Details

sample92.0ms

Algorithm

intervals

Results

36.0ms	86×	body	1280	valid
15.0ms	54×	body	640	valid
8.0ms	154×	body	80	valid
6.0ms	35×	body	320	valid
2.0ms	15×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	18
3	18
2	16
1	13
0	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.7b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
4.6b	(- (exp x) 1)

rewrite53.0ms

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-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 64

Calls

2 calls:

32.0ms	(/ (- (exp x) 1) x)
19.0ms	(- (exp x) 1)

series62.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1) x)
18.0ms	(- (exp x) 1)

simplify1.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	5004
3	1887
2	592
1	239
0	108

prune251.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
2×	`pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

2 → 42

Calls

2 calls:

19.0ms	(* x (+ 1/2 (* 1/6 x)))
14.0ms	(* 1/6 x)

series89.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(* x (+ 1/2 (* 1/6 x)))
17.0ms	(* 1/6 x)

simplify3.0s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
3	3789
2	664
1	205
0	72

prune189.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 1) (exp x))
0.0b	(/ (/ (+ -1 (exp (* 3 x))) (+ (* (+ (exp x) 1) (exp x)) 1)) x)
0.0b	(/ (+ -1 (exp (* 3 x))) (+ (* (+ (exp x) 1) (exp x)) 1))
4.6b	(+ -1 (exp (* 3 x)))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
102×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
22×	`associate-/l*`
18×	`distribute-lft-out`
13×	`add-cbrt-cube`
12×	`add-exp-log`
10×	`associate-/r/`
8×	`flip3-+` `flip-+`
6×	`pow1` `associate-/r*` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-l` `insert-posit16`
3×	`associate-r` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-*l/`
1×	`+-commutative` `sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

46.0ms	(* (+ (exp x) 1) (exp x))
101.0ms	(/ (/ (+ -1 (exp (* 3 x))) (+ (* (+ (exp x) 1) (exp x)) 1)) x)
77.0ms	(/ (+ -1 (exp (* 3 x))) (+ (* (+ (exp x) 1) (exp x)) 1))
13.0ms	(+ -1 (exp (* 3 x)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (+ (exp x) 1) (exp x))
115.0ms	(/ (/ (+ -1 (exp (* 3 x))) (+ (* (+ (exp x) 1) (exp x)) 1)) x)
63.0ms	(/ (+ -1 (exp (* 3 x))) (+ (* (+ (exp x) 1) (exp x)) 1))
27.0ms	(+ -1 (exp (* 3 x)))

simplify2.1s

Counts

174 → 174

Iterations

Iter	Nodes
done	5002
2	2126
1	671
0	267

prune805.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 1) (sqrt (exp x)))
0.0b	(/ (/ (+ -1 (exp (* 3 x))) (+ (* (* (+ (exp x) 1) (sqrt (exp x))) (sqrt (exp x))) 1)) x)
0.0b	(/ (+ -1 (exp (* 3 x))) (+ (* (* (+ (exp x) 1) (sqrt (exp x))) (sqrt (exp x))) 1))
4.6b	(+ -1 (exp (* 3 x)))

rewrite576.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
103×	`*-un-lft-identity`
71×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
22×	`associate-/l*`
18×	`distribute-lft-out`
13×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
8×	`flip3-+` `flip-+`
6×	`pow1` `associate-/r` `associate-r*` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-l` `sqrt-prod` `insert-posit16`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `associate-*l/` `unswap-sqr`
1×	`+-commutative` `sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 166

Calls

4 calls:

43.0ms	(* (+ (exp x) 1) (sqrt (exp x)))
339.0ms	(/ (/ (+ -1 (exp (* 3 x))) (+ (* (* (+ (exp x) 1) (sqrt (exp x))) (sqrt (exp x))) 1)) x)
171.0ms	(/ (+ -1 (exp (* 3 x))) (+ (* (* (+ (exp x) 1) (sqrt (exp x))) (sqrt (exp x))) 1))
14.0ms	(+ -1 (exp (* 3 x)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (+ (exp x) 1) (sqrt (exp x)))
121.0ms	(/ (/ (+ -1 (exp (* 3 x))) (+ (* (* (+ (exp x) 1) (sqrt (exp x))) (sqrt (exp x))) 1)) x)
76.0ms	(/ (+ -1 (exp (* 3 x))) (+ (* (* (+ (exp x) 1) (sqrt (exp x))) (sqrt (exp x))) 1))
29.0ms	(+ -1 (exp (* 3 x)))

simplify2.5s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
2	2212
1	697
0	279

prune748.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes22.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch44.0ms

Steps

Iters	Range		Point
10	-3720466.2051109266	-6.803810524357175e-07	-0.00010786855983473736

simplify4.0ms

Iterations

Iter	Nodes
done	36
1	36
0	24

end0.0ms

sample2.3s

Algorithm

intervals

Results

793.0ms	2283×	body	1280	valid
709.0ms	5518×	body	80	valid
362.0ms	1645×	body	640	valid
198.0ms	831×	body	320	valid
35.0ms	411×	body	160	valid