Details

sample329.0ms

Algorithm

intervals

Results

6.0ms	205×	body	80	valid
5.0ms	26×	body	2560	valid
4.0ms	26×	body	1280	valid
4.0ms	83×	body	80	nan
1.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7
done	49	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

78.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Counts

183 → 183

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5001	2063
done	5001	2063

prune346.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

91.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
31.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Counts

181 → 181

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	609	2985
1	2334	1993
2	5001	1940
done	5001	1940

prune309.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

74.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
76.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Counts

183 → 183

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5001	2063
done	5001	2063

prune284.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2 (/ b_2 a))
0.0b	(* 1/2 (/ c b_2))
0.0b	(- (* 1/2 (/ c b_2)) (* 2 (/ b_2 a)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`associate-r`
20×	`times-frac`
19×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l`
5×	`add-log-exp`
4×	`associate-*r/` `prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `frac-sub` `flip--`

Counts

3 → 85

Calls

3 calls:

17.0ms	(* 2 (/ b_2 a))
13.0ms	(* 1/2 (/ c b_2))
13.0ms	(- (* 1/2 (/ c b_2)) (* 2 (/ b_2 a)))

series85.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(* 2 (/ b_2 a))
18.0ms	(* 1/2 (/ c b_2))
45.0ms	(- (* 1/2 (/ c b_2)) (* 2 (/ b_2 a)))

simplify49.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	401	412
1	1827	386
2	5002	385
done	5002	385

prune180.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.1b

regimes345.0ms

Accuracy

81.3% (5.3b remaining)

Error of 10.9b against oracle of 5.6b and baseline of 33.9b

bsearch145.0ms

Steps

Iters	Range		Point
6	9.002760019060421e+93	3.662435776182418e+94	2.578980439773997e+94
11	-1.7080554663773614e-124	-7.974260657123443e-153	-1.642868784686772e-124
6	-1.8076892665891905e-94	-1.4815128553801987e-95	-2.3326374314473646e-95
6	-28599.531274954297	-2140.8108186447075	-2200.0149638847433

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	33
1	45	33
done	45	33

end0.0ms

sample1.0s

Algorithm

intervals

Results

197.0ms	1087×	body	2560	valid
179.0ms	5912×	body	80	valid
126.0ms	871×	body	1280	valid
82.0ms	2847×	body	80	nan
52.0ms	448×	body	640	valid
27.0ms	112×	body	5120	valid
18.0ms	213×	body	320	valid
6.0ms	102×	body	160	valid