Details

sample54.0ms

Algorithm

intervals

Results

12.0ms	38×	body	2560	valid
10.0ms	178×	body	80	valid
7.0ms	28×	body	1280	valid
4.0ms	79×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify65.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize37.0ms

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)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite134.0ms

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:

75.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
36.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
127.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
80.0ms	(- (* b b) (* 4.0 (* a c)))
119.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify767.0ms

Counts: 82 → 82

prune362.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

176.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
23.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
116.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms	(- (* b b) (* 4.0 (* a c)))
111.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts: 92 → 92

prune364.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

99.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series529.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
131.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
66.0ms	(- (* b b) (* 4.0 (* a c)))
97.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts: 126 → 126

prune431.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize17.0ms

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)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite145.0ms

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:

94.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
28.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
135.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms	(- (* b b) (* 4.0 (* a c)))
118.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify735.0ms

Counts: 82 → 82

prune294.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.1b

regimes350.0ms

Accuracy

89.1% (3.1b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 34.3b

bsearch289.0ms

Steps

Iters	Range	Point
4	9.936283634246925e+77	1.8488019868481542e+78	1.4479393508684064e+78
11	-1.0472779812871276e-269	-2.473343252086336e-295	-3.07345244398039e-291
8	-6.990724105819741e+111	-2.6156774686163576e+108	-1.569310777886352e+111

Iters

Range

Point

9.936283634246925e+77

1.8488019868481542e+78

1.4479393508684064e+78

-1.0472779812871276e-269

-2.473343252086336e-295

-3.07345244398039e-291

-6.990724105819741e+111

-2.6156774686163576e+108

-1.569310777886352e+111

simplify581.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	5806×	body	80	valid
958.0ms	1087×	body	2560	valid
413.0ms	2994×	body	80	nan
379.0ms	930×	body	1280	valid
132.0ms	446×	body	640	valid
106.0ms	117×	body	5120	valid
81.0ms	210×	body	320	valid
17.0ms	116×	body	160	valid