Details

sample57.0ms

Algorithm

intervals

Results

11.0ms	196×	body	80	valid
8.0ms	27×	body	2560	valid
8.0ms	31×	body	1280	valid
5.0ms	92×	body	80	nan
3.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify96.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

88.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
57.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
128.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	167	1697
1	452	1588
2	2090	1361
done	5001	1352

prune455.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 0 (- b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.9b	(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
19×	`prod-diff`
13×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`times-frac` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `fma-neg` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `sub0-neg` `pow1/2` `div-sub` `distribute-frac-neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 104

Calls

4 calls:

184.0ms	(/ (- 0 (- b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- 0 (- b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
95.0ms	(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
54.0ms	(- (* b b) (* (* 4.0 a) c))
87.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

116 → 116

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	214	3250
1	562	2548
2	2836	2111
done	5001	2086

prune343.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.9b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b	(- (* b b) (* (* 4.0 a) c))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

68.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
62.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
89.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
50.0ms	(- (* b b) (* (* 4.0 a) c))
86.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

164 → 164

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	261	4025
1	674	3498
2	3234	3147
done	5000	3070

prune374.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

localize28.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (* b b) (* (* 4.0 a) c))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

10.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b b) (* (* 4.0 a) c))
58.0ms	(- (* b b) (* (* 4.0 a) c))
85.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify642.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	71	1146
1	185	1058
2	843	952
done	5000	952

prune358.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.5b

regimes278.0ms

Accuracy

88% (3.5b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 34.4b

bsearch266.0ms

Steps

Iters	Range		Point
8	6412590.878131424	2116652649.122401	683389336.5992492
10	7.683585266441067e-90	6.043928490067347e-79	7.752932492055354e-90
8	-1.5489453231745737e+155	-2.021963087226922e+151	-2.2976245343188767e+152

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	69
1	43	66
2	46	66
done	46	66

end0.0ms

sample2.6s

Algorithm

intervals

Results

605.0ms	5754×	body	80	valid
601.0ms	917×	body	1280	valid
563.0ms	1069×	body	2560	valid
153.0ms	2912×	body	80	nan
135.0ms	488×	body	640	valid
48.0ms	109×	body	5120	valid
40.0ms	246×	body	320	valid
9.0ms	91×	body	160	valid