Details

sample122.0ms

Algorithm

intervals

Results

29.0ms	186×	body	80	valid
24.0ms	41×	body	2560	valid
13.0ms	28×	body	1280	valid
10.0ms	108×	body	80	nan
6.0ms	17×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify154.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	35	17
2	109	17
3	154	17
4	170	17
done	170	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

101.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms	(- (* b b) (* 4.0 (* a c)))
24.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
63.0ms	(- (* b b) (* 4.0 (* a c)))
112.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
97.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts

89 → 89

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	157	1750
1	971	1623
done	5000	1482

prune425.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize42.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.1b	(/ (/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.3b	(/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
66×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
24×	`associate-/l*`
22×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-rgt-neg-in`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*` `associate-/r/`
5×	`pow1` `flip3-+` `flip-+`
4×	`div-inv`
3×	`sqrt-prod` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `sum-log` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `neg-log` `flip--`

Counts

4 → 131

Calls

4 calls:

23.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
125.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
90.0ms	(/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series762.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
240.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
300.0ms	(/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
120.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0m

Counts

143 → 143

Iterations

Useful iterations: done (2.0m)

Iter	Nodes	Cost
0	236	4221
done	5000	3717

prune573.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize27.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.2b	(* (/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
10.3b	(/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite386.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
51×	`add-exp-log`
34×	`times-frac`
32×	`add-sqr-sqrt`
27×	`add-cbrt-cube`
26×	`add-cube-cbrt`
21×	`associate-l`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out`
8×	`cbrt-undiv` `distribute-rgt-neg-in` `cbrt-unprod` `add-log-exp`
7×	`pow1` `associate-r`
5×	`associate-/r*`
4×	`rec-exp` `flip3-+` `1-exp` `associate-/r/` `flip-+`
3×	`sqrt-prod` `div-inv` `associate-/l*`
2×	`sqrt-div` `sum-log` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `frac-times` `associate-+l-` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip--`

Counts

4 → 132

Calls

4 calls:

41.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
208.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
117.0ms	(/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series787.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
254.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
294.0ms	(/ (+ 0 (* 4.0 (* a c))) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
115.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.2m

Counts

144 → 144

Iterations

Useful iterations: done (2.2m)

Iter	Nodes	Cost
0	247	4113
done	5000	3538

prune389.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.5b	(/ (* 4.0 (* a c)) (* 2.0 a))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
27.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series216.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* 4.0 (* a c)))
84.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify6.1s

Counts

79 → 79

Iterations

Useful iterations: done (6.1s)

Iter	Nodes	Cost
0	148	1248
1	1587	1110
done	5000	975

prune172.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

regimes152.0ms

Accuracy

77.2% (5.5b remaining)

Error of 11.3b against oracle of 5.9b and baseline of 30.0b

bsearch90.0ms

Steps

Iters	Range		Point
6	1.6855676195581707e-170	7.565529323099765e-170	7.455592343308264e-170
5	-2.3823986784004295e+101	-6.644598008915225e+100	-1.8696623466311214e+101

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	39
1	33	39
done	33	39

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	5893×	body	80	valid
425.0ms	1050×	body	2560	valid
281.0ms	831×	body	1280	valid
168.0ms	2996×	body	80	nan
85.0ms	449×	body	640	valid
49.0ms	135×	body	5120	valid
43.0ms	123×	body	160	valid
30.0ms	225×	body	320	valid