Details

sample162.0ms

Algorithm

intervals

Results

103.0ms	895×	body	80	nan
31.0ms	291×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

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)
0.2b	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

rewrite198.0ms

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:

39.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
14.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
107.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
36.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
56.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
196.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
107.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify1.1s

Counts

148 → 148

Iterations

Iter	Nodes
done	2001
2	2001
1	802
0	289

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize25.0ms

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)))))

rewrite112.0ms

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:

42.0ms	(* 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)))
24.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
40.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* 9 (- a (/ 1.0 3.0)))
84.0ms	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
71.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
117.0ms	(/ (- 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

prune2.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize21.0ms

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)))
0.3b	(/ (sqrt (- a (/ 1.0 3.0))) 3)

rewrite35.0ms

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))
11.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1) rand (- a (/ 1.0 3.0)))
15.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)

series233.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- a (/ 1.0 3.0))
40.0ms	(sqrt (- a (/ 1.0 3.0)))
86.0ms	(fma (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1) rand (- a (/ 1.0 3.0)))
77.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)

simplify992.0ms

Counts

160 → 160

Iterations

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

prune1.5s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))) rand)
0.3b	(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.3b	(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.5b	(* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))))

rewrite823.0ms

Algorithm

rewrite-expression-head

Rules

180×	`add-sqr-sqrt`
178×	`times-frac`
126×	`sqrt-prod`
119×	`*-un-lft-identity`
110×	`add-exp-log`
97×	`add-cube-cbrt`
86×	`sqrt-pow1`
84×	`pow1`
74×	`pow-flip`
49×	`prod-exp`
38×	`add-cbrt-cube`
36×	`div-exp`
35×	`swap-sqr`
30×	`associate-r`
29×	`pow-prod-down`
28×	`associate-l`
26×	`unswap-sqr`
24×	`sqrt-div`
22×	`pow1/2`
18×	`rec-exp` `1-exp` `pow-prod-up`
14×	`associate-/r` `associate-r/`
13×	`cbrt-unprod`
12×	`associate-/r/`
10×	`cbrt-undiv` `pow-sqr` `inv-pow`
8×	`div-inv`
6×	`flip3--` `associate-l/` `flip--` `associate-/l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `clear-num` `frac-2neg` `un-div-inv` `*-commutative`
1×	`pow2` `pow-plus`

Counts

4 → 347

Calls

4 calls:

580.0ms	(* (* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))) rand)
26.0ms	(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
38.0ms	(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
168.0ms	(* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))))

series968.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(* (* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))) rand)
229.0ms	(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
232.0ms	(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
194.0ms	(* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))))

simplify1.3s

Counts

359 → 359

Iterations

Iter	Nodes
done	2000
2	2000
1	1305
0	431

prune4.7s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes223.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.6s	27625×	body	80	nan
1.5s	9120×	body	80	valid