Details

sample95.0ms

Algorithm

intervals

Results

20.0ms	193×	body	80	valid
20.0ms	31×	body	2560	valid
10.0ms	97×	body	80	nan
10.0ms	18×	body	1280	valid
8.0ms	18×	body	640	valid
4.0ms	6×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify210.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.4b	(- (* b b) (* 4 (* a c)))
0.6b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
23.1b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `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` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 81

Calls

4 calls:

94.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
10.0ms	(- (* b b) (* 4 (* a c)))
28.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
59.0ms	(- (* b b) (* 4 (* a c)))
131.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
113.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1254
1	400
0	154

prune540.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
0.4b	(+ (* b b) (* c (* a -4)))
0.6b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
23.1b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`insert-posit16`
3×	`distribute-rgt-neg-in`
2×	`cbrt-undiv` `flip3-+` `flip3--` `sqrt-div` `diff-log` `div-exp` `flip-+` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 80

Calls

4 calls:

101.0ms	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
20.0ms	(+ (* b b) (* c (* a -4)))
44.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
9.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
69.0ms	(+ (* b b) (* c (* a -4)))
125.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
109.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify1.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1334
1	412
0	156

prune463.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* c (* a -4)))))))
0.4b	(+ (* b b) (* c (* a -4)))
0.6b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
23.1b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3--` `div-inv` `flip--`
4×	`insert-posit16`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`flip3-+` `sqrt-div` `diff-log` `flip-+`
1×	`associate--l-` `neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 128

Calls

4 calls:

90.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* c (* a -4)))))))
21.0ms	(+ (* b b) (* c (* a -4)))
46.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
9.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series433.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* c (* a -4)))))))
75.0ms	(+ (* b b) (* c (* a -4)))
106.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
104.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify1.8s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
2	1858
1	585
0	231

prune628.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
23.1b	(sqrt (+ (* b b) (* c (* a -4))))
23.1b	(sqrt (+ (* b b) (* c (* a -4))))
23.1b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `flip3--` `neg-log` `flip--`

Counts

4 → 67

Calls

4 calls:

25.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
9.0ms	(sqrt (+ (* b b) (* c (* a -4))))
9.0ms	(sqrt (+ (* b b) (* c (* a -4))))
10.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
95.0ms	(sqrt (+ (* b b) (* c (* a -4))))
101.0ms	(sqrt (+ (* b b) (* c (* a -4))))
96.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify2.4s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
3	2165
2	644
1	211
0	88

prune636.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.2b

regimes407.0ms

Accuracy

82.8% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 33.1b

bsearch173.0ms

Steps

Iters	Range		Point
8	2.5230591910300896e+45	6.095379443414697e+48	5.6488521390017767e+48
8	-1.0278134165845925e-62	-2.127595877901746e-66	-1.1962309819144974e-65

simplify20.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	1066×	body	2560	valid
625.0ms	5849×	body	80	valid
498.0ms	903×	body	1280	valid
315.0ms	3069×	body	80	nan
206.0ms	464×	body	640	valid
137.0ms	122×	body	5120	valid
58.0ms	218×	body	320	valid
20.0ms	114×	body	160	valid