Details

sample99.0ms

Algorithm

intervals

Results

33.0ms	38×	body	2560	valid
15.0ms	178×	body	80	valid
11.0ms	28×	body	1280	valid
6.0ms	79×	body	80	nan
4.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify130.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite153.0ms

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:

91.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
25.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
111.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(- (* b b) (* 4.0 (* a c)))
113.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	165	1697
1	434	1584
2	1464	1361
done	5000	1347

prune522.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
16×	`add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`fma-def` `add-log-exp`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`prod-exp`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `distribute-rgt-neg-in` `cbrt-unprod` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`flip3--` `flip3-+` `sqrt-div` `1-exp` `associate-*r/` `sum-log` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 87

Calls

4 calls:

71.0ms	(/ (* 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
46.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
29.0ms	(- (* b b) (* 4.0 (* a c)))
25.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series417.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (* 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
107.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
53.0ms	(- (* b b) (* 4.0 (* a c)))
110.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

99 → 99

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	174	1743
1	469	1560
2	1833	1275
done	5000	1265

prune435.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-exp-log`
44×	`prod-exp`
25×	`add-cbrt-cube`
14×	`*-un-lft-identity`
13×	`1-exp`
12×	`div-exp`
11×	`add-sqr-sqrt` `cbrt-unprod`
10×	`pow1` `add-cube-cbrt` `fma-def` `add-log-exp`
7×	`associate-r`
6×	`rec-exp`
5×	`associate-*r/`
4×	`cbrt-undiv` `expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3-+` `times-frac` `pow-prod-down` `sqrt-prod` `flip-+`
2×	`frac-times` `flip3--` `sqrt-div` `associate-*l/` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 113

Calls

4 calls:

156.0ms	(* (* 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
31.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (* 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
104.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
62.0ms	(- (* b b) (* 4.0 (* a c)))
100.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

125 → 125

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	216	2530
1	542	2108
2	1889	1718
done	5000	1697

prune480.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite65.0ms

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:

20.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b b) (* 4.0 (* a c)))
64.0ms	(- (* b b) (* 4.0 (* a c)))
97.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
127.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.8s

Counts

78 → 78

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	69	1146
1	169	1050
2	551	952
3	2261	952
done	5000	936

prune501.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.2b

regimes262.0ms

Accuracy

89.2% (3.1b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 34.4b

bsearch284.0ms

Steps

Iters	Range	Point
4	9.936283634246925e+77	1.8488019868481542e+78	1.4479393508684064e+78
11	-1.0472779812871276e-269	-2.473343252086336e-295	-2.0759438211365155e-290
8	-6.990724105819741e+111	-2.6156774686163576e+108	-1.569310777886352e+111

Iters

Range

Point

9.936283634246925e+77

1.8488019868481542e+78

1.4479393508684064e+78

-1.0472779812871276e-269

-2.473343252086336e-295

-2.0759438211365155e-290

-6.990724105819741e+111

-2.6156774686163576e+108

-1.569310777886352e+111

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	40	72
1	49	68
done	49	68

end0.0ms

sample4.0s

Algorithm

intervals

Results

876.0ms	930×	body	1280	valid
762.0ms	5806×	body	80	valid
696.0ms	1087×	body	2560	valid
503.0ms	210×	body	320	valid
296.0ms	2994×	body	80	nan
137.0ms	446×	body	640	valid
67.0ms	117×	body	5120	valid
17.0ms	116×	body	160	valid