Details

sample99.0ms

Algorithm

intervals

Results

22.0ms	32×	body	1280	valid
21.0ms	182×	body	80	valid
20.0ms	30×	body	2560	valid
10.0ms	86×	body	80	nan
4.0ms	5×	body	5120	valid
3.0ms	9×	body	640	valid
3.0ms	9×	body	320	valid
2.0ms	7×	body	160	valid

simplify83.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.4b	(- (* b b) (* (* c a) 4))
2.5b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
21.7b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

75.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
16.0ms	(- (* b b) (* (* c a) 4))
65.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
86.0ms	(- (* b b) (* (* c a) 4))
123.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
116.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.5s

Counts

100 → 100

Iterations

Iter	Nodes
3	3521
2	1091
1	400
0	161

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
1.4b	(- (* b b) (* (* c a) 4))
2.5b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
21.7b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `insert-posit16` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

128.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
13.0ms	(- (* b b) (* (* c a) 4))
33.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
58.0ms	(- (* b b) (* (* c a) 4))
120.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
96.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.4s

Counts

101 → 101

Iterations

Iter	Nodes
3	4877
2	1495
1	462
0	181

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
1.4b	(- (* b b) (* (* c a) 4))
2.5b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
21.7b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-l` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `prod-exp` `insert-posit16` `difference-of-squares`
3×	`unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `diff-log` `div-exp` `associate-*r/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 92

Calls

4 calls:

114.0ms	(* (/ 1 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
7.0ms	(- (* b b) (* (* c a) 4))
45.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (/ 1 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
58.0ms	(- (* b b) (* (* c a) 4))
125.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
116.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.2s

Counts

104 → 104

Iterations

Iter	Nodes
3	4499
2	1452
1	444
0	169

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* a (* c -4))
1.4b	(+ (* a (* c -4)) (* b b))
2.5b	(- (sqrt (+ (* a (* c -4)) (* b b))) b)
21.7b	(sqrt (+ (* a (* c -4)) (* b b)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-r` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

13.0ms	(* a (* c -4))
18.0ms	(+ (* a (* c -4)) (* b b))
107.0ms	(- (sqrt (+ (* a (* c -4)) (* b b))) b)
20.0ms	(sqrt (+ (* a (* c -4)) (* b b)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* a (* c -4))
104.0ms	(+ (* a (* c -4)) (* b b))
150.0ms	(- (sqrt (+ (* a (* c -4)) (* b b))) b)
131.0ms	(sqrt (+ (* a (* c -4)) (* b b)))

simplify1.4s

Counts

75 → 75

Iterations

Iter	Nodes
3	3373
2	863
1	262
0	111

prune777.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.0b

regimes291.0ms

Accuracy

82.6% (4.8b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 33.2b

bsearch187.0ms

Steps

Iters	Range		Point
7	6.1141969789339016e-111	5.505912162480727e-109	9.831724396970673e-110
8	-1.7996802595953755e+64	-1.2634430355867738e+61	-1.7194502457644758e+64

simplify9.0ms

Iterations

Iter	Nodes
2	36
1	36
0	29

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.7s	1109×	body	2560	valid
1.1s	885×	body	1280	valid
1.0s	5850×	body	80	valid
407.0ms	2882×	body	80	nan
255.0ms	419×	body	640	valid
122.0ms	229×	body	320	valid
118.0ms	114×	body	5120	valid
33.0ms	127×	body	160	valid