Details

sample75.0ms

Algorithm

intervals

Results

25.0ms	43×	body	2560	valid
10.0ms	164×	body	80	valid
8.0ms	32×	body	1280	valid
4.0ms	80×	body	80	nan
3.0ms	8×	body	5120	valid
3.0ms	16×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	111
5	111
4	102
3	78
2	44
1	24
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

18.0ms	(* (* 4.0 a) c)
69.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
18.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* 4.0 a) c)
132.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
124.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2486
1	473
0	172

prune516.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.8b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
6.9b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite170.0ms

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:

18.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
64.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series731.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
207.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
297.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

166 → 166

Iterations

Iter	Nodes
done	5000
2	3736
1	659
0	254

prune915.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b	(* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.8b	(/ (* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) a)
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-cbrt-cube` `add-exp-log`
42×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
28×	`times-frac`
27×	`associate-r`
21×	`cbrt-undiv` `div-exp`
20×	`add-cube-cbrt`
16×	`prod-exp` `cbrt-unprod`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `associate-l` `sqrt-prod`
4×	`distribute-rgt-neg-in`
3×	`associate-/r*` `flip3--` `div-inv` `flip--` `associate-/l/`
2×	`frac-times` `sqrt-div` `diff-log` `associate-l/` `associate-r/` `associate-/r/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `-commutative` `associate-/l`

Counts

4 → 127

Calls

4 calls:

37.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
143.0ms	(* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
49.0ms	(/ (* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) a)
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
240.0ms	(* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
173.0ms	(/ (* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) a)
118.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify373.0ms

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
1	795
0	262

prune765.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

localize92.0ms

Local error

Found 4 expressions with local error:

13.2b	(cbrt (+ 0 (* (* 4.0 a) c)))
13.2b	(cbrt (+ 0 (* (* 4.0 a) c)))
13.2b	(cbrt (* 4.0 (* a c)))
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`cbrt-prod` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`cbrt-div` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 50

Calls

4 calls:

2.0ms	(cbrt (+ 0 (* (* 4.0 a) c)))
2.0ms	(cbrt (+ 0 (* (* 4.0 a) c)))
8.0ms	(cbrt (* 4.0 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (+ 0 (* (* 4.0 a) c)))
142.0ms	(cbrt (+ 0 (* (* 4.0 a) c)))
160.0ms	(cbrt (* 4.0 (* a c)))
98.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify716.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5002
2	1143
1	288
0	116

prune523.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

regimes335.0ms

Accuracy

88.5% (3.0b remaining)

Error of 8.3b against oracle of 5.3b and baseline of 31.7b

bsearch213.0ms

Steps

Iters	Range		Point
4	1.2765290296533779e-46	2.1214586855945932e-46	2.08020794476041e-46
8	2.7577530367966546e-234	6.998473114738861e-230	2.829508521752968e-234
7	-5.856362438573669e+138	-1.280729871585891e+137	-3.450829996567048e+138

simplify5.0ms

Iterations

Iter	Nodes
done	52
1	52
0	41

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	5792×	body	80	valid
613.0ms	1094×	body	2560	valid
464.0ms	887×	body	1280	valid
259.0ms	2874×	body	80	nan
126.0ms	467×	body	640	valid
94.0ms	243×	body	320	valid
57.0ms	108×	body	5120	valid
15.0ms	117×	body	160	valid