Details

sample69.0ms

Algorithm

intervals

Results

14.0ms	40×	body	2560	valid
12.0ms	183×	body	80	valid
10.0ms	35×	body	1280	valid
5.0ms	79×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid
0.0ms	2×	body	320	valid

simplify119.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	129
5	129
4	120
3	87
2	46
1	25
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

84.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms	(- (* b b) (* 4.0 (* a c)))
24.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
65.0ms	(- (* b b) (* 4.0 (* a c)))
133.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
88.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1873
1	448
0	165

prune711.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize58.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (fma a (* c (- 4.0)) (pow b 2))))
3.6b	(/ (/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (fma a (* c (- 4.0)) (pow b 2))))) (* 2.0 a))
7.8b	(/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (fma a (* c (- 4.0)) (pow b 2)))))
24.2b	(sqrt (fma a (* c (- 4.0)) (pow b 2)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube` `add-exp-log`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `div-inv` `flip--`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `diff-log` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 230

Calls

4 calls:

24.0ms	(- (- b) (sqrt (fma a (* c (- 4.0)) (pow b 2))))
61.0ms	(/ (/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (fma a (* c (- 4.0)) (pow b 2))))) (* 2.0 a))
62.0ms	(/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (fma a (* c (- 4.0)) (pow b 2)))))
2.0ms	(sqrt (fma a (* c (- 4.0)) (pow b 2)))

series736.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (- b) (sqrt (fma a (* c (- 4.0)) (pow b 2))))
223.0ms	(/ (/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (fma a (* c (- 4.0)) (pow b 2))))) (* 2.0 a))
312.0ms	(/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (fma a (* c (- 4.0)) (pow b 2)))))
99.0ms	(sqrt (fma a (* c (- 4.0)) (pow b 2)))

simplify1.9s

Counts

242 → 242

Iterations

Iter	Nodes
done	5000
2	3999
1	781
0	319

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 2.0) (* (/ a a) (/ (* 4.0 c) (- (- b) (sqrt (fma a (* (- 4.0) c) (* b b)))))))
0.1b	(/ (* 4.0 c) (- (- b) (sqrt (fma a (* (- 4.0) c) (* b b)))))
1.6b	(- (- b) (sqrt (fma a (* (- 4.0) c) (* b b))))
24.2b	(sqrt (fma a (* (- 4.0) c) (* b b)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-exp-log`
74×	`add-cbrt-cube`
68×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`prod-exp`
60×	`prod-diff`
55×	`add-cube-cbrt`
44×	`div-exp`
36×	`sqrt-prod`
31×	`cbrt-unprod`
24×	`distribute-rgt-neg-in`
23×	`cbrt-undiv`
21×	`distribute-lft-neg-in`
16×	`times-frac`
13×	`associate-l`
10×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`rec-exp` `associate-/r*` `neg-mul-1` `1-exp`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `associate-*l/`
2×	`flip3--` `diff-log` `associate-/r/` `div-inv` `flip--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `neg-log` `-commutative` `associate-/l`

Counts

4 → 213

Calls

4 calls:

102.0ms	(* (/ 1 2.0) (* (/ a a) (/ (* 4.0 c) (- (- b) (sqrt (fma a (* (- 4.0) c) (* b b)))))))
27.0ms	(/ (* 4.0 c) (- (- b) (sqrt (fma a (* (- 4.0) c) (* b b)))))
43.0ms	(- (- b) (sqrt (fma a (* (- 4.0) c) (* b b))))
3.0ms	(sqrt (fma a (* (- 4.0) c) (* b b)))

series765.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(* (/ 1 2.0) (* (/ a a) (/ (* 4.0 c) (- (- b) (sqrt (fma a (* (- 4.0) c) (* b b)))))))
291.0ms	(/ (* 4.0 c) (- (- b) (sqrt (fma a (* (- 4.0) c) (* b b)))))
143.0ms	(- (- b) (sqrt (fma a (* (- 4.0) c) (* b b))))
109.0ms	(sqrt (fma a (* (- 4.0) c) (* b b)))

simplify542.0ms

Counts

225 → 225

Iterations

Iter	Nodes
done	5000
1	999
0	341

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* a 2.0) (- (sqrt (fma a (* c (- 4.0)) (pow b 2))) b))
0.2b	(/ 1 (/ (* a 2.0) (- (sqrt (fma a (* c (- 4.0)) (pow b 2))) b)))
1.3b	(- (sqrt (fma a (* c (- 4.0)) (pow b 2))) b)
24.2b	(sqrt (fma a (* c (- 4.0)) (pow b 2)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
66×	`times-frac`
56×	`*-un-lft-identity`
42×	`add-cube-cbrt`
30×	`add-exp-log`
22×	`sqrt-prod`
18×	`associate-/r*` `add-cbrt-cube` `prod-diff`
14×	`div-exp` `difference-of-squares`
11×	`associate-/r/`
7×	`cbrt-undiv` `distribute-lft-out--`
6×	`pow1` `flip3--` `fma-neg` `div-inv` `flip--` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 165

Calls

4 calls:

31.0ms	(/ (* a 2.0) (- (sqrt (fma a (* c (- 4.0)) (pow b 2))) b))
24.0ms	(/ 1 (/ (* a 2.0) (- (sqrt (fma a (* c (- 4.0)) (pow b 2))) b)))
17.0ms	(- (sqrt (fma a (* c (- 4.0)) (pow b 2))) b)
2.0ms	(sqrt (fma a (* c (- 4.0)) (pow b 2)))

series784.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(/ (* a 2.0) (- (sqrt (fma a (* c (- 4.0)) (pow b 2))) b))
175.0ms	(/ 1 (/ (* a 2.0) (- (sqrt (fma a (* c (- 4.0)) (pow b 2))) b)))
136.0ms	(- (sqrt (fma a (* c (- 4.0)) (pow b 2))) b)
125.0ms	(sqrt (fma a (* c (- 4.0)) (pow b 2)))

simplify1.3s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
2	2841
1	607
0	242

prune887.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.6b

regimes327.0ms

Accuracy

93.6% (1.6b remaining)

Error of 6.9b against oracle of 5.4b and baseline of 29.6b

bsearch263.0ms

Steps

Iters	Range	Point
9	2.1340360609407003e+79	6.102484722804822e+84	2.3453700250865973e+84
6	-9.106238092000907e-243	-2.101224228167501e-243	-2.1209008810311313e-243
8	-7.706925888451307e+24	-4.0529501114613944e+21	-7.604193036648139e+24

Iters

Range

Point

2.1340360609407003e+79

6.102484722804822e+84

2.3453700250865973e+84

-9.106238092000907e-243

-2.101224228167501e-243

-2.1209008810311313e-243

-7.706925888451307e+24

-4.0529501114613944e+21

-7.604193036648139e+24

simplify8.0ms

Iterations

Iter	Nodes
done	57
2	57
1	54
0	44

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.3s	1094×	body	2560	valid
708.0ms	5779×	body	80	valid
644.0ms	448×	body	640	valid
373.0ms	931×	body	1280	valid
291.0ms	2886×	body	80	nan
60.0ms	93×	body	5120	valid
54.0ms	226×	body	320	valid
19.0ms	125×	body	160	valid