Details

sample86.0ms

Algorithm

intervals

Results

8.0ms	196×	body	80	valid
8.0ms	25×	body	2560	valid
5.0ms	24×	body	1280	valid
4.0ms	95×	body	80	nan
3.0ms	20×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms

Counts: 1 → 1

prune99.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

152.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
116.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify83.0ms

Counts: 92 → 92

prune413.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

69.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
11.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
42.0ms	(- (* b_2 b_2) (* a c))
124.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
117.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Counts: 174 → 174

prune672.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.8b	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0b	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
58×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
29×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
10×	`associate-/r*` `sqrt-prod` `associate-/r/`
8×	`add-log-exp`
7×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `div-exp` `flip--`
6×	`div-inv`
5×	`pow1`
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` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 136

Calls

4 calls:

47.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
110.0ms	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
76.0ms	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series694.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
212.0ms	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
293.0ms	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify78.0ms

Counts: 148 → 148

prune462.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b	(* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.8b	(/ (* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
27×	`associate-r`
25×	`times-frac`
19×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
5×	`cbrt-undiv` `div-exp`
4×	`distribute-rgt-neg-in` `prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-l` `associate-/r*` `flip--`
2×	`sqrt-div` `diff-log` `associate-*r/` `associate-/r/` `div-inv` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 103

Calls

4 calls:

91.0ms	(* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
41.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(/ (* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
32.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series777.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
127.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
243.0ms	(/ (* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
117.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Counts: 115 → 115

prune356.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.0b

regimes288.0ms

Accuracy

94.5% (1.4b remaining)

Error of 6.9b against oracle of 5.5b and baseline of 30.3b

bsearch150.0ms

Steps

Iters	Range	Point
9	1.126266178272183e+86	9.307219265615864e+90	3.1208661751691065e+88
6	-5.389093119374413e-224	-1.2009980409229352e-224	-1.7959174319660695e-224
4	-1.0608558557274316e+69	-6.171584865865653e+68	-1.039316568980459e+69

Iters

Range

Point

1.126266178272183e+86

9.307219265615864e+90

3.1208661751691065e+88

-5.389093119374413e-224

-1.2009980409229352e-224

-1.7959174319660695e-224

-1.0608558557274316e+69

-6.171584865865653e+68

-1.039316568980459e+69

simplify85.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

578.0ms	5838×	body	80	valid
559.0ms	1089×	body	2560	valid
465.0ms	222×	body	320	valid
359.0ms	916×	body	1280	valid
169.0ms	2916×	body	80	nan
134.0ms	443×	body	640	valid
56.0ms	132×	body	5120	valid
15.0ms	96×	body	160	valid