Details

sample85.0ms

Algorithm

intervals

Results

17.0ms	191×	body	80	valid
12.0ms	25×	body	2560	valid
10.0ms	26×	body	1280	valid
7.0ms	92×	body	80	nan
6.0ms	18×	body	640	valid
4.0ms	6×	body	5120	valid
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify97.0ms

Counts: 1 → 1

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize31.0ms

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))))

rewrite539.0ms

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:

455.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
113.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
85.0ms	(- (* b b) (* 4.0 (* a c)))
118.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify904.0ms

Counts: 82 → 82

prune361.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite318.0ms

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)))))
142.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
93.0ms	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series834.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
285.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
311.0ms	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
124.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts: 166 → 166

prune813.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize43.0ms

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 (* c a)))
24.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite141.0ms

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:

21.0ms	(- (* b b) (* 4.0 (* a c)))
43.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(/ (* 2.0 a) (* 4.0 (* c a)))
30.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* b b) (* 4.0 (* a c)))
100.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms	(/ (* 2.0 a) (* 4.0 (* c a)))
106.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts: 82 → 82

prune359.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 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))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

75.0ms	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.0ms	(- (* b b) (* 4.0 (* a c)))
29.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
64.0ms	(- (* b b) (* 4.0 (* a c)))
131.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
120.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify820.0ms

Counts: 94 → 94

prune330.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

regimes277.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 29.8b

bsearch288.0ms

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

simplify1.6s

end0.0ms

sample3.0s

Algorithm

intervals

Results

871.0ms	5781×	body	80	valid
622.0ms	1063×	body	2560	valid
417.0ms	893×	body	1280	valid
263.0ms	2847×	body	80	nan
159.0ms	502×	body	640	valid
88.0ms	235×	body	320	valid
56.0ms	118×	body	5120	valid
14.0ms	109×	body	160	valid