Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
1.0ms	47×	body	80	nan

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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))))

rewrite98.0ms

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:

13.0ms	(sqrt (+ x 1.0))
22.0ms	(+ 1.0 (sqrt (+ x 1.0)))
60.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series362.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(sqrt (+ x 1.0))
83.0ms	(+ 1.0 (sqrt (+ x 1.0)))
220.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.5s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1149
1	336
0	146

prune880.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize143.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (fma (sqrt (+ x 1.0)) (+ x 1.0) (* 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)))
4.6b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.3b	(/ x (fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0))))

rewrite573.0ms

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` `insert-posit16` `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 → 174

Calls

4 calls:

394.0ms	(* (/ x (fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
76.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
56.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
13.0ms	(/ x (fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

910.0ms	(* (/ x (fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
37.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
117.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
466.0ms	(/ x (fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0))))

simplify8.7s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
2	4787
1	1244
0	394

prune1.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize94.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0)))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.6b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
9.4b	(/ (* x (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))))) (fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0))))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
31×	`flip3-+` `flip-+`
30×	`associate-*r/`
28×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `sqrt-prod`
19×	`pow1`
16×	`frac-sub`
14×	`add-cube-cbrt`
12×	`frac-times`
11×	`add-cbrt-cube` `swap-sqr` `add-exp-log`
8×	`sqrt-pow1` `pow1/2` `associate-*l/`
7×	`associate-r` `associate-l`
6×	`distribute-lft-out` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`associate-/r*` `times-frac` `pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`pow2` `clear-num` `sub-neg` `rem-square-sqrt` `frac-2neg` `pow-plus` `flip3--` `distribute-rgt-out--` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff` `-commutative` `fma-udef` `div-inv` `flip--` `associate-/l`

Counts

4 → 140

Calls

4 calls:

1.0ms	(fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0)))
96.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
49.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
140.0ms	(/ (* x (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))))) (fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

131.0ms	(fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0)))
33.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
84.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
870.0ms	(/ (* x (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))))) (fma (sqrt (+ x 1.0)) (+ x 1.0) (* 1.0 (* 1.0 1.0))))

simplify6.7s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	3772
1	1009
0	338

prune1.6s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite342.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
52×	`times-frac`
40×	`add-cube-cbrt`
39×	`sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r*` `flip3-+` `associate-/r/` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-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/` `-commutative` `hypot-def`

Counts

4 → 148

Calls

4 calls:

22.0ms	(sqrt (+ x 1.0))
44.0ms	(+ 1.0 (sqrt (+ x 1.0)))
87.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
167.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series864.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ x 1.0))
85.0ms	(+ 1.0 (sqrt (+ x 1.0)))
471.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
264.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify4.1s

Counts

160 → 160

Iterations

Iter	Nodes
done	5001
2	1972
1	576
0	225

prune1.3s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes271.0ms

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	8
1	8
0	6

end0.0ms

sample775.0ms

Algorithm

intervals

Results

396.0ms	7999×	body	80	valid
78.0ms	2672×	body	80	nan
0.0ms	1×	body	1280	valid