Details

sample153.0ms

Algorithm

intervals

Results

68.0ms	860×	body	80	nan
24.0ms	288×	body	80	valid

simplify3.8s

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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)))
0.3b	(/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
0.4b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

rewrite125.0ms

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)
61.0ms	(* (fma (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) rand 1.0) (- a (/ 1.0 3.0)))
33.0ms	(/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
23.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

series715.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(fma (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) rand 1.0)
224.0ms	(* (fma (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))) rand 1.0) (- a (/ 1.0 3.0)))
165.0ms	(/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
97.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

simplify2.2s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	4685
1	990
0	453

prune890.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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)))
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

rewrite156.0ms

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)
53.0ms	(* (fma (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) rand 1.0) (- a (/ 1.0 3.0)))
23.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
38.0ms	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

318.0ms	(fma (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) rand 1.0)
286.0ms	(* (fma (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) rand 1.0) (- a (/ 1.0 3.0)))
98.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
301.0ms	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify924.0ms

Counts

438 → 438

Iterations

Iter	Nodes
done	5001
1	1709
0	743

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cbrt 1.0) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.6b	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (/ (cbrt 1.0) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

113×	`times-frac`
106×	`add-sqr-sqrt`
83×	`sqrt-prod`
64×	`*-un-lft-identity` `add-cube-cbrt`
51×	`cbrt-prod`
48×	`associate-r`
27×	`add-exp-log`
19×	`add-cbrt-cube`
16×	`sqrt-div`
15×	`unswap-sqr`
13×	`associate-l`
12×	`pow1`
11×	`associate-*r/`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
7×	`associate-/r*`
6×	`associate-/r/` `associate-/l*`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`pow1/2`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `-commutative`

Counts

4 → 203

Calls

4 calls:

20.0ms	(/ (cbrt 1.0) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
70.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
70.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
189.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (/ (cbrt 1.0) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))

series743.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(/ (cbrt 1.0) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
103.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
81.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
221.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (/ (cbrt 1.0) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))

simplify556.0ms

Counts

215 → 215

Iterations

Iter	Nodes
done	5001
1	1077
0	367

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
0.4b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.4b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.4b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
39×	`sqrt-prod`
27×	`associate-r`
24×	`*-un-lft-identity`
18×	`associate-l` `add-cube-cbrt`
16×	`pow1`
15×	`add-cbrt-cube` `add-exp-log`
12×	`unswap-sqr`
9×	`pow-prod-down`
8×	`sqrt-div` `associate-*r/`
6×	`sqrt-pow1` `times-frac` `pow1/2` `difference-of-squares`
4×	`expm1-log1p-u` `flip3--` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`sqrt-unprod` `-commutative` `associate-/l` `distribute-lft-out--`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 136

Calls

4 calls:

30.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
63.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
67.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
52.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

series641.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
108.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
117.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
158.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

simplify979.0ms

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
2	1728
1	407
0	168

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes277.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.7s	27472×	body	80	nan
871.0ms	9133×	body	80	valid