Details

sample89.0ms

Algorithm

intervals

Results

38.0ms	915×	body	80	nan
13.0ms	294×	body	80	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2429
5	1149
4	547
3	208
2	76
1	27
0	13

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) rand 1.0)
0.1b	(* (fma (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) rand 1.0) (- a (/ 1.0 3.0)))
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.3b	(/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

rewrite106.0ms

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`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-/r` `sqrt-div` `associate-l/` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-l` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-pow1` `pow-prod-down` `associate-*r/` `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 → 167

Calls

4 calls:

0.0ms	(fma (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) rand 1.0)
70.0ms	(* (fma (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) rand 1.0) (- a (/ 1.0 3.0)))
13.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
15.0ms	(/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

series854.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(fma (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) rand 1.0)
254.0ms	(* (fma (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) rand 1.0) (- a (/ 1.0 3.0)))
133.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
223.0ms	(/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

simplify2.0s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	4681
1	990
0	453

prune815.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) rand 1.0)
0.1b	(* (fma (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) rand 1.0) (- a (/ 1.0 3.0)))
0.2b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

494×	`times-frac`
404×	`add-sqr-sqrt`
324×	`*-un-lft-identity`
272×	`add-cube-cbrt`
252×	`sqrt-prod`
78×	`prod-diff`
52×	`difference-of-squares`
41×	`distribute-rgt-in` `distribute-lft-in`
36×	`associate-/l*`
26×	`distribute-lft-out--`
16×	`sqrt-div` `associate-/r/`
15×	`associate-/r*` `div-inv`
13×	`add-cbrt-cube` `add-exp-log`
9×	`flip3--` `flip--`
6×	`pow1` `associate-r`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`clear-num` `sub-neg` `frac-2neg` `associate-*r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 426

Calls

4 calls:

0.0ms	(fma (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) rand 1.0)
51.0ms	(* (fma (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) rand 1.0) (- a (/ 1.0 3.0)))
40.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
70.0ms	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

662.0ms	(fma (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) rand 1.0)
316.0ms	(* (fma (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) rand 1.0) (- a (/ 1.0 3.0)))
123.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
255.0ms	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify1.1s

Counts

438 → 438

Iterations

Iter	Nodes
done	5001
1	1709
0	743

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(* (+ (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) 1.0) (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite409.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
156×	`prod-diff`
152×	`*-un-lft-identity`
146×	`add-cube-cbrt`
114×	`times-frac`
82×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-cbrt-cube` `add-exp-log` `div-inv`
12×	`associate-r`
11×	`pow1`
8×	`associate-*r/`
7×	`associate-l`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `sub-neg` `sqrt-div` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `associate-l/` `associate-/r/` `-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow1/2` `distribute-lft-out` `associate-/l*`

Counts

4 → 263

Calls

4 calls:

50.0ms	(* 9.0 (- a (/ 1.0 3.0)))
226.0ms	(* (+ (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) 1.0) (- a (/ 1.0 3.0)))
68.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
34.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series609.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* 9.0 (- a (/ 1.0 3.0)))
163.0ms	(* (+ (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) 1.0) (- a (/ 1.0 3.0)))
115.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
261.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify1.0s

Counts

275 → 275

Iterations

Iter	Nodes
done	5000
1	1793
0	588

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (+ (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) 1.0)) (cbrt (+ (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) 1.0)))
0.2b	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.2b	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.2b	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`cbrt-prod`
21×	`add-exp-log`
19×	`add-cbrt-cube`
18×	`add-cube-cbrt`
12×	`cbrt-div` `associate-/r*` `times-frac`
11×	`pow1`
9×	`swap-sqr`
8×	`associate-*r/`
7×	`associate-r` `associate-l`
6×	`cbrt-undiv` `flip3-+` `pow1/3` `sqrt-div` `div-exp` `associate-/r/` `sqrt-prod` `flip-+` `distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `flip3--` `div-inv` `flip--` `associate-/l*`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `*-commutative`

Counts

4 → 136

Calls

4 calls:

286.0ms	(* (cbrt (+ (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) 1.0)) (cbrt (+ (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) 1.0)))
37.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
32.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
33.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

426.0ms	(* (cbrt (+ (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) 1.0)) (cbrt (+ (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) 1.0)))
259.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
241.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
303.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify1.4s

Counts

148 → 148

Iterations

Iter	Nodes
done	5001
2	2792
1	616
0	235

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes237.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.7s	26426×	body	80	nan
1.4s	9076×	body	80	valid