Details

sample169.0ms

Algorithm

intervals

Results

109.0ms	809×	body	80	nan
30.0ms	289×	body	80	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
6	3095
5	1346
4	543
3	191
2	75
1	28
0	14

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.8b	(sqrt (* 9 (- a (/ 1.0 3.0))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 171

Calls

4 calls:

43.0ms	(* 9 (- a (/ 1.0 3.0)))
0.0ms	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
19.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
14.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

series454.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* 9 (- a (/ 1.0 3.0)))
119.0ms	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
171.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
100.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify1.1s

Counts

183 → 183

Iterations

Iter	Nodes
2	2149
1	879
0	432

prune2.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

29.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
23.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
39.0ms	(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (- a (/ 1.0 3.0)))
129.0ms	(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
148.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
175.0ms	(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify2.3s

Counts

156 → 156

Iterations

Iter	Nodes
3	4942
2	1615
1	610
0	263

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
0.2b	(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))
0.8b	(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

164×	`distribute-rgt-in` `distribute-lft-in`
156×	`prod-diff`
151×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
120×	`times-frac`
15×	`pow1`
13×	`div-inv`
12×	`associate-*r/`
11×	`add-cbrt-cube` `add-exp-log`
8×	`sqrt-prod`
6×	`associate-l` `pow-prod-down`
4×	`expm1-log1p-u` `associate-/r*` `sub-neg` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `flip3--` `prod-exp` `cbrt-unprod` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `div-exp` `associate-r` `*-commutative` `fma-udef`

Counts

4 → 254

Calls

4 calls:

0.0ms	(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
53.0ms	(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
53.0ms	(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))
70.0ms	(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
174.0ms	(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
61.0ms	(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))
99.0ms	(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))

simplify3.9s

Counts

266 → 266

Iterations

Iter	Nodes
2	2887
1	1261
0	653

prune3.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.3b	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.8b	(sqrt (* 9 (- a (/ 1.0 3.0))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`times-frac`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
13×	`pow1`
11×	`add-cbrt-cube`
8×	`sqrt-prod`
7×	`associate-*r/`
6×	`sqrt-div`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-pow1` `div-exp` `prod-exp` `associate-/r/` `insert-posit16` `log1p-expm1-u` `pow-flip` `add-log-exp`
3×	`flip3--` `associate-l` `pow-prod-down` `flip--` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `un-div-inv` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 114

Calls

4 calls:

0.0ms	(fma (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
83.0ms	(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
17.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
18.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

series536.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(fma (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
196.0ms	(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
143.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
90.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify3.6s

Counts

126 → 126

Iterations

Iter	Nodes
3	4885
2	1590
1	567
0	237

prune1.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes144.0ms

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
2	12
1	12
0	11

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.6s	27909×	body	80	nan
1.2s	9197×	body	80	valid