Details

sample86.0ms

Algorithm

intervals

Results

29.0ms	191×	body	80	valid
9.0ms	25×	body	2560	valid
8.0ms	26×	body	1280	valid
6.0ms	92×	body	80	nan
5.0ms	18×	body	640	valid
3.0ms	6×	body	5120	valid
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify98.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite172.0ms

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:

111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
39.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series506.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
125.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
74.0ms	(- (* b b) (* (* 3.0 a) c))
121.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify749.0ms

Counts: 82 → 82

prune358.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.2b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.4b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite209.0ms

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:

28.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
96.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
64.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
166.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
223.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
102.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.9s

Counts: 166 → 166

prune809.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.1b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
10.4b	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

38.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
77.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
68.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
188.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
203.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
91.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify396.0ms

Counts: 128 → 128

prune461.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize30.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 3.0 c) a))))
2.2b	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a)))) (* a c)))) (* 3.0 a))
10.5b	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a)))) (* a c))
24.3b	(sqrt (- (* b b) (* (* 3.0 c) a)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-exp-log`
54×	`add-cbrt-cube`
40×	`div-exp`
30×	`prod-exp`
22×	`cbrt-undiv`
20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
16×	`cbrt-unprod`
8×	`times-frac` `1-exp` `associate-/l*` `add-log-exp`
7×	`add-cube-cbrt`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
3×	`flip3--` `distribute-rgt-neg-in` `flip--` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num` `associate-/r*` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub` `associate-*r/` `neg-log`

Counts

4 → 107

Calls

4 calls:

28.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 c) a))))
61.0ms	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a)))) (* a c)))) (* 3.0 a))
110.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a)))) (* a c))
22.0ms	(sqrt (- (* b b) (* (* 3.0 c) a)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 c) a))))
123.0ms	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a)))) (* a c)))) (* 3.0 a))
113.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a)))) (* a c))
91.0ms	(sqrt (- (* b b) (* (* 3.0 c) a)))

simplify1.3s

Counts: 119 → 119

prune263.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.9b

regimes303.0ms

Accuracy

89.4% (2.9b remaining)

Error of 8.3b against oracle of 5.4b and baseline of 32.6b

bsearch284.0ms

Steps

Iters	Range	Point
10	1.1938117014962488e+94	7.783906932586822e+104	1.4426376927073088e+94
11	6.58330393002148e-278	1.956105787515721e-252	6.517962713462532e-274
8	-1.3338943710063638e+156	-3.6861430206638164e+153	-1.0742365643007952e+154

Iters

Range

Point

1.1938117014962488e+94

7.783906932586822e+104

1.4426376927073088e+94

6.58330393002148e-278

1.956105787515721e-252

6.517962713462532e-274

-1.3338943710063638e+156

-3.6861430206638164e+153

-1.0742365643007952e+154

simplify577.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

877.0ms	1063×	body	2560	valid
472.0ms	5780×	body	80	valid
342.0ms	896×	body	1280	valid
305.0ms	2847×	body	80	nan
146.0ms	499×	body	640	valid
57.0ms	118×	body	5120	valid
41.0ms	235×	body	320	valid
12.0ms	109×	body	160	valid