Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	39×	body	2560	valid
6.0ms	36×	body	1280	valid
6.0ms	165×	body	80	valid
3.0ms	87×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify494.0ms

Counts

82 → 82

Iterations

Useful iterations: done (492.0ms)

Iter	Nodes	Cost
0	154	1565
1	406	1461
2	1378	1245
done	5000	1235

prune219.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

54.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
2.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify655.0ms

Counts

92 → 92

Iterations

Useful iterations: done (652.0ms)

Iter	Nodes	Cost
0	181	1881
1	480	1671
2	1758	1400
done	5001	1399

prune219.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
5.2b	(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.9b	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

2.0ms	(- (* b b) (* (* 4.0 a) c))
50.0ms	(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
37.0ms	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
148.0ms	(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
182.0ms	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify835.0ms

Counts

160 → 160

Iterations

Useful iterations: done (829.0ms)

Iter	Nodes	Cost
0	252	5624
1	652	5105
2	2445	4357
done	5000	4343

prune434.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
14.6b	(/ (+ 0 (* 4.0 (* a c))) a)
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ (+ 0 (* 4.0 (* a c))) a)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(/ (+ 0 (* 4.0 (* a c))) a)
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify688.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (152.0ms)

Iter	Nodes	Cost
0	154	1396
1	354	1207
2	1387	1117
done	5000	1117

prune259.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes196.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 30.2b

bsearch172.0ms

Steps

Iters	Range	Point
8	2.1878188410446244e+107	3.8616146939177386e+111	3.154484283905746e+110
7	-5.014716607248407e-148	-7.269591797660499e-150	-7.386362469499411e-150
8	-1.4395777107888637e+138	-2.299948591329529e+133	-1.9827654008890006e+134

Iters

Range

Point

2.1878188410446244e+107

3.8616146939177386e+111

3.154484283905746e+110

-5.014716607248407e-148

-7.269591797660499e-150

-7.386362469499411e-150

-1.4395777107888637e+138

-2.299948591329529e+133

-1.9827654008890006e+134

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	66
1	48	66
done	48	66

end0.0ms

sample1.1s

Algorithm

intervals

Results

228.0ms	5914×	body	80	valid
225.0ms	1025×	body	2560	valid
162.0ms	891×	body	1280	valid
116.0ms	2997×	body	80	nan
66.0ms	450×	body	640	valid
29.0ms	107×	body	5120	valid
22.0ms	209×	body	320	valid
10.0ms	104×	body	160	valid