Details

sample77.0ms

Algorithm

intervals

Results

17.0ms	43×	body	2560	valid
12.0ms	190×	body	80	valid
8.0ms	24×	body	1280	valid
6.0ms	85×	body	80	nan
3.0ms	12×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify453.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	139
7	139
6	137
5	132
4	127
3	106
2	61
1	28
0	14

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize86.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite217.0ms

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:

126.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
21.0ms	(- (* b b) (* 4.0 (* a c)))
39.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series636.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
103.0ms	(- (* b b) (* 4.0 (* a c)))
194.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
129.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify7.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5029
3	4634
2	1246
1	406
0	159

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize67.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

199.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
21.0ms	(- (* b b) (* 4.0 (* a c)))
44.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series655.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
80.0ms	(- (* b b) (* 4.0 (* a c)))
180.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
152.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	1653
1	476
0	185

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize95.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `div-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `rec-exp` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-div` `1-exp` `associate-*r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

189.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
30.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series661.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
104.0ms	(- (* b b) (* 4.0 (* a c)))
150.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
151.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	5002
2	1656
1	499
0	181

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize94.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.8b	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (* 2.0 a))
17.8b	(- (* b b) (* b b))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

36.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
141.0ms	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (* 2.0 a))
18.0ms	(- (* b b) (* b b))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
32.0ms	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (* 2.0 a))
2.0ms	(- (* b b) (* b b))
116.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.8s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1180
1	408
0	158

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.7b

regimes1.4s

Accuracy

92.9% (1.8b remaining)

Error of 7.1b against oracle of 5.3b and baseline of 30.3b

bsearch334.0ms

Steps

Iters	Range		Point
8	4.664337482673326e-05	0.17679972651571432	0.17389787404847717
10	-2.8267030274469295e-306	1.290469777777001e-296	3.411004807395853e-303
8	-1.3198903247987554e+155	-1.1250773400730914e+152	-6.056690026719334e+153

simplify46.0ms

Iterations

Iter	Nodes
done	40
1	40
0	33

end0.0ms

sample3.5s

Algorithm

intervals

Results

919.0ms	5823×	body	80	valid
559.0ms	440×	body	640	valid
547.0ms	1103×	body	2560	valid
422.0ms	877×	body	1280	valid
351.0ms	2975×	body	80	nan
102.0ms	125×	body	5120	valid
93.0ms	249×	body	320	valid
17.0ms	121×	body	160	valid