Details

sample182.0ms

Algorithm

intervals

Results

47.0ms	256×	body	80	valid
46.0ms	260×	body	80	nan

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1302
3	350
2	100
1	50
0	28

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
1.7b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.0b	(/ (* z (sqrt (+ t a))) t)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub`
16×	`add-cbrt-cube` `add-exp-log`
15×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`associate-r`
6×	`pow1` `times-frac` `associate--r+` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `associate-/r` `sqrt-div` `div-exp` `insert-posit16` `associate-/l`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `associate-*l/` `associate--l+` `div-inv` `unswap-sqr` `associate-/l/`
1×	`diff-log` `pow-prod-down` `*-commutative` `distribute-lft-out`

Counts

4 → 105

Calls

4 calls:

43.0ms	(* z (sqrt (+ t a)))
13.0ms	(/ 2.0 (* t 3.0))
33.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
24.0ms	(/ (* z (sqrt (+ t a))) t)

series510.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* z (sqrt (+ t a)))
33.0ms	(/ 2.0 (* t 3.0))
263.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
112.0ms	(/ (* z (sqrt (+ t a))) t)

simplify2.7s

Counts

117 → 117

Iterations

Iter	Nodes
done	5033
2	4401
1	1044
0	350

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
1.7b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (* (/ (/ 2.0 t) 3.0) (* (/ (/ 2.0 t) 3.0) (/ (/ 2.0 t) 3.0)))))))
5.0b	(/ (* z (sqrt (+ t a))) t)
40.2b	(cbrt (* (/ (/ 2.0 t) 3.0) (* (/ (/ 2.0 t) 3.0) (/ (/ 2.0 t) 3.0))))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

92×	`frac-sub`
67×	`frac-times`
55×	`associate-*r/`
49×	`cbrt-div`
23×	`flip3-+` `associate-*l/` `flip-+`
21×	`flip3--` `flip--`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
9×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow1` `associate--r+` `add-log-exp`
5×	`sqrt-prod`
4×	`sqrt-div` `insert-posit16`
3×	`distribute-rgt-in` `associate-/r` `sub-neg` `distribute-lft-in` `times-frac` `associate-l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`cbrt-prod` `clear-num` `frac-2neg` `pow1/3` `diff-log` `cube-unmult` `pow-prod-down` `-commutative` `rem-cbrt-cube` `div-inv` `distribute-lft-out` `associate-/l`

Counts

4 → 137

Calls

4 calls:

42.0ms	(* z (sqrt (+ t a)))
132.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (* (/ (/ 2.0 t) 3.0) (* (/ (/ 2.0 t) 3.0) (/ (/ 2.0 t) 3.0)))))))
15.0ms	(/ (* z (sqrt (+ t a))) t)
67.0ms	(cbrt (* (/ (/ 2.0 t) 3.0) (* (/ (/ 2.0 t) 3.0) (/ (/ 2.0 t) 3.0))))

series742.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* z (sqrt (+ t a)))
483.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (* (/ (/ 2.0 t) 3.0) (* (/ (/ 2.0 t) 3.0) (/ (/ 2.0 t) 3.0)))))))
102.0ms	(/ (* z (sqrt (+ t a))) t)
56.0ms	(cbrt (* (/ (/ 2.0 t) 3.0) (* (/ (/ 2.0 t) 3.0) (/ (/ 2.0 t) 3.0))))

simplify2.1s

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
1	1454
0	525

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize102.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
1.7b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (posit16->real (real->posit16 (/ (/ 2.0 t) 3.0))))))
5.0b	(/ (* z (sqrt (+ t a))) t)
59.9b	(posit16->real (real->posit16 (/ (/ 2.0 t) 3.0)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

40.0ms	(* z (sqrt (+ t a)))
36.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (posit16->real (real->posit16 (/ (/ 2.0 t) 3.0))))))
19.0ms	(/ (* z (sqrt (+ t a))) t)
1.0ms	(posit16->real (real->posit16 (/ (/ 2.0 t) 3.0)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* z (sqrt (+ t a)))
300.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (posit16->real (real->posit16 (/ (/ 2.0 t) 3.0))))))
127.0ms	(/ (* z (sqrt (+ t a))) t)
28.0ms	(posit16->real (real->posit16 (/ (/ 2.0 t) 3.0)))

simplify2.8s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	3281
1	786
0	272

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* t 3.0))
1.7b	(- (/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.0b	(/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t)
55.2b	(posit16->real (real->posit16 (* z (sqrt (+ t a)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
11×	`add-cbrt-cube` `add-exp-log`
9×	`flip3--` `flip--`
8×	`frac-times`
6×	`associate-/l*` `associate--r+` `add-log-exp`
4×	`pow1` `associate-/r` `associate-r/` `insert-posit16`
3×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `flip3-+` `div-exp` `flip-+`
2×	`clear-num` `frac-2neg` `associate-*l/` `associate--l+` `div-inv`
1×	`diff-log` `prod-exp` `cbrt-unprod` `remove-posit16`

Counts

4 → 92

Calls

4 calls:

11.0ms	(/ 2.0 (* t 3.0))
44.0ms	(- (/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.0ms	(/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t)
0.0ms	(posit16->real (real->posit16 (* z (sqrt (+ t a)))))

series509.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 2.0 (* t 3.0))
270.0ms	(- (/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
113.0ms	(/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t)
89.0ms	(posit16->real (real->posit16 (* z (sqrt (+ t a)))))

simplify2.3s

Counts

104 → 104

Iterations

Iter	Nodes
done	5063
2	3989
1	923
0	321

prune1.7s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes860.0ms

Accuracy

8.3% (5.9b remaining)

Error of 6.9b against oracle of 1.0b and baseline of 7.4b

bsearch171.0ms

Steps

Iters	Range		Point
5	-9.692925807459561e-256	-3.587855715163873e-256	-6.383228782902789e-256

simplify41.0ms

Iterations

Iter	Nodes
done	56
1	56
0	44

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.0s	8062×	body	80	nan
1.5s	8000×	body	80	valid