Details

sample78.0ms

Algorithm

intervals

Results

21.0ms	6×	body	5120	valid
11.0ms	191×	body	80	valid
8.0ms	25×	body	2560	valid
7.0ms	26×	body	1280	valid
6.0ms	92×	body	80	nan
4.0ms	18×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify99.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite498.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

437.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
32.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
119.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms	(- (* b b) (* (* 4.0 a) c))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify904.0ms

Counts: 82 → 82

prune376.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize48.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`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 → 154

Calls

4 calls:

49.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
126.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
223.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
250.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts: 166 → 166

prune714.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.6b	(/ (* 2.0 a) (* 4.0 (* a c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
34.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts: 82 → 82

prune311.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
40×	`div-exp`
31×	`times-frac`
25×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`1-exp`
14×	`prod-exp`
13×	`associate-/l*`
11×	`cbrt-undiv`
10×	`add-log-exp`
6×	`rec-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`sqrt-prod` `cbrt-unprod`
3×	`diff-log` `div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

48.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
65.0ms	(- (* b b) (* (* 4.0 a) c))
127.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts: 127 → 127

prune396.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

regimes256.0ms

Accuracy

87.9% (2.9b remaining)

Error of 8.4b against oracle of 5.4b and baseline of 29.8b

bsearch255.0ms

Steps

Iters	Range		Point
10	1.1938117014962488e+94	7.783906932586822e+104	2.747556913740804e+103
5	-2.940400160132089e-121	-1.4047689219315184e-121	-1.4209185959447507e-121
5	-986703.3404809777	-447673.70935774763	-977083.9042033921

simplify848.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

821.0ms	5781×	body	80	valid
473.0ms	1063×	body	2560	valid
289.0ms	893×	body	1280	valid
270.0ms	2847×	body	80	nan
180.0ms	502×	body	640	valid
85.0ms	118×	body	5120	valid
67.0ms	235×	body	320	valid
12.0ms	109×	body	160	valid