Details

sample63.0ms

Algorithm

intervals

Results

21.0ms	31×	body	2560	valid
9.0ms	205×	body	80	valid
6.0ms	31×	body	1280	valid
3.0ms	89×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize30.0ms

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)
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 171

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
51.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b_2 b_2) (* a c))
146.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
112.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2158
1	584
0	244

prune871.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
118.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
42.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b_2 b_2) (* a c))
138.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
123.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.9s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	3750
1	653
0	263

prune884.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize28.0ms

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)
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `neg-mul-1` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `distribute-frac-neg` `div-inv`

Counts

4 → 119

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
96.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b_2 b_2) (* a c))
110.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
89.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1901
1	473
0	199

prune747.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))) a)
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
3.4b	(exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
54×	`times-frac`
48×	`add-sqr-sqrt`
47×	`add-cube-cbrt`
36×	`log-prod` `exp-sum`
28×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
18×	`associate-/l*`
10×	`distribute-lft-out`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log-div` `exp-prod` `neg-mul-1` `exp-diff` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `flip3-+` `sqrt-prod` `flip-+`
2×	`sqrt-div` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `div-exp` `distribute-frac-neg` `log-pow` `div-inv` `flip--` `rem-exp-log`

Counts

4 → 147

Calls

4 calls:

115.0ms	(/ (- (exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))) a)
21.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))) a)
78.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
125.0ms	(exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

159 → 159

Iterations

Iter	Nodes
done	5000
2	1945
1	553
0	251

prune824.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

regimes368.0ms

Accuracy

87.2% (3.7b remaining)

Error of 8.9b against oracle of 5.2b and baseline of 34.1b

bsearch261.0ms

Steps

Iters	Range		Point
8	2.072994944964499e+129	8.571507078369983e+131	2.8233354537966034e+131
8	-8.904680992578465e-52	-2.849527055171251e-56	-5.546621280225112e-56
5	-1.0933554809811831e-44	-3.3311956001427126e-45	-3.4083546428522886e-45
7	-5.856362438573669e+138	-1.280729871585891e+137	-2.1229423973235387e+137

simplify15.0ms

Iterations

Iter	Nodes
done	47
2	47
1	46
0	36

end0.0ms

sample2.8s

Algorithm

intervals

Results

516.0ms	455×	body	640	valid
504.0ms	5835×	body	80	valid
466.0ms	1029×	body	2560	valid
352.0ms	922×	body	1280	valid
223.0ms	2877×	body	80	nan
88.0ms	122×	body	5120	valid
81.0ms	242×	body	320	valid
14.0ms	123×	body	160	valid