Details

sample106.0ms

Algorithm

intervals

Results

33.0ms	71×	body	1280	valid
31.0ms	75×	body	10240	exit
14.0ms	45×	body	640	valid
9.0ms	36×	body	320	valid
6.0ms	91×	body	80	valid
2.0ms	13×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.9b

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ (exp x) (- (exp x) 1))
4.7b	(- (exp x) 1)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `add-exp-log` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3--` `div-exp` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-inv`

Counts

2 → 64

Calls

2 calls:

47.0ms	(/ (exp x) (- (exp x) 1))
11.0ms	(- (exp x) 1)

series53.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ (exp x) (- (exp x) 1))
26.0ms	(- (exp x) 1)

simplify1.8s

Counts

70 → 70

Iterations

Iter	Nodes
done	5016
3	1648
2	490
1	207
0	103

prune241.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.4b	(* 1/12 x)

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
10×	`distribute-lft-out`
7×	`add-log-exp`
6×	`add-sqr-sqrt` `associate-l`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r`
2×	`+-commutative` `associate-+r+` `insert-posit16` `div-inv`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 40

Calls

2 calls:

120.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
8.0ms	(* 1/12 x)

series59.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
32.0ms	(* 1/12 x)

simplify1.8s

Counts

46 → 46

Iterations

Iter	Nodes
done	5004
3	1738
2	480
1	158
0	61

prune168.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (+ (exp x) 1))
0.8b	(/ (exp x) (/ (+ -1 (exp (+ x (+ x x)))) (+ 1 (* (exp x) (+ (exp x) 1)))))
0.9b	(/ (+ -1 (exp (+ x (+ x x)))) (+ 1 (* (exp x) (+ (exp x) 1))))
5.1b	(+ -1 (exp (+ x (+ x x))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

232×	`*-un-lft-identity`
178×	`times-frac`
88×	`add-sqr-sqrt`
86×	`add-cube-cbrt`
73×	`distribute-lft-out`
36×	`associate-/r*`
25×	`associate-l`
24×	`associate-/r/`
17×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`associate-/l*`
9×	`flip3-+` `flip-+`
7×	`div-exp`
6×	`pow1` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `associate-r` `insert-posit16` `associate-/l/`
3×	`+-commutative` `clear-num` `frac-2neg`
2×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `associate-*r/`
1×	`sum-log` `pow-prod-down` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

48.0ms	(* (exp x) (+ (exp x) 1))
468.0ms	(/ (exp x) (/ (+ -1 (exp (+ x (+ x x)))) (+ 1 (* (exp x) (+ (exp x) 1)))))
411.0ms	(/ (+ -1 (exp (+ x (+ x x)))) (+ 1 (* (exp x) (+ (exp x) 1))))
84.0ms	(+ -1 (exp (+ x (+ x x))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (exp x) (+ (exp x) 1))
120.0ms	(/ (exp x) (/ (+ -1 (exp (+ x (+ x x)))) (+ 1 (* (exp x) (+ (exp x) 1)))))
77.0ms	(/ (+ -1 (exp (+ x (+ x x)))) (+ 1 (* (exp x) (+ (exp x) 1))))
23.0ms	(+ -1 (exp (+ x (+ x x))))

simplify2.4s

Counts

236 → 236

Iterations

Iter	Nodes
done	5019
2	2961
1	757
0	277

prune985.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.4b	(* 1/12 x)
2.1b	(exp (log (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
30×	`distribute-lft-out`
18×	`log-prod`
12×	`associate-l`
11×	`add-sqr-sqrt`
10×	`add-log-exp`
9×	`exp-sum` `add-cube-cbrt`
8×	`pow1`
7×	`add-exp-log`
6×	`add-cbrt-cube` `div-inv`
4×	`log-div` `exp-prod` `insert-posit16`
3×	`sum-log` `flip3-+` `associate-r` `flip-+`
2×	`+-commutative` `associate-+r+` `exp-diff` `log-pow` `rem-exp-log`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

85.0ms	(log (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
83.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
11.0ms	(* 1/12 x)
64.0ms	(exp (log (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(log (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
17.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
18.0ms	(* 1/12 x)
22.0ms	(exp (log (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

simplify2.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5020
3	2922
2	707
1	266
0	119

prune271.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

regimes81.0ms

Accuracy

99% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 20.6b

bsearch48.0ms

Steps

Iters	Range		Point
9	-101227.54480913779	-0.0005350557287305616	-0.0014285877116162612

simplify8.0ms

Iterations

Iter	Nodes
done	32
1	32
0	22

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2513×	body	10240	exit
922.0ms	2262×	body	1280	valid
424.0ms	1624×	body	640	valid
255.0ms	891×	body	320	valid
224.0ms	2763×	body	80	valid
53.0ms	460×	body	160	valid