Details

sample61.0ms

Algorithm

intervals

Results

31.0ms	75×	body	1280	valid
8.0ms	59×	body	640	valid
5.0ms	172×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	16×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.1b	(- (exp x) 1.0)

rewrite75.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

49.0ms	(/ (- (exp x) 1.0) x)
23.0ms	(- (exp x) 1.0)

series86.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- (exp x) 1.0) x)
34.0ms	(- (exp x) 1.0)

simplify2.4s

Counts

58 → 58

Iterations

Useful iterations: 3 (889.0ms)

Iter	Nodes	Cost
0	99	596
1	227	572
2	802	544
3	4675	537
done	5002	537

prune229.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (+ 1/2 (* 1/6 x))) 1)
0.0b	(+ 1/2 (* 1/6 x))
0.0b	(* x (+ 1/2 (* 1/6 x)))
0.3b	(* 1/6 x)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

15.0ms	(+ (* x (+ 1/2 (* 1/6 x))) 1)
6.0ms	(+ 1/2 (* 1/6 x))
24.0ms	(* x (+ 1/2 (* 1/6 x)))
7.0ms	(* 1/6 x)

series169.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (* x (+ 1/2 (* 1/6 x))) 1)
33.0ms	(+ 1/2 (* 1/6 x))
87.0ms	(* x (+ 1/2 (* 1/6 x)))
25.0ms	(* 1/6 x)

simplify1.3s

Counts

76 → 76

Iterations

Useful iterations: 2 (340.0ms)

Iter	Nodes	Cost
0	101	708
1	310	650
2	1528	604
done	5001	604

prune278.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite534.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
136×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
82×	`add-cube-cbrt`
44×	`difference-of-squares`
31×	`associate-/l*`
27×	`distribute-lft-out`
22×	`exp-sum`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
8×	`add-log-exp`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`+-commutative` `sub-neg` `diff-log` `sum-log`

Counts

4 → 195

Calls

4 calls:

18.0ms	(+ (exp x) 1.0)
205.0ms	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
202.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
87.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series211.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (exp x) 1.0)
104.0ms	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
65.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
22.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.2s

Counts

207 → 207

Iterations

Useful iterations: 2 (922.0ms)

Iter	Nodes	Cost
0	301	4684
1	782	4503
2	3980	4251
done	5000	4251

prune927.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (exp (* x 4)) (pow 1.0 4)) (+ (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0))
0.0b	(/ (/ (/ (- (exp (* x 4)) (pow 1.0 4)) (+ (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)) x)
0.0b	(/ (- (exp (* x 4)) (pow 1.0 4)) (+ (exp (+ x x)) (* 1.0 1.0)))
4.0b	(- (exp (* x 4)) (pow 1.0 4))

rewrite688.0ms

Algorithm

rewrite-expression-head

Rules

1344×	`times-frac`
910×	`*-un-lft-identity`
842×	`add-sqr-sqrt`
502×	`add-cube-cbrt`
204×	`difference-of-squares`
148×	`associate-/l*`
136×	`distribute-lft-out`
68×	`unpow-prod-down` `distribute-lft-out--` `sqr-pow`
54×	`associate-/r/`
28×	`div-inv`
27×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`div-sub` `add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 698

Calls

4 calls:

200.0ms	(/ (/ (- (exp (* x 4)) (pow 1.0 4)) (+ (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0))
251.0ms	(/ (/ (/ (- (exp (* x 4)) (pow 1.0 4)) (+ (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)) x)
134.0ms	(/ (- (exp (* x 4)) (pow 1.0 4)) (+ (exp (+ x x)) (* 1.0 1.0)))
28.0ms	(- (exp (* x 4)) (pow 1.0 4))

series326.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (/ (- (exp (* x 4)) (pow 1.0 4)) (+ (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0))
153.0ms	(/ (/ (/ (- (exp (* x 4)) (pow 1.0 4)) (+ (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)) x)
66.0ms	(/ (- (exp (* x 4)) (pow 1.0 4)) (+ (exp (+ x x)) (* 1.0 1.0)))
21.0ms	(- (exp (* x 4)) (pow 1.0 4))

simplify1.5s

Counts

710 → 710

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	911	30554
1	2385	29204
done	5001	28692

prune3.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.1b

bsearch38.0ms

Steps

Iters	Range		Point
8	-0.001242952878385433	-3.7186071738290686e-06	-0.00014256029521601964

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	51
1	37	51
done	37	51

end0.0ms

sample1.8s

Algorithm

intervals

Results

716.0ms	2301×	body	1280	valid
329.0ms	1653×	body	640	valid
208.0ms	5405×	body	80	valid
204.0ms	828×	body	320	valid
33.0ms	417×	body	160	valid