Details

sample200.0ms

Algorithm

intervals

Results

125.0ms	916×	body	80	nan
34.0ms	285×	body	80	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	2234
4	794
3	241
2	80
1	30
0	14

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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)))))

rewrite75.0ms

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:

23.0ms	(* 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)))
22.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
26.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

series363.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* 9 (- a (/ 1.0 3.0)))
131.0ms	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
80.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
83.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify2.1s

Counts

201 → 201

Iterations

Iter	Nodes
done	5000
2	2430
1	953
0	432

prune904.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

344×	`add-sqr-sqrt`
308×	`sqrt-prod`
214×	`*-un-lft-identity`
202×	`times-frac`
130×	`add-cube-cbrt`
96×	`prod-diff`
90×	`difference-of-squares`
34×	`distribute-lft-out--`
16×	`associate-/l*`
12×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log` `div-inv` `distribute-lft-out`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-div` `div-exp` `associate-/r/`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `flip-+` `fma-udef`

Counts

4 → 315

Calls

4 calls:

18.0ms	(- (sqrt a) (sqrt (/ 1.0 3.0)))
0.0ms	(fma (* (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) 3) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
49.0ms	(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
43.0ms	(/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) 3)

series905.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (sqrt a) (sqrt (/ 1.0 3.0)))
526.0ms	(fma (* (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) 3) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
247.0ms	(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
80.0ms	(/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) 3)

simplify2.3s

Counts

327 → 327

Iterations

Iter	Nodes
done	5007
2	3341
1	1255
0	535

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

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)))))

rewrite159.0ms

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:

28.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
29.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
83.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
18.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
79.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
217.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
102.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify2.4s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
2	2684
1	802
0	289

prune777.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)))
0.1b	(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
0.2b	(* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
79×	`add-cube-cbrt`
78×	`prod-diff`
56×	`times-frac`
42×	`distribute-rgt-in` `distribute-lft-in`
19×	`add-exp-log`
14×	`associate-l`
12×	`associate-r`
11×	`pow1`
10×	`add-cbrt-cube`
8×	`prod-exp`
6×	`div-inv`
4×	`expm1-log1p-u` `frac-times` `flip3--` `pow-exp` `associate-*r/` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`pow-unpow` `flip3-+` `pow-prod-down` `*-commutative` `cbrt-unprod` `flip-+` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `unpow-prod-down` `pow-pow` `associate-*l/` `distribute-lft-out--`

Counts

4 → 188

Calls

4 calls:

34.0ms	(* 9 (- a (/ 1.0 3.0)))
27.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)))
9.0ms	(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
17.0ms	(* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)

series598.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* 9 (- a (/ 1.0 3.0)))
132.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)))
144.0ms	(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
244.0ms	(* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)

simplify2.9s

Counts

200 → 200

Iterations

Iter	Nodes
done	5000
2	3510
1	1161
0	476

prune776.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes112.0ms

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	18
1	18
0	16

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.9s	27044×	body	80	nan
1.1s	9082×	body	80	valid