Details

sample66.0ms

Algorithm

intervals

Results

10.0ms	38×	body	2560	valid
9.0ms	190×	body	80	valid
8.0ms	36×	body	1280	valid
4.0ms	79×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify93.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	83	16
4	112	16
5	120	16
done	120	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

15.0ms	(- (* b b) (* (* 3.0 a) c))
125.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
32.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* (* 3.0 a) c))
182.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
126.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
116.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.7s

Counts

102 → 102

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	167	1697
1	445	1590
2	2092	1363
done	5001	1354

prune404.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.9b	(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
7.6b	(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

34.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
95.0ms	(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
76.0ms	(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
27.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series637.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
227.0ms	(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
240.0ms	(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
83.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify489.0ms

Counts

244 → 244

Iterations

Useful iterations: done (477.0ms)

Iter	Nodes	Cost
0	337	10067
1	858	7629
done	5000	6631

prune750.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.9b	(/ (/ (/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
7.6b	(/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

376×	`times-frac`
233×	`add-sqr-sqrt`
232×	`*-un-lft-identity`
172×	`add-cube-cbrt`
60×	`prod-diff`
48×	`sqrt-prod`
44×	`associate-/l*`
36×	`distribute-rgt-neg-in`
33×	`add-exp-log` `add-cbrt-cube`
30×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/r/`
21×	`distribute-lft-neg-in`
18×	`div-inv`
15×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
10×	`fma-neg` `associate-/r*`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 340

Calls

4 calls:

41.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
131.0ms	(/ (/ (/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
87.0ms	(/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
18.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series687.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
238.0ms	(/ (/ (/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
251.0ms	(/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
107.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify807.0ms

Counts

352 → 352

Iterations

Useful iterations: done (792.0ms)

Iter	Nodes	Cost
0	582	14652
1	1487	12136
done	5000	11033

prune989.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* c 3.0) (/ (/ (/ a (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a))
0.3b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.5b	(/ (/ (/ a (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

1518×	`times-frac`
902×	`add-sqr-sqrt`
901×	`*-un-lft-identity`
645×	`add-cube-cbrt`
259×	`associate-r`
128×	`distribute-lft-out--` `difference-of-squares`
97×	`sqrt-prod`
85×	`distribute-rgt-neg-in` `associate-/l*`
60×	`prod-diff`
45×	`add-exp-log` `add-cbrt-cube`
42×	`associate-/r/`
30×	`div-inv`
23×	`flip3--` `flip--`
21×	`distribute-lft-neg-in`
18×	`cbrt-undiv` `div-exp`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `associate-/r*`
2×	`sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `neg-log` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 758

Calls

4 calls:

153.0ms	(* (* c 3.0) (/ (/ (/ a (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a))
33.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
94.0ms	(/ (/ (/ a (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
18.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series728.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(* (* c 3.0) (/ (/ (/ a (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a))
127.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
227.0ms	(/ (/ (/ a (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
95.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.0s

Counts

770 → 770

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	968	27323
1	3295	23935
done	5000	22667

prune2.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

regimes296.0ms

Accuracy

93.1% (1.6b remaining)

Error of 7.5b against oracle of 5.9b and baseline of 29.7b

bsearch283.0ms

Steps

Iters	Range		Point
8	3932480935863.943	2020002846347102.2	929319867835151.5
9	-7.152300718152866e-253	-1.7963911490351415e-262	-1.8359597498390082e-262
9	-7.561250615295736e+156	-1.350243324689865e+150	-4.919628179067154e+153

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	67
1	44	67
done	44	67

end0.0ms

sample2.9s

Algorithm

intervals

Results

834.0ms	5920×	body	80	valid
598.0ms	1055×	body	2560	valid
334.0ms	903×	body	1280	valid
313.0ms	2893×	body	80	nan
165.0ms	459×	body	640	valid
91.0ms	220×	body	320	valid
43.0ms	85×	body	5120	valid
15.0ms	121×	body	160	valid