Details

sample54.0ms

Algorithm

intervals

Results

10.0ms	191×	body	80	valid
7.0ms	25×	body	2560	valid
6.0ms	26×	body	1280	valid
4.0ms	92×	body	80	nan
3.0ms	18×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify94.0ms

Counts: 1 → 1

prune4.0ms

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)))

rewrite153.0ms

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:

81.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
29.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
130.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms	(- (* b b) (* (* 4.0 a) c))
103.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify682.0ms

Counts: 82 → 82

prune258.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize32.0ms

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)))

rewrite246.0ms

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:

27.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
102.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
89.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
180.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
200.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts: 166 → 166

prune658.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize21.0ms

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)))

rewrite92.0ms

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:

10.0ms	(- (* b b) (* (* 4.0 a) c))
33.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
35.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
85.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify887.0ms

Counts: 82 → 82

prune370.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 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)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

295×	`add-exp-log`
166×	`div-exp`
119×	`prod-exp`
64×	`1-exp`
60×	`add-cbrt-cube`
34×	`rec-exp`
31×	`times-frac`
26×	`cbrt-undiv`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`cbrt-unprod`
14×	`associate-/r/`
13×	`associate-/l*`
11×	`frac-times`
10×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`associate-*l/`
5×	`pow1` `associate-*r/`
4×	`sqrt-prod`
3×	`diff-log` `un-div-inv` `div-inv`
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` `pow1/2` `neg-log` `clear-num` `associate-/r*` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

113.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
33.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
55.0ms	(- (* b b) (* (* 4.0 a) c))
86.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify391.0ms

Counts: 191 → 191

prune327.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

regimes171.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 29.8b

bsearch235.0ms

Steps

Iters	Range	Point
10	1.1938117014962488e+94	7.783906932586822e+104	1.2749218400875242e+104
8	-1.373264203576674e-281	-7.437867491150874e-285	-1.0518595521494322e-283
8	-9.386613231324957e+115	-9.035077376741492e+112	-3.01058925795013e+115

Iters

Range

Point

1.1938117014962488e+94

7.783906932586822e+104

1.2749218400875242e+104

-1.373264203576674e-281

-7.437867491150874e-285

-1.0518595521494322e-283

-9.386613231324957e+115

-9.035077376741492e+112

-3.01058925795013e+115

simplify728.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

830.0ms	5781×	body	80	valid
711.0ms	1063×	body	2560	valid
289.0ms	893×	body	1280	valid
174.0ms	2847×	body	80	nan
98.0ms	502×	body	640	valid
75.0ms	118×	body	5120	valid
39.0ms	235×	body	320	valid
11.0ms	109×	body	160	valid