Details

sample35.0ms

Algorithm

intervals

Results

12.0ms	65×	body	1280	valid
8.0ms	70×	body	640	valid
4.0ms	178×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	14×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
3	15
2	13
1	10
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.0b	(- (exp x) 1.0)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

28.0ms	(/ (- (exp x) 1.0) x)
8.0ms	(- (exp x) 1.0)

series61.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- (exp x) 1.0) x)
22.0ms	(- (exp x) 1.0)

simplify1.6s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
3	1947
2	569
1	224
0	99

prune331.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ (* 1/6 x) 1/2))
0.4b	(* 1/6 x)

rewrite49.0ms

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` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

2 → 40

Calls

2 calls:

37.0ms	(* x (+ (* 1/6 x) 1/2))
11.0ms	(* 1/6 x)

series125.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(* x (+ (* 1/6 x) 1/2))
28.0ms	(* 1/6 x)

simplify3.3s

Counts

46 → 46

Iterations

Iter	Nodes
done	5019
3	3635
2	646
1	204
0	70

prune211.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
2.7b	(- (/ (exp x) x) (/ 1.0 x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
4×	`add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `add-exp-log` `div-inv` `associate-/l`
2×	`pow1`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `distribute-rgt-out--` `diff-log` `div-exp` `frac-sub` `flip--` `sub-div`

Counts

2 → 50

Calls

2 calls:

7.0ms	(/ (exp x) x)
51.0ms	(- (/ (exp x) x) (/ 1.0 x))

series110.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (exp x) x)
61.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify1.5s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
3	1805
2	602
1	226
0	105

prune306.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0)))) x)
0.0b	(/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0))))
0.0b	(* (exp x) (exp x))
2.9b	(- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
68×	`add-sqr-sqrt`
66×	`*-un-lft-identity` `add-cube-cbrt`
18×	`exp-prod` `associate-/l*`
13×	`add-cbrt-cube`
11×	`pow1` `add-exp-log`
10×	`associate-/r/`
6×	`associate-/r*` `div-inv` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp` `pow-prod-down` `pow-sqr` `pow-prod-up`
3×	`div-sub` `swap-sqr` `associate-r` `associate-l` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 157

Calls

4 calls:

552.0ms	(/ (/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0)))) x)
485.0ms	(/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0))))
14.0ms	(* (exp x) (exp x))
266.0ms	(- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0))

series337.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0)))) x)
108.0ms	(/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0))))
17.0ms	(* (exp x) (exp x))
32.0ms	(- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0))

simplify2.5s

Counts

169 → 169

Iterations

Iter	Nodes
done	5014
2	3027
1	754
0	278

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.5b

bsearch73.0ms

Steps

Iters	Range		Point
10	-733100.9210806559	-4.034181863829644e-08	-9.248950464724179e-05

simplify8.0ms

Iterations

Iter	Nodes
done	51
1	51
0	35

end0.0ms

sample1.5s

Algorithm

intervals

Results

649.0ms	2264×	body	1280	valid
309.0ms	1639×	body	640	valid
225.0ms	5476×	body	80	valid
117.0ms	836×	body	320	valid
27.0ms	405×	body	160	valid