Details

sample144.0ms

Algorithm

intervals

Results

45.0ms	534×	pre	80	true
25.0ms	152×	body	160	valid
21.0ms	278×	body	80	nan
9.0ms	39×	body	320	valid
5.0ms	65×	body	80	valid

simplify106.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
36.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite143.0ms

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:

16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
86.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
52.0ms	(- (* b b) (* (* 4.0 a) c))
114.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
99.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.3s

Counts

102 → 102

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	167	1697
1	433	1584
2	1481	1361
done	5000	1347

prune320.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite245.0ms

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:

32.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
78.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
59.0ms	(- (* b b) (* (* 4.0 a) c))
198.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
250.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.0s

Counts

243 → 243

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	340	10026
1	812	7598
2	3236	6483
done	5001	6397

prune596.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) (* 2.0 a))
0.3b	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4))))))
0.3b	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))
0.7b	(pow (* (* 4.0 a) c) 3)

rewrite590.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt`
142×	`times-frac`
105×	`*-un-lft-identity`
57×	`add-cube-cbrt`
54×	`difference-of-squares`
43×	`associate-/l*`
26×	`add-exp-log` `add-cbrt-cube`
24×	`distribute-lft-out--`
21×	`sqr-pow`
20×	`sqrt-prod`
12×	`associate-/r*`
10×	`pow1` `distribute-rgt-neg-in`
9×	`unpow-prod-down`
8×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-pow` `frac-2neg` `pow-prod-down` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `flip3-+` `unpow3` `div-sub` `cube-prod` `flip-+`

Counts

4 → 222

Calls

4 calls:

269.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) (* 2.0 a))
211.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4))))))
70.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))
19.0ms	(pow (* (* 4.0 a) c) 3)

series1.0s

Counts

4 → 12

Calls

4 calls:

361.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) (* 2.0 a))
363.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4))))))
202.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))
88.0ms	(pow (* (* 4.0 a) c) 3)

simplify2.4s

Counts

234 → 234

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	392	12095
1	918	11333
2	3791	10629
done	5000	10627

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2.0 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) a)
0.3b	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))
0.4b	(/ (+ 0 (* (* a c) 4.0)) (* (* 2.0 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) a))
0.7b	(pow (* (* 4.0 a) c) 3)

rewrite898.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
33×	`times-frac`
31×	`*-un-lft-identity`
26×	`add-exp-log` `add-cbrt-cube`
24×	`difference-of-squares`
23×	`add-cube-cbrt`
21×	`sqr-pow`
15×	`pow1`
13×	`associate-/l*`
9×	`unpow-prod-down` `prod-exp` `cbrt-unprod`
6×	`pow-prod-down`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `associate-l/` `associate-/r*` `log1p-expm1-u` `associate-/l/` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `flip3--` `pow-pow` `associate-r` `pow-exp` `flip--` `rem-cube-cbrt`
2×	`frac-2neg` `clear-num` `associate-/r/` `div-inv`
1×	`cube-mult` `pow-to-exp` `flip3-+` `unpow3` `div-sub` `cube-prod` `associate-l` `*-commutative` `flip-+`

Counts

4 → 138

Calls

4 calls:

382.0ms	(* (* 2.0 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) a)
59.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))
434.0ms	(/ (+ 0 (* (* a c) 4.0)) (* (* 2.0 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) a))
17.0ms	(pow (* (* 4.0 a) c) 3)

series940.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(* (* 2.0 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) a)
219.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))
310.0ms	(/ (+ 0 (* (* a c) 4.0)) (* (* 2.0 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) a))
91.0ms	(pow (* (* 4.0 a) c) 3)

simplify2.8s

Counts

150 → 150

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	301	6236
1	747	5890
2	3758	5218
done	5000	5216

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes195.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	45
1	38	43
done	38	43

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.1s	16128×	pre	80	true
907.0ms	4874×	body	160	valid
787.0ms	8128×	body	80	nan
294.0ms	1334×	body	320	valid
157.0ms	1792×	body	80	valid