma 1.0 1.0 (* (- (sqrt (+ x 1.0)) 1.0) (sqrt (+ x 1.0)))))

simplify4.5s

Counts

201 → 201

Iterations

Iter	Nodes
done	5000
2	4738
1	1326
0	489

prune950.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes116.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	8

end0.0ms

sample859.0ms

Algorithm

intervals

Results

557.0ms	7995×	body	80	valid
127.0ms	2550×	body	80	nan
2.0ms	5×	body	1280	valid