Details

sample188.0ms

Algorithm

intervals

Results

101.0ms	862×	body	80	nan
34.0ms	296×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
5	2001
4	794
3	241
2	80
1	30
0	14

prune368.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
86×	`add-cube-cbrt`
84×	`times-frac`
78×	`prod-diff`
41×	`distribute-rgt-in` `distribute-lft-in`
12×	`difference-of-squares`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
7×	`div-inv`
6×	`associate-r` `associate-r/` `associate-/l` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-/r*` `flip3--` `sqrt-div` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`associate-l`
2×	`sub-neg` `sqrt-pow1` `pow-prod-down` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `div-sub` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 189

Calls

4 calls:

31.0ms	(* 9 (- a (/ 1.0 3.0)))
0.0ms	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
16.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
27.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

series368.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* 9 (- a (/ 1.0 3.0)))
143.0ms	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
64.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
78.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify1.0s

Counts

201 → 201

Iterations

Iter	Nodes
done	2000
2	2000
1	953
0	432

prune829.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.0b	(/ (- a (/ 1.0 3.0)) 3)
0.1b	(fma (/ (/ (- a (/ 1.0 3.0)) 3) (sqrt (- a (/ 1.0 3.0)))) rand (- a (/ 1.0 3.0)))
0.3b	(/ (/ (- a (/ 1.0 3.0)) 3) (sqrt (- a (/ 1.0 3.0))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

454×	`times-frac`
453×	`add-sqr-sqrt`
278×	`*-un-lft-identity`
162×	`add-cube-cbrt`
144×	`sqrt-prod`
116×	`difference-of-squares`
58×	`distribute-lft-out--`
28×	`associate-/l*`
12×	`associate-/r*` `div-inv`
11×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `sqrt-div` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `div-sub` `flip--` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 327

Calls

4 calls:

14.0ms	(sqrt (- a (/ 1.0 3.0)))
18.0ms	(/ (- a (/ 1.0 3.0)) 3)
0.0ms	(fma (/ (/ (- a (/ 1.0 3.0)) 3) (sqrt (- a (/ 1.0 3.0)))) rand (- a (/ 1.0 3.0)))
24.0ms	(/ (/ (- a (/ 1.0 3.0)) 3) (sqrt (- a (/ 1.0 3.0))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt (- a (/ 1.0 3.0)))
45.0ms	(/ (- a (/ 1.0 3.0)) 3)
85.0ms	(fma (/ (/ (- a (/ 1.0 3.0)) 3) (sqrt (- a (/ 1.0 3.0)))) rand (- a (/ 1.0 3.0)))
89.0ms	(/ (/ (- a (/ 1.0 3.0)) 3) (sqrt (- a (/ 1.0 3.0))))

simplify1.0s

Counts

339 → 339

Iterations

Iter	Nodes
done	2001
2	2001
1	1075
0	466

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
0.3b	(/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0)))))
0.3b	(* 3 (sqrt (- a (/ 1.0 3.0))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log`
10×	`times-frac` `add-cube-cbrt`
9×	`associate-r`
8×	`difference-of-squares`
7×	`pow1`
6×	`sqrt-div` `associate-/l*`
4×	`expm1-log1p-u` `flip3--` `associate-*r/` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `add-log-exp`
3×	`associate-l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `pow-prod-down` `-commutative` `fma-udef` `div-inv`

Counts

4 → 97

Calls

4 calls:

10.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
28.0ms	(/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0)))))
20.0ms	(* 3 (sqrt (- a (/ 1.0 3.0))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (- a (/ 1.0 3.0)))
81.0ms	(fma (/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
73.0ms	(/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0)))))
68.0ms	(* 3 (sqrt (- a (/ 1.0 3.0))))

simplify1.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	2001
3	2001
2	1578
1	490
0	196

prune522.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `times-frac`
24×	`associate-l` `add-cube-cbrt`
19×	`add-exp-log`
15×	`pow1`
13×	`add-cbrt-cube`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
5×	`prod-exp`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `sqrt-pow1` `div-exp` `pow-prod-down` `associate-/r/` `insert-posit16` `log1p-expm1-u` `pow-flip` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `associate-l/` `cbrt-unprod` `flip-+` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `pow1/2` `1-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `distribute-lft-out--` `inv-pow`

Counts

4 → 136

Calls

4 calls:

44.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
13.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
62.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
26.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
62.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
170.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
114.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify850.0ms

Counts

148 → 148

Iterations

Iter	Nodes
done	2001
2	2001
1	802
0	289

prune594.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.8s	26837×	body	80	nan
1.0s	9085×	body	80	valid