Details

sample125.0ms

Algorithm

intervals

Results

27.0ms	299×	body	80	nan
26.0ms	142×	body	160	valid
20.0ms	555×	pre	80	true
11.0ms	114×	body	80	valid

simplify124.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (33.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite209.0ms

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)))
18.0ms	(- (* b b) (* (* 4.0 a) c))
148.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(- (* b b) (* (* 4.0 a) c))
155.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
97.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

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

prune361.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* 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)))))

rewrite284.0ms

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:

54.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
120.0ms	(/ (/ (+ 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)))))

series674.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms	(- (* b b) (* (* 4.0 a) c))
231.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
275.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.2s

Counts

243 → 243

Iterations

Useful iterations: done (2.2s)

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

prune769.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (+ 0 (* (* a c) 4.0)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

rewrite449.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
135×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
125×	`add-cube-cbrt`
92×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
15×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
7×	`associate-r`
6×	`pow1`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `associate-*r/` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `times-frac` `diff-log` `div-exp` `associate-l` `associate-/l*`
2×	`associate-*l/` `associate-/r/` `associate-/l/`
1×	`associate--l-` `neg-sub0` `frac-2neg` `flip3-+` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 285

Calls

4 calls:

64.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
145.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
214.0ms	(/ (+ 0 (* (* a c) 4.0)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

series524.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
56.0ms	(- (* b b) (* (* 4.0 a) c))
244.0ms	(/ (+ 0 (* (* a c) 4.0)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

simplify2.3s

Counts

297 → 297

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	375	17028
1	786	11195
2	3235	8620
done	5001	8367

prune695.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
0.2b	(+ (* (- b) a) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (+ 0 (* (* a c) 4.0)) (* (+ (* (- b) a) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a)) 2.0))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-l`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
5×	`distribute-lft-neg-out`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u`
3×	`flip3-+` `times-frac` `associate-r` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `sqrt-div` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/` `distribute-neg-frac`
1×	`+-commutative` `neg-mul-1` `sub-neg` `distribute-rgt-out` `distribute-neg-out` `fma-def` `frac-2neg` `fma-neg` `diff-log` `unsub-neg` `prod-diff` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

62.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
10.0ms	(+ (* (- b) a) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
45.0ms	(/ (+ 0 (* (* a c) 4.0)) (* (+ (* (- b) a) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a)) 2.0))

series661.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
182.0ms	(+ (* (- b) a) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
72.0ms	(- (* b b) (* (* 4.0 a) c))
288.0ms	(/ (+ 0 (* (* a c) 4.0)) (* (+ (* (- b) a) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a)) 2.0))

simplify1.7s

Counts

109 → 109

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	208	2385
1	567	2069
2	2722	1819
done	5000	1816

prune546.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes245.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify14.0ms

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	21	28
1	34	26
2	45	25
3	55	25
4	58	25
done	58	25

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.3s	8495×	body	80	nan
892.0ms	4493×	body	160	valid
786.0ms	16495×	pre	80	true
278.0ms	3507×	body	80	valid