Details

sample103.0ms

Algorithm

intervals

Results

29.0ms	38×	body	2560	valid
18.0ms	178×	body	80	valid
13.0ms	28×	body	1280	valid
7.0ms	79×	body	80	nan
4.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify171.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

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

localize17.0ms

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))))

rewrite195.0ms

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:

115.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
28.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(- (* b b) (* 4.0 (* a c)))
34.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series824.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
110.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
455.0ms	(- (* b b) (* 4.0 (* a c)))
116.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

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

prune480.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize32.0ms

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))))

rewrite176.0ms

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:

114.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
27.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(- (* b b) (* 4.0 (* a c)))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
113.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms	(- (* b b) (* 4.0 (* a c)))
137.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

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

prune448.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- 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))))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

182.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
32.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
128.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms	(- (* b b) (* 4.0 (* a c)))
91.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

112 → 112

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	192	2017
1	499	1794
2	1766	1516
done	5001	1490

prune623.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.2b

localize47.0ms

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))))

rewrite73.0ms

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)))
20.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b b) (* 4.0 (* a c)))
69.0ms	(- (* b b) (* 4.0 (* a c)))
104.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
131.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.7s

Counts

78 → 78

Iterations

Useful iterations: done (2.7s)

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

prune451.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.2b

regimes296.0ms

Accuracy

89.2% (3.1b remaining)

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

bsearch308.0ms

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 (4.0ms)

Iter	Nodes	Cost
0	44	78
1	55	68
done	55	68

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	1087×	body	2560	valid
666.0ms	5806×	body	80	valid
424.0ms	930×	body	1280	valid
268.0ms	2994×	body	80	nan
180.0ms	446×	body	640	valid
73.0ms	117×	body	5120	valid
44.0ms	210×	body	320	valid
17.0ms	116×	body	160	valid