Details

sample35.0ms

Algorithm

intervals

Results

15.0ms	275×	body	80	valid
4.0ms	92×	body	80	nan

simplify96.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	20	38
1	36	38
2	66	37
3	121	37
4	149	37
5	161	37
6	162	37
done	162	37

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.5b

localize121.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
2.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 140

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify720.0ms

Counts

152 → 152

Iterations

Useful iterations: done (715.0ms)

Iter	Nodes	Cost
0	181	6137
1	406	4178
2	1191	3279
done	5001	3272

prune415.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize125.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
3.5b	(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* -2 b)))
4.8b	(/ (* a c) b)
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 79

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* -2 b)))
3.0ms	(/ (* a c) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* -2 b)))
20.0ms	(/ (* a c) b)
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify772.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (127.0ms)

Iter	Nodes	Cost
0	161	1254
1	370	1192
2	1374	1029
done	5000	1029

prune367.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize130.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.5b	(/ (* 2.0 c) (fma (* (/ a (sqrt b)) (/ c (sqrt b))) 2.0 (* -2 b)))
1.6b	(* (/ a (sqrt b)) (/ c (sqrt b)))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
51×	`times-frac`
33×	`add-cube-cbrt` `*-un-lft-identity`
27×	`sqrt-prod`
22×	`associate-r` `associate-l`
21×	`add-exp-log` `add-cbrt-cube`
9×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*` `div-inv`
2×	`flip3--` `sqrt-div` `flip--`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 131

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(/ (* 2.0 c) (fma (* (/ a (sqrt b)) (/ c (sqrt b))) 2.0 (* -2 b)))
23.0ms	(* (/ a (sqrt b)) (/ c (sqrt b)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
112.0ms	(/ (* 2.0 c) (fma (* (/ a (sqrt b)) (/ c (sqrt b))) 2.0 (* -2 b)))
43.0ms	(* (/ a (sqrt b)) (/ c (sqrt b)))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

143 → 143

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	264	2274
1	718	2155
2	2602	1738
done	5000	1690

prune594.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.6b

localize136.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (/ a (sqrt b)) (/ c (sqrt b)))
12.6b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
48×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
30×	`sqrt-prod`
22×	`associate-r` `associate-l`
16×	`add-exp-log` `add-cbrt-cube`
10×	`fma-def`
9×	`unswap-sqr`
8×	`pow1` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sum-log` `flip--` `div-inv`
1×	`+-commutative` `neg-sub0` `frac-times` `associate-+l-` `neg-mul-1` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

23.0ms	(* (/ a (sqrt b)) (/ c (sqrt b)))
6.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (/ a (sqrt b)) (/ c (sqrt b)))
87.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify969.0ms

Counts

146 → 146

Iterations

Useful iterations: done (966.0ms)

Iter	Nodes	Cost
0	220	2296
1	638	1826
2	2255	1615
done	5001	1568

prune699.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.6b

regimes155.0ms

Accuracy

91.1% (1.3b remaining)

Error of 7.9b against oracle of 6.6b and baseline of 21.4b

bsearch198.0ms

Steps

Iters	Range		Point
9	2.944023772201993e+37	9.447687191993962e+42	8.949232802794837e+42
8	-6.10058349091927e+155	-9.408528429616011e+151	-1.3696490745623736e+154

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	160
1	63	160
done	63	160

end0.0ms

sample871.0ms

Algorithm

intervals

Results

477.0ms	8720×	body	80	valid
142.0ms	2864×	body	80	nan