Details

sample259.0ms

Algorithm

intervals

Results

165.0ms	882×	body	80	nan
46.0ms	297×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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)))))

rewrite86.0ms

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:

25.0ms	(* 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)))
18.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
36.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* 9 (- a (/ 1.0 3.0)))
115.0ms	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
73.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
92.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify1.3s

Counts

201 → 201

Iterations

Iter	Nodes
done	2000
2	2000
1	953
0	432

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(- a (/ 1.0 3.0))
0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1) rand (- a (/ 1.0 3.0)))
0.2b	(/ (sqrt (- a (/ 1.0 3.0))) 3)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
60×	`times-frac`
58×	`add-cube-cbrt`
39×	`prod-diff`
30×	`sqrt-prod`
12×	`difference-of-squares`
9×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-/r*` `flip3--` `fma-neg` `flip--`
2×	`associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `fma-udef`

Counts

4 → 148

Calls

4 calls:

7.0ms	(- a (/ 1.0 3.0))
13.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1) rand (- a (/ 1.0 3.0)))
29.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)

series273.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- a (/ 1.0 3.0))
47.0ms	(sqrt (- a (/ 1.0 3.0)))
100.0ms	(fma (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1) rand (- a (/ 1.0 3.0)))
75.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)

simplify1.2s

Counts

160 → 160

Iterations

Iter	Nodes
done	2000
3	2000
2	1627
1	653
0	300

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.0b	(+ (* rand (/ (sqrt (- a (/ 1.0 3.0))) 3)) (- a (/ 1.0 3.0)))
0.2b	(/ (sqrt (- a (/ 1.0 3.0))) 3)
0.2b	(* rand (/ (sqrt (- a (/ 1.0 3.0))) 3))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt`
91×	`times-frac`
90×	`*-un-lft-identity`
74×	`add-cube-cbrt`
49×	`sqrt-prod`
41×	`associate-+r+`
39×	`prod-diff`
31×	`associate-r`
16×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*` `add-log-exp`
8×	`distribute-lft-out--`
7×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `associate-l` `associate-r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `sum-log` `div-exp` `frac-add` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-+r-` `sub-neg` `fma-def` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 191

Calls

4 calls:

12.0ms	(sqrt (- a (/ 1.0 3.0)))
32.0ms	(+ (* rand (/ (sqrt (- a (/ 1.0 3.0))) 3)) (- a (/ 1.0 3.0)))
14.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)
36.0ms	(* rand (/ (sqrt (- a (/ 1.0 3.0))) 3))

series343.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (- a (/ 1.0 3.0)))
89.0ms	(+ (* rand (/ (sqrt (- a (/ 1.0 3.0))) 3)) (- a (/ 1.0 3.0)))
75.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)
127.0ms	(* rand (/ (sqrt (- a (/ 1.0 3.0))) 3))

simplify1.2s

Counts

203 → 203

Iterations

Iter	Nodes
done	2002
2	2002
1	1010
0	388

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- a (/ 1.0 3.0))) 3)
1.0b	(* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0)))
1.0b	(* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0)))
61.9b	(fma (- (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

154×	`add-sqr-sqrt`
128×	`cbrt-prod`
115×	`times-frac`
94×	`*-un-lft-identity`
86×	`add-cube-cbrt`
32×	`swap-sqr` `associate-r` `associate-l`
24×	`sqrt-prod`
18×	`pow1` `unswap-sqr`
12×	`pow1/3`
10×	`add-exp-log`
9×	`div-inv` `associate-/l*`
8×	`cbrt-div` `difference-of-squares`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`associate-/r*`
2×	`pow2` `frac-times` `pow-plus` `sqrt-div` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `fma-udef` `flip--`

Counts

4 → 229

Calls

4 calls:

15.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)
17.0ms	(* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0)))
16.0ms	(* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0)))
0.0ms	(fma (- (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0)))))

series112.0ms

Counts

4 → 6

Calls

4 calls:

112.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)
0.0ms	(* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0)))
0.0ms	(* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0)))
0.0ms	(fma (- (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0)))))

simplify1.3s

Counts

235 → 235

Iterations

Iter	Nodes
done	2002
3	2002
2	1089
1	468
0	268

prune3.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes188.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	18
1	18
0	16

end0.0ms

sample6.0s

Algorithm

intervals

Results

4.0s	27172×	body	80	nan
1.2s	9137×	body	80	valid