Details

sample254.0ms

Algorithm

intervals

Results

114.0ms	256×	body	80	valid
85.0ms	269×	body	80	nan

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
5	2003
4	1440
3	365
2	102
1	50
0	28

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2.0 (* t 3.0))
0.2b	(* z (sqrt (+ a t)))
2.6b	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (/ (* z (sqrt (+ a t))) t))
6.4b	(/ (* z (sqrt (+ a t))) t)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-cbrt-cube` `add-exp-log`
15×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow1` `times-frac`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r` `sqrt-div` `div-exp` `associate-r/` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `div-inv` `unswap-sqr` `associate-/l/`
1×	`pow-prod-down` `*-commutative` `fma-udef` `distribute-lft-out`

Counts

4 → 89

Calls

4 calls:

6.0ms	(/ 2.0 (* t 3.0))
22.0ms	(* z (sqrt (+ a t)))
0.0ms	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (/ (* z (sqrt (+ a t))) t))
12.0ms	(/ (* z (sqrt (+ a t))) t)

series464.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 2.0 (* t 3.0))
88.0ms	(* z (sqrt (+ a t)))
226.0ms	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (/ (* z (sqrt (+ a t))) t))
127.0ms	(/ (* z (sqrt (+ a t))) t)

simplify1.3s

Counts

101 → 101

Iterations

Iter	Nodes
done	2000
3	2000
2	1726
1	564
0	233

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize105.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
2.2b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t)))
2.6b	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
58×	`times-frac`
47×	`*-un-lft-identity`
46×	`associate-r`
35×	`add-cube-cbrt`
31×	`cbrt-prod`
28×	`sqrt-prod`
25×	`add-exp-log`
18×	`add-cbrt-cube`
10×	`unswap-sqr`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `div-inv`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

4 → 129

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
50.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t)))
0.0ms	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t))))

series1.0s

Counts

4 → 12

Calls

4 calls:

242.0ms	(cbrt t)
263.0ms	(cbrt t)
161.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t)))
335.0ms	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t))))

simplify1.1s

Counts

141 → 141

Iterations

Iter	Nodes
done	2002
2	2002
1	729
0	249

prune3.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
2.2b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t)))
2.6b	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t))))))
52.7b	(posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
58×	`times-frac`
46×	`-un-lft-identity` `associate-r*`
34×	`add-cube-cbrt`
28×	`cbrt-prod` `sqrt-prod`
25×	`add-exp-log`
18×	`add-cbrt-cube`
10×	`unswap-sqr`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`div-inv`
1×	`frac-times` `pow1/3` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `remove-posit16`

Counts

4 → 126

Calls

4 calls:

1.0ms	(cbrt t)
54.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t)))
0.0ms	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t))))))
0.0ms	(posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t)))))

series922.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(cbrt t)
176.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t)))
288.0ms	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t))))))
172.0ms	(posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ a t)) (cbrt t)))))

simplify1.2s

Counts

138 → 138

Iterations

Iter	Nodes
done	2001
2	2001
1	745
0	260

prune5.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ a t)))
2.6b	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (/ (posit16->real (real->posit16 (* z (sqrt (+ a t))))) t))
6.4b	(/ (posit16->real (real->posit16 (* z (sqrt (+ a t))))) t)
54.9b	(posit16->real (real->posit16 (* z (sqrt (+ a t)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-r`
6×	`pow1`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `associate-/l`
2×	`sqrt-div` `associate-*r/` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `remove-posit16` `distribute-lft-out`

Counts

4 → 80

Calls

4 calls:

29.0ms	(* z (sqrt (+ a t)))
0.0ms	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (/ (posit16->real (real->posit16 (* z (sqrt (+ a t))))) t))
7.0ms	(/ (posit16->real (real->posit16 (* z (sqrt (+ a t))))) t)
0.0ms	(posit16->real (real->posit16 (* z (sqrt (+ a t)))))

series604.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* z (sqrt (+ a t)))
266.0ms	(fma (- c b) (- (+ (/ 5.0 6.0) a) (/ 2.0 (* t 3.0))) (/ (posit16->real (real->posit16 (* z (sqrt (+ a t))))) t))
138.0ms	(/ (posit16->real (real->posit16 (* z (sqrt (+ a t))))) t)
101.0ms	(posit16->real (real->posit16 (* z (sqrt (+ a t)))))

simplify1.4s

Counts

92 → 92

Iterations

Iter	Nodes
done	2003
3	2003
2	1286
1	467
0	203

prune3.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes640.0ms

Accuracy

-77.4% (2.6b remaining)

Error of 2.8b against oracle of 0.1b and baseline of 1.6b

bsearch541.0ms

Steps

Iters	Range		Point
8	1.1593160082027975e-229	3.509697963527615e-227	1.0654066290336557e-228
7	-1.9808904324337393e-87	-5.488403640925928e-89	-1.9603767098720115e-87

simplify36.0ms

Iterations

Iter	Nodes
done	59
1	59
0	51

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.6s	8000×	body	80	valid
2.5s	7941×	body	80	nan