Details

sample125.0ms

Algorithm

intervals

Results

69.0ms	819×	body	80	nan
22.0ms	290×	body	80	valid

simplify3.3s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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)))))

rewrite203.0ms

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:

70.0ms	(* 9 (- a (/ 1.0 3.0)))
1.0ms	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
49.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
75.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

series320.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* 9 (- a (/ 1.0 3.0)))
110.0ms	(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))))
78.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify1.9s

Counts

201 → 201

Iterations

Iter	Nodes
done	5000
2	2430
1	953
0	432

prune846.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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)

rewrite88.0ms

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:

19.0ms	(- a (/ 1.0 3.0))
36.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1) rand (- a (/ 1.0 3.0)))
27.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)

series273.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- a (/ 1.0 3.0))
45.0ms	(sqrt (- a (/ 1.0 3.0)))
96.0ms	(fma (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1) rand (- a (/ 1.0 3.0)))
94.0ms	(/ (sqrt (- a (/ 1.0 3.0))) 3)

simplify2.5s

Counts

160 → 160

Iterations

Iter	Nodes
done	5000
3	4852
2	1627
1	653
0	300

prune626.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0)))))) rand (- a (/ 1.0 3.0)))
0.1b	(sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0)))))
0.3b	(/ (- a (/ 1.0 3.0)) (sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0))))))
0.4b	(* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0))))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

177×	`add-sqr-sqrt`
164×	`distribute-rgt-in` `distribute-lft-in`
162×	`*-un-lft-identity`
156×	`prod-diff`
152×	`add-cube-cbrt`
137×	`times-frac`
29×	`pow1`
18×	`add-exp-log`
16×	`pow-prod-down`
13×	`div-inv`
12×	`add-cbrt-cube` `associate-*r/`
10×	`difference-of-squares`
8×	`prod-exp` `sqrt-prod` `cbrt-unprod`
6×	`associate-/l*`
5×	`sqrt-pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-/r*` `sub-neg` `flip3--` `sqrt-div` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `div-sub` `div-exp` `associate-r` `associate-l` `*-commutative` `fma-udef`

Counts

4 → 275

Calls

4 calls:

0.0ms	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0)))))) rand (- a (/ 1.0 3.0)))
177.0ms	(sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0)))))
114.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0))))))
121.0ms	(* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0))))

series665.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0)))))) rand (- a (/ 1.0 3.0)))
130.0ms	(sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0)))))
136.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0))))))
224.0ms	(* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0))))

simplify3.1s

Counts

287 → 287

Iterations

Iter	Nodes
done	5048
2	4090
1	1908
0	663

prune807.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

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)))))

rewrite249.0ms

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:

49.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
44.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
109.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
43.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
74.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
215.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
100.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify2.5s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
2	2684
1	802
0	289

prune675.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes267.0ms

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	17
1	17
0	13

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.9s	27544×	body	80	nan
749.0ms	9156×	body	80	valid