Details

sample96.0ms

Algorithm

intervals

Results

19.0ms	37×	body	2560	valid
17.0ms	192×	body	80	valid
12.0ms	30×	body	1280	valid
7.0ms	81×	body	80	nan
4.0ms	12×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify91.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	104
5	104
4	96
3	76
2	41
1	21
0	12

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
1.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

16.0ms	(* (* 3.0 a) c)
12.0ms	(- (* b b) (* (* 3.0 a) c))
61.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* 3.0 a) c)
59.0ms	(- (* b b) (* (* 3.0 a) c))
124.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
106.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.5s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1593
1	302
0	120

prune528.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (* a 3.0))
0.4b	(- (* b b) (* c (* a 3.0)))
1.2b	(- (sqrt (- (* b b) (* c (* a 3.0)))) b)
22.3b	(sqrt (- (* b b) (* c (* a 3.0))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

13.0ms	(* c (* a 3.0))
7.0ms	(- (* b b) (* c (* a 3.0)))
38.0ms	(- (sqrt (- (* b b) (* c (* a 3.0)))) b)
8.0ms	(sqrt (- (* b b) (* c (* a 3.0))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* c (* a 3.0))
83.0ms	(- (* b b) (* c (* a 3.0)))
152.0ms	(- (sqrt (- (* b b) (* c (* a 3.0)))) b)
110.0ms	(sqrt (- (* b b) (* c (* a 3.0))))

simplify666.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1225
1	288
0	119

prune397.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
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×	`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*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
11.0ms	(- (* b b) (* (* 3.0 a) c))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
65.0ms	(- (* b b) (* (* 3.0 a) c))
106.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
107.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify924.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1881
1	414
0	154

prune456.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))
4.2b	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))) (* 3.0 a))
9.8b	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0)))))
22.3b	(sqrt (- (* b b) (* (* a c) 3.0)))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `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 → 154

Calls

4 calls:

36.0ms	(- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))
123.0ms	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))) (* 3.0 a))
50.0ms	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0)))))
7.0ms	(sqrt (- (* b b) (* (* a c) 3.0)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))
208.0ms	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))) (* 3.0 a))
246.0ms	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0)))))
99.0ms	(sqrt (- (* b b) (* (* a c) 3.0)))

simplify1.9s

Counts

166 → 166

Iterations

Iter	Nodes
done	5000
2	3835
1	657
0	253

prune766.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

regimes578.0ms

Accuracy

86.2% (3.7b remaining)

Error of 9.5b against oracle of 5.8b and baseline of 32.6b

bsearch314.0ms

Steps

Iters	Range		Point
8	2.3014094695989884e+42	1.986834535258986e+46	5.4949852679786824e+45
9	4.53350468731089e-289	7.749510238072602e-284	7.476271090407513e-284
10	-6.622314338184697e+74	-4.7924972520805885e+61	-2.1597879728155908e+74

simplify5.0ms

Iterations

Iter	Nodes
done	54
1	54
0	43

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	1070×	body	2560	valid
475.0ms	5831×	body	80	valid
419.0ms	936×	body	1280	valid
220.0ms	2812×	body	80	nan
134.0ms	451×	body	640	valid
118.0ms	94×	body	5120	valid
91.0ms	224×	body	320	valid
16.0ms	115×	body	160	valid