Details

sample72.0ms

Algorithm

intervals

Results

14.0ms	45×	body	1280	valid
13.0ms	184×	body	80	valid
9.0ms	25×	body	2560	valid
5.0ms	17×	body	640	valid
4.0ms	69×	body	80	nan
2.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify149.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
22.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
33.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (* 3.0 a) c)
103.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
71.0ms	(- (* b b) (* (* 3.0 a) c))
116.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.9s

Counts

92 → 92

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	135	1109
1	332	1006
2	1193	900
3	4662	889
done	5000	889

prune435.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.0b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
3.5b	(/ (/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.2b	(/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 158

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
168.0ms	(/ (/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
126.0ms	(/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* (* 3.0 a) c))
207.0ms	(/ (/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
264.0ms	(/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
92.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.5s

Counts

170 → 170

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	262	5076
1	653	4509
2	2832	4180
done	5000	4178

prune701.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.9b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
3.5b	(/ (/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
10.2b	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

376×	`times-frac`
188×	`add-sqr-sqrt`
187×	`*-un-lft-identity`
131×	`add-cube-cbrt`
44×	`associate-/l*`
33×	`add-exp-log` `add-cbrt-cube`
28×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/r/`
18×	`div-inv`
17×	`sqrt-prod`
15×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
14×	`distribute-rgt-neg-in`
10×	`associate-/r*`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 266

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
123.0ms	(/ (/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
104.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
18.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b b) (* (* 3.0 a) c))
250.0ms	(/ (/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
240.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
84.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.6s

Counts

278 → 278

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	507	9705
1	1267	9064
2	4812	8567
done	5000	8566

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.9b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
3.5b	(/ (/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
10.2b	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

376×	`times-frac`
188×	`add-sqr-sqrt`
187×	`*-un-lft-identity`
131×	`add-cube-cbrt`
44×	`associate-/l*`
28×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/r/`
23×	`add-exp-log` `add-cbrt-cube`
18×	`div-inv`
17×	`sqrt-prod`
15×	`flip3--` `flip--`
14×	`distribute-rgt-neg-in`
11×	`cbrt-undiv` `div-exp`
10×	`associate-/r*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 262

Calls

4 calls:

15.0ms	(- (* b b) (* (* 3.0 a) c))
112.0ms	(/ (/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
80.0ms	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series596.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* (* 3.0 a) c))
209.0ms	(/ (/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
244.0ms	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
84.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.8s

Counts

274 → 274

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	494	8983
1	1209	8368
2	3963	7971
done	5002	7968

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.9b

regimes524.0ms

Accuracy

89.6% (2.4b remaining)

Error of 11.6b against oracle of 9.3b and baseline of 32.0b

bsearch344.0ms

Steps

Iters	Range	Point
7	1.8931325595256007e+133	5.341589198600723e+134	9.53632028454962e+133
9	9.448397398655464e-278	1.4829972419072586e-270	1.6982775252499256e-273
9	-8.712513212907472e+114	-1.0414090820182828e+108	-2.8954145393623046e+111

Iters

Range

Point

1.8931325595256007e+133

5.341589198600723e+134

9.53632028454962e+133

9.448397398655464e-278

1.4829972419072586e-270

1.6982775252499256e-273

-8.712513212907472e+114

-1.0414090820182828e+108

-2.8954145393623046e+111

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	45	111
1	53	111
done	53	111

end0.0ms

sample3.1s

Algorithm

intervals

Results

556.0ms	480×	body	640	valid
542.0ms	5850×	body	80	valid
533.0ms	1055×	body	2560	valid
400.0ms	923×	body	1280	valid
390.0ms	2941×	body	80	nan
57.0ms	113×	body	5120	valid
40.0ms	206×	body	320	valid
14.0ms	108×	body	160	valid