Details

sample95.0ms

Algorithm

intervals

Results

22.0ms	92×	body	80	nan
18.0ms	40×	body	2560	valid
13.0ms	181×	body	80	valid
9.0ms	26×	body	1280	valid
4.0ms	7×	body	5120	valid
4.0ms	14×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify155.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	64	17
3	114	17
4	130	17
5	137	17
6	141	17
done	141	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

112.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
18.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
54.0ms	(- (* b b) (* 4.0 (* a c)))
90.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
97.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.4s

Counts

89 → 89

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	157	1750
1	402	1650
2	1317	1474
3	4966	1459
done	5000	1459

prune306.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.8b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.4b	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

76.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
144.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
116.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series872.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
276.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
367.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
131.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

153 → 153

Iterations

Useful iterations: 2 (584.0ms)

Iter	Nodes	Cost
0	253	4579
1	619	4057
2	2460	3753
done	5000	3753

prune640.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize36.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.9b	(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
8.4b	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
51×	`add-exp-log`
44×	`*-un-lft-identity`
40×	`times-frac`
28×	`add-cube-cbrt`
27×	`add-cbrt-cube`
24×	`associate-l`
20×	`prod-exp`
16×	`div-exp` `difference-of-squares`
11×	`sqrt-prod`
8×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
7×	`pow1` `associate-r`
6×	`associate-/r*` `add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 139

Calls

4 calls:

45.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
193.0ms	(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
121.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series789.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
273.0ms	(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
297.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
105.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts

151 → 151

Iterations

Useful iterations: 2 (707.0ms)

Iter	Nodes	Cost
0	258	4293
1	678	3713
2	2668	3279
done	5000	3279

prune625.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.3b

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b	(/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
8.4b	(/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite343.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
32×	`add-sqr-sqrt`
30×	`times-frac`
21×	`*-un-lft-identity`
18×	`associate-/r*`
17×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/r/`
6×	`add-log-exp`
5×	`pow1` `flip3--` `flip--` `distribute-lft-out--`
4×	`div-inv`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l*`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 113

Calls

4 calls:

77.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
113.0ms	(/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
129.0ms	(/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series635.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
136.0ms	(/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
317.0ms	(/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
93.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

125 → 125

Iterations

Useful iterations: 2 (676.0ms)

Iter	Nodes	Cost
0	226	3312
1	606	3108
2	2861	2560
done	5001	2560

prune433.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

regimes238.0ms

Accuracy

95.7% (1.1b remaining)

Error of 6.3b against oracle of 5.3b and baseline of 29.6b

bsearch345.0ms

Steps

Iters	Range	Point
10	4.61796087672408e+142	1.3206820209921783e+153	3.1607591925776442e+143
10	-8.239971213717205e-281	-2.1361244948559116e-295	-2.182382645844659e-295
8	-1.769171722317776e+149	-1.7344183351890289e+146	-5.263290697710818e+146

Iters

Range

Point

4.61796087672408e+142

1.3206820209921783e+153

3.1607591925776442e+143

-8.239971213717205e-281

-2.1361244948559116e-295

-2.182382645844659e-295

-1.769171722317776e+149

-1.7344183351890289e+146

-5.263290697710818e+146

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	38	69
1	46	67
done	46	67

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	5729×	body	80	valid
693.0ms	2914×	body	80	nan
654.0ms	1095×	body	2560	valid
348.0ms	956×	body	1280	valid
158.0ms	457×	body	640	valid
105.0ms	119×	body	5120	valid
50.0ms	241×	body	320	valid
17.0ms	115×	body	160	valid