Details

sample55.0ms

Algorithm

intervals

Results

17.0ms	63×	body	640	valid
17.0ms	138×	body	80	valid
6.0ms	19×	body	1280	valid
6.0ms	28×	body	320	valid
1.0ms	8×	body	160	valid

simplify105.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	195
10	195
9	187
8	132
7	94
6	83
5	75
4	63
3	43
2	33
1	19
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
1.6b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
35×	`times-frac`
29×	`add-sqr-sqrt`
17×	`distribute-lft-out`
14×	`distribute-lft-out--`
12×	`add-cube-cbrt`
10×	`add-log-exp`
7×	`add-exp-log` `div-inv`
6×	`difference-of-squares`
5×	`add-cbrt-cube`
4×	`pow1` `associate-/r*`
3×	`frac-add` `insert-posit16` `associate-/l*`
2×	`associate-+l+` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `div-exp` `associate-/r/` `frac-sub` `flip-+` `flip--`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-+l-` `pow-flip` `inv-pow`

Counts

3 → 91

Calls

3 calls:

8.0ms	(/ 1 (+ x 1))
65.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
202.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ 1 (+ x 1))
26.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
133.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify5.3s

Counts

100 → 100

Iterations

Iter	Nodes
3	4070
2	1127
1	394
0	166

prune798.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
1.6b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
35×	`times-frac`
29×	`add-sqr-sqrt`
17×	`distribute-lft-out`
14×	`distribute-lft-out--`
12×	`add-cube-cbrt`
10×	`add-log-exp`
7×	`add-exp-log` `div-inv`
6×	`difference-of-squares`
5×	`add-cbrt-cube`
4×	`pow1` `associate-/r*`
3×	`frac-add` `insert-posit16` `associate-/l*`
2×	`associate-+l+` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `div-exp` `associate-/r/` `frac-sub` `flip-+` `flip--`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-+l-` `pow-flip` `inv-pow`

Counts

3 → 91

Calls

3 calls:

17.0ms	(/ 1 (+ x 1))
43.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
172.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series190.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ 1 (+ x 1))
38.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
138.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify5.3s

Counts

100 → 100

Iterations

Iter	Nodes
3	4070
2	1127
1	394
0	166

prune767.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
0.2b	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
1.6b	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
16.3b	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

rewrite897.0ms

Algorithm

rewrite-expression-head

Rules

440×	`*-un-lft-identity`
306×	`times-frac`
271×	`add-sqr-sqrt`
196×	`frac-sub`
146×	`distribute-lft-out--`
112×	`frac-times`
87×	`difference-of-squares`
82×	`add-cube-cbrt`
80×	`flip3--` `flip--`
62×	`swap-sqr` `associate-/l/`
58×	`associate-l/` `associate-r/`
48×	`add-exp-log`
40×	`associate-r` `associate-l` `div-inv`
31×	`un-div-inv`
26×	`pow1`
20×	`add-cbrt-cube`
18×	`difference-of-sqr-1`
17×	`div-exp` `prod-exp`
16×	`associate-/r*` `distribute-lft-out`
13×	`associate-/r/`
10×	`unswap-sqr`
8×	`rec-exp` `1-exp` `pow-flip` `inv-pow`
6×	`pow-prod-up` `add-log-exp`
5×	`cbrt-undiv` `sub-neg` `cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate--l+` `pow-sqr` `insert-posit16` `associate-/l*`
2×	`pow2` `pow-plus` `*-commutative`
1×	`clear-num` `frac-2neg` `diff-log` `div-sub`

Counts

4 → 476

Calls

4 calls:

64.0ms	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
240.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
124.0ms	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
449.0ms	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

series573.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
46.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
134.0ms	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
364.0ms	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

simplify1.3s

Counts

488 → 488

Iterations

Iter	Nodes
1	2130
0	662

prune5.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (- (log (+ x 1)))) (/ 2 x))
1.4b	(exp (- (log (+ x 1))))
2.8b	(log (+ x 1))
12.3b	(+ (- (exp (- (log (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))

rewrite680.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

56.0ms	(- (exp (- (log (+ x 1)))) (/ 2 x))
6.0ms	(exp (- (log (+ x 1))))
3.0ms	(log (+ x 1))
613.0ms	(+ (- (exp (- (log (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (exp (- (log (+ x 1)))) (/ 2 x))
45.0ms	(exp (- (log (+ x 1))))
38.0ms	(log (+ x 1))
93.0ms	(+ (- (exp (- (log (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))

simplify2.4s

Counts

100 → 100

Iterations

Iter	Nodes
3	4218
2	1213
1	434
0	195

prune936.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes62.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 24.3b

bsearch177.0ms

Steps

Iters	Range		Point
11	1.0334628320549359e-08	2.7368728718549235e+26	91.04565691167721
9	-128555.04713805256	-0.18430940072566707	-1.0055170474121684

simplify11.0ms

Iterations

Iter	Nodes
2	37
1	37
0	29

end0.0ms

sample2.5s

Algorithm

intervals

Results

983.0ms	1853×	body	640	valid
525.0ms	4191×	body	80	valid
449.0ms	622×	body	1280	valid
320.0ms	901×	body	320	valid
91.0ms	436×	body	160	valid