Details

sample205.0ms

Algorithm

intervals

Results

47.0ms	52×	body	1280	valid
47.0ms	45×	body	10240	exit
36.0ms	292×	body	80	valid
19.0ms	31×	body	640	valid
9.0ms	25×	body	320	valid
4.0ms	14×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
4	1357
3	352
2	122
1	46
0	19

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- eps 1.0) x)
0.0b	(exp (* x (+ 1.0 eps)))
0.0b	(exp (* (- eps 1.0) x))
4.1b	(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

rewrite329.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`associate-l`
4×	`insert-posit16`
3×	`exp-to-pow` `associate-r`
2×	`distribute-rgt-in` `associate-+r+` `exp-prod` `distribute-lft-in` `flip3-+` `exp-sum` `associate-l/` `frac-add` `associate-r/` `flip-+` `rem-exp-log`
1×	`+-commutative` `sum-log` `flip3--` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

53.0ms	(* (- eps 1.0) x)
15.0ms	(exp (* x (+ 1.0 eps)))
24.0ms	(exp (* (- eps 1.0) x))
231.0ms	(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- eps 1.0) x)
27.0ms	(exp (* x (+ 1.0 eps)))
34.0ms	(exp (* (- eps 1.0) x))
455.0ms	(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

simplify3.4s

Counts

77 → 77

Iterations

Iter	Nodes
done	5006
2	1636
1	435
0	166

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.4b	(/ 2.7755575615628914e-17 (/ eps (* (* x x) x)))
4.3b	(+ (* 1.0 (* x x)) (/ 2.7755575615628914e-17 (/ eps (* (* x x) x))))
4.9b	(/ eps (* (* x x) x))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
32×	`add-cbrt-cube` `add-exp-log`
24×	`add-sqr-sqrt`
23×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-/r*`
6×	`pow-plus` `pow-prod-up` `div-inv` `associate-/l*` `add-log-exp`
4×	`insert-posit16`
3×	`associate-r` `pow-prod-down`
2×	`pow2` `clear-num` `frac-2neg` `pow-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `associate-l` `pow3` `associate-/r/` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

50.0ms	(* (* x x) x)
40.0ms	(/ 2.7755575615628914e-17 (/ eps (* (* x x) x)))
88.0ms	(+ (* 1.0 (* x x)) (/ 2.7755575615628914e-17 (/ eps (* (* x x) x))))
53.0ms	(/ eps (* (* x x) x))

series306.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* x x) x)
116.0ms	(/ 2.7755575615628914e-17 (/ eps (* (* x x) x)))
79.0ms	(+ (* 1.0 (* x x)) (/ 2.7755575615628914e-17 (/ eps (* (* x x) x))))
66.0ms	(/ eps (* (* x x) x))

simplify4.0s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	1715
1	445
0	172

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x)))))
0.1b	(* (* x x) x)
1.0b	(log (exp (* (* x x) x)))
4.3b	(+ (* 1.0 (* x x)) (/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x))))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
70×	`add-sqr-sqrt`
69×	`*-un-lft-identity` `add-cube-cbrt`
39×	`log-pow`
36×	`pow1`
22×	`associate-/r*`
19×	`add-log-exp`
14×	`add-cbrt-cube` `add-exp-log`
13×	`exp-prod` `exp-to-pow`
6×	`pow-plus` `pow-prod-up`
5×	`div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `log-prod` `div-exp` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`pow2` `pow-sqr`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `rem-log-exp` `associate-l` `pow3` `associate-/r/` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 163

Calls

4 calls:

16.0ms	(/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x)))))
26.0ms	(* (* x x) x)
5.0ms	(log (exp (* (* x x) x)))
69.0ms	(+ (* 1.0 (* x x)) (/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x))))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x)))))
62.0ms	(* (* x x) x)
69.0ms	(log (exp (* (* x x) x)))
94.0ms	(+ (* 1.0 (* x x)) (/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x))))))

simplify4.2s

Counts

175 → 175

Iterations

Iter	Nodes
done	5002
2	2209
1	660
0	248

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize103.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2.7755575615628914e-17 (posit16->real (real->posit16 (/ eps (* (* x x) x)))))
4.3b	(+ (* 1.0 (* x x)) (/ 2.7755575615628914e-17 (posit16->real (real->posit16 (/ eps (* (* x x) x))))))
4.9b	(/ eps (* (* x x) x))
34.0b	(posit16->real (real->posit16 (/ eps (* (* x x) x))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `cbrt-undiv` `associate-/r*` `div-exp` `insert-posit16`
3×	`prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `remove-posit16`

Counts

4 → 73

Calls

4 calls:

7.0ms	(/ 2.7755575615628914e-17 (posit16->real (real->posit16 (/ eps (* (* x x) x)))))
30.0ms	(+ (* 1.0 (* x x)) (/ 2.7755575615628914e-17 (posit16->real (real->posit16 (/ eps (* (* x x) x))))))
58.0ms	(/ eps (* (* x x) x))
2.0ms	(posit16->real (real->posit16 (/ eps (* (* x x) x))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ 2.7755575615628914e-17 (posit16->real (real->posit16 (/ eps (* (* x x) x)))))
76.0ms	(+ (* 1.0 (* x x)) (/ 2.7755575615628914e-17 (posit16->real (real->posit16 (/ eps (* (* x x) x))))))
63.0ms	(/ eps (* (* x x) x))
67.0ms	(posit16->real (real->posit16 (/ eps (* (* x x) x))))

simplify2.8s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	1102
1	311
0	131

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

regimes494.0ms

Accuracy

94.1% (1.0b remaining)

Error of 1.6b against oracle of 0.6b and baseline of 17.7b

bsearch200.0ms

Steps

Iters	Range		Point
8	4.1750260115318935e-11	1.508099977930646e-06	1.4798868095701662e-06

simplify41.0ms

Iterations

Iter	Nodes
done	44
1	44
0	34

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.4s	10203×	body	80	valid
2.3s	1971×	body	10240	exit
1.7s	1717×	body	1280	valid
981.0ms	1176×	body	640	valid
309.0ms	656×	body	320	valid
91.0ms	277×	body	160	valid