Details

sample136.0ms

Algorithm

intervals

Results

35.0ms	135×	body	160	valid
28.0ms	313×	body	80	nan
21.0ms	569×	pre	80	true
11.0ms	121×	body	80	valid

simplify142.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
27.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite126.0ms

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:

12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
121.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
86.0ms	(- (* b b) (* (* 4.0 a) c))
115.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	167	1697
1	433	1584
2	1484	1361
done	5000	1347

prune424.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`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`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

133.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
59.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(- (* b b) (* (* 4.0 a) c))
106.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
134.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms	(- (* b b) (* (* 4.0 a) c))
288.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.9s

Counts

243 → 243

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	338	10026
1	802	7598
2	3039	6483
done	5001	6397

prune638.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ 1 1) (/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
0.3b	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

719×	`times-frac`
330×	`add-exp-log`
257×	`add-sqr-sqrt` `*-un-lft-identity`
214×	`div-exp`
185×	`add-cube-cbrt`
138×	`add-cbrt-cube`
83×	`prod-exp`
72×	`cbrt-undiv`
52×	`div-inv`
50×	`associate-/r/`
45×	`1-exp`
38×	`associate-/r*`
36×	`distribute-lft-out--` `difference-of-squares`
33×	`cbrt-unprod`
18×	`rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-prod` `flip--`
15×	`associate-/l*`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 467

Calls

4 calls:

59.0ms	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(/ (/ 1 1) (/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
69.0ms	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms	(- (* b b) (* (* 4.0 a) c))
214.0ms	(/ (/ 1 1) (/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
205.0ms	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.6s

Counts

479 → 479

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	704	19852
1	1780	16706
2	4673	14936
done	5000	14934

prune715.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (/ (* 2.0 a) (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b	(- (* b b) (* (* 4.0 a) c))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

285×	`times-frac`
226×	`add-sqr-sqrt` `*-un-lft-identity`
138×	`add-cube-cbrt`
121×	`add-exp-log`
63×	`add-cbrt-cube`
61×	`prod-diff`
60×	`div-exp`
52×	`sqrt-prod`
44×	`distribute-lft-out--` `difference-of-squares`
43×	`distribute-rgt-neg-in`
36×	`prod-exp`
34×	`div-inv`
27×	`cbrt-undiv`
21×	`distribute-lft-neg-in` `associate-/l*`
18×	`cbrt-unprod`
11×	`fma-neg`
10×	`associate-/r/` `add-log-exp`
8×	`associate-/r*`
7×	`neg-mul-1` `rec-exp` `1-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`associate--l-` `neg-sub0` `neg-log` `associate-/l/`

Counts

4 → 345

Calls

4 calls:

97.0ms	(/ (/ 1 (/ (* 2.0 a) (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
62.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
16.0ms	(- (* b b) (* (* 4.0 a) c))

series429.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(/ (/ 1 (/ (* 2.0 a) (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
105.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
82.0ms	(- (* b b) (* (* 4.0 a) c))

simplify2.7s

Counts

357 → 357

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	516	15080
1	1294	12475
2	4293	9942
done	5001	9941

prune802.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes247.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	28
1	26	28
done	26	28

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	4481×	body	160	valid
741.0ms	8809×	body	80	nan
713.0ms	16809×	pre	80	true
355.0ms	3519×	body	80	valid