Details

sample187.0ms

Algorithm

intervals

Results

116.0ms	882×	body	80	nan
36.0ms	297×	body	80	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
7	3296
6	1984
5	1152
4	612
3	202
2	71
1	28
0	14

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.3b	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
59×	`times-frac`
50×	`*-un-lft-identity`
36×	`associate-r`
30×	`add-cube-cbrt`
20×	`difference-of-squares`
14×	`sqrt-prod`
13×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
10×	`distribute-lft-out--`
9×	`associate-*r/`
6×	`sqrt-div` `associate-l` `associate-/l*`
5×	`flip3--` `flip--`
4×	`associate-/r*` `associate-/r/` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `associate-/l/`
1×	`clear-num` `frac-2neg` `pow1/2` `div-sub`

Counts

4 → 144

Calls

4 calls:

20.0ms	(* 9 (- a (/ 1.0 3.0)))
7.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
82.0ms	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
42.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* 9 (- a (/ 1.0 3.0)))
102.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
136.0ms	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
82.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify3.3s

Counts

156 → 156

Iterations

Iter	Nodes
3	6186
2	1965
1	664
0	256

prune822.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
32×	`times-frac`
30×	`sqrt-prod`
24×	`add-cube-cbrt`
20×	`add-exp-log`
15×	`add-cbrt-cube`
10×	`pow1` `difference-of-squares`
9×	`prod-exp` `associate-/l*` `add-log-exp`
5×	`cbrt-unprod` `distribute-lft-out--`
4×	`sqrt-div` `insert-posit16`
3×	`associate-/r` `flip3--` `div-exp` `associate-l` `pow-prod-down` `associate-l/` `associate-*r/` `flip--`
2×	`cbrt-undiv` `associate-+l+` `sum-log` `1-exp` `frac-add` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r` `*-commutative` `associate-+l-` `flip-+` `div-inv`

Counts

4 → 115

Calls

4 calls:

15.0ms	(sqrt (- a (/ 1.0 3.0)))
66.0ms	(+ (- a (/ 1.0 3.0)) (* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)))
29.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)
57.0ms	(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))

series384.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (- a (/ 1.0 3.0)))
135.0ms	(+ (- a (/ 1.0 3.0)) (* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)))
77.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)
117.0ms	(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))

simplify2.8s

Counts

127 → 127

Iterations

Iter	Nodes
3	5134
2	1552
1	568
0	249

prune561.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

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)))))

rewrite144.0ms

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×	`frac-times` `associate-/r*` `sqrt-pow1` `div-exp` `pow-prod-down` `associate-/r/` `insert-posit16` `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 → 128

Calls

4 calls:

42.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
7.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
68.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
25.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series532.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
80.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
224.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
115.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify1.8s

Counts

140 → 140

Iterations

Iter	Nodes
2	2380
1	742
0	281

prune765.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.0b	(+ (- a (/ 1.0 3.0)) (/ (* rand (sqrt (- a (/ 1.0 3.0)))) 3))
0.3b	(* rand (sqrt (- a (/ 1.0 3.0))))
0.5b	(/ (* rand (sqrt (- a (/ 1.0 3.0)))) 3)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
13×	`sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log`
10×	`add-cube-cbrt`
9×	`associate-r` `add-log-exp`
7×	`pow1`
6×	`sqrt-div`
5×	`times-frac`
4×	`flip3--` `associate-*r/` `insert-posit16` `flip--` `difference-of-squares`
3×	`associate-/r` `associate-l*` `distribute-lft-out--`
2×	`cbrt-undiv` `associate-+l+` `sum-log` `div-exp` `frac-add` `prod-exp` `cbrt-unprod` `distribute-lft-out` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `associate-+l-` `flip-+` `div-inv` `associate-/l`

Counts

4 → 91

Calls

4 calls:

14.0ms	(sqrt (- a (/ 1.0 3.0)))
35.0ms	(+ (- a (/ 1.0 3.0)) (/ (* rand (sqrt (- a (/ 1.0 3.0)))) 3))
44.0ms	(* rand (sqrt (- a (/ 1.0 3.0))))
17.0ms	(/ (* rand (sqrt (- a (/ 1.0 3.0)))) 3)

series348.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (- a (/ 1.0 3.0)))
100.0ms	(+ (- a (/ 1.0 3.0)) (/ (* rand (sqrt (- a (/ 1.0 3.0)))) 3))
85.0ms	(* rand (sqrt (- a (/ 1.0 3.0))))
95.0ms	(/ (* rand (sqrt (- a (/ 1.0 3.0)))) 3)

simplify2.5s

Counts

103 → 103

Iterations

Iter	Nodes
3	5273
2	1470
1	484
0	203

prune464.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes176.0ms

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	16
1	16
0	13

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.1s	27172×	body	80	nan
1.7s	9137×	body	80	valid