Details

sample230.0ms

Algorithm

intervals

Results

18.0ms	40×	body	1280	valid
17.0ms	32×	body	2560	valid
16.0ms	183×	body	80	valid
8.0ms	98×	body	80	nan
7.0ms	13×	body	640	valid
3.0ms	9×	body	320	valid
3.0ms	4×	body	5120	valid
1.0ms	3×	body	160	valid

simplify8.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.1b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite174.0ms

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:

8.0ms	(- (* b_2 b_2) (* a c))
92.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
24.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
47.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b_2 b_2) (* a c))
170.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
116.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify99.0ms

Counts: 92 → 92

prune348.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.6b	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
7.2b	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite218.0ms

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:

34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
95.0ms	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
66.0ms	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series699.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
196.0ms	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
257.0ms	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify77.0ms

Counts: 148 → 148

prune544.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.3b	(* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
3.6b	(/ (* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite263.0ms

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:

24.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
144.0ms	(* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
74.0ms	(/ (* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series705.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
260.0ms	(* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
231.0ms	(/ (* a (/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify78.0ms

Counts: 115 → 115

prune437.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.4b	(/ 1 (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

144.0ms	(* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
113.0ms	(/ 1 (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
57.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
280.0ms	(/ 1 (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
120.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
119.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Counts: 135 → 135

prune442.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

regimes199.0ms

Accuracy

91.1% (2.2b remaining)

Error of 7.9b against oracle of 5.7b and baseline of 30.1b

bsearch205.0ms

Steps

Iters	Range		Point
8	6.830756908302209e+71	2.772849885831336e+75	2.730494439370032e+75
9	-9.135136184186538e-305	3.248654678508165e-307	-7.171823963984e-310
8	-0.19973978490672425	-0.00024022063624403673	-0.1973887031618164

simplify89.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	1082×	body	2560	valid
653.0ms	5889×	body	80	valid
399.0ms	897×	body	1280	valid
171.0ms	2883×	body	80	nan
104.0ms	432×	body	640	valid
50.0ms	103×	body	5120	valid
39.0ms	226×	body	320	valid
12.0ms	101×	body	160	valid