Details

sample187.0ms

Algorithm

intervals

Results

55.0ms	190×	body	80	valid
49.0ms	43×	body	2560	valid
23.0ms	25×	body	1280	valid
15.0ms	85×	body	80	nan
9.0ms	13×	body	640	valid
6.0ms	11×	body	320	valid
4.0ms	3×	body	5120	valid
1.0ms	2×	body	160	valid

simplify153.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a) 2)
0.5b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
1.0b	(- (* b b) (* (* c a) 4))
24.5b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

90.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a) 2)
57.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms	(- (* b b) (* (* c a) 4))
19.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a) 2)
97.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
47.0ms	(- (* b b) (* (* c a) 4))
109.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.1s

Counts

165 → 165

Iterations

Iter	Nodes
done	2001
2	2001
1	676
0	278

prune765.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* 4 (* a c)))) b) (/ (/ 1 a) 2))
0.5b	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
1.0b	(- (* b b) (* 4 (* a c)))
24.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

135.0ms	(* (- (sqrt (- (* b b) (* 4 (* a c)))) b) (/ (/ 1 a) 2))
40.0ms	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
8.0ms	(- (* b b) (* 4 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (- (sqrt (- (* b b) (* 4 (* a c)))) b) (/ (/ 1 a) 2))
94.0ms	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
58.0ms	(- (* b b) (* 4 (* a c)))
101.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify739.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	2000
2	2000
1	724
0	263

prune665.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize46.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4 (* a c)))
1.0b	(- (* b b) (* 4 (* a c)))
24.5b	(sqrt (- (* b b) (* 4 (* a c))))
24.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

13.0ms	(- (* b b) (* 4 (* a c)))
12.0ms	(- (* b b) (* 4 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4 (* a c))))
12.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b b) (* 4 (* a c)))
64.0ms	(- (* b b) (* 4 (* a c)))
99.0ms	(sqrt (- (* b b) (* 4 (* a c))))
82.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	2005
4	2005
3	1783
2	454
1	156
0	61

prune396.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* c a) 4))
1.0b	(- (* b b) (* (* c a) 4))
24.5b	(sqrt (- (* b b) (* (* c a) 4)))
24.5b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

8.0ms	(- (* b b) (* (* c a) 4))
8.0ms	(- (* b b) (* (* c a) 4))
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))
8.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* (* c a) 4))
47.0ms	(- (* b b) (* (* c a) 4))
93.0ms	(sqrt (- (* b b) (* (* c a) 4)))
85.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	2001
4	2001
3	1900
2	486
1	161
0	63

prune463.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

regimes337.0ms

Accuracy

82.4% (4.9b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 33.3b

bsearch521.0ms

Steps

Iters	Range		Point
10	1.3859530517218358e-142	9.527435083115218e-125	9.354082991670835e-125
8	-4.336983712965787e+155	-6.488343844980391e+152	-9.088000531423294e+152

simplify7.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.1s	5926×	body	80	valid
999.0ms	1069×	body	2560	valid
612.0ms	874×	body	1280	valid
409.0ms	3004×	body	80	nan
299.0ms	467×	body	640	valid
120.0ms	108×	body	5120	valid
77.0ms	218×	body	320	valid
27.0ms	112×	body	160	valid