Details

sample33.0ms

Algorithm

intervals

Results

15.0ms	67×	body	1280	valid
5.0ms	48×	body	640	valid
4.0ms	191×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize4.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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:

10.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series59.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify2.3s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	99	596
1	221	572
2	501	542
3	1229	537
4	4072	536
done	5001	536

prune115.0ms

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 (* (* x x) (+ (* x 1/6) 1/2)))
0.1b	(* (* x x) (+ (* x 1/6) 1/2))
0.4b	(* x 1/6)
2.6b	(/ (+ x (* (* x x) (+ (* x 1/6) 1/2))) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`times-frac`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 83

Calls

4 calls:

2.0ms	(+ x (* (* x x) (+ (* x 1/6) 1/2)))
14.0ms	(* (* x x) (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)
9.0ms	(/ (+ x (* (* x x) (+ (* x 1/6) 1/2))) x)

series156.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ x (* (* x x) (+ (* x 1/6) 1/2)))
66.0ms	(* (* x x) (+ (* x 1/6) 1/2))
17.0ms	(* x 1/6)
45.0ms	(/ (+ x (* (* x x) (+ (* x 1/6) 1/2))) x)

simplify854.0ms

Counts

95 → 95

Iterations

Useful iterations: 2 (208.0ms)

Iter	Nodes	Cost
0	143	1386
1	360	1280
2	1310	1168
done	5001	1168

prune159.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `exp-prod`
13×	`pow1` `add-cbrt-cube`
11×	`add-exp-log`
7×	`associate-r`
6×	`associate-l` `add-log-exp`
5×	`pow-prod-down`
4×	`times-frac` `associate-r/` `pow-sqr` `pow-prod-up` `associate-/l`
3×	`swap-sqr` `prod-exp` `cbrt-unprod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-/r/` `*-commutative` `flip--` `flip-+` `associate-/l/` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-plus` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

13.0ms	(* x (+ (exp x) 1.0))
22.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
9.0ms	(* (exp x) (exp x))
7.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series158.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* x (+ (exp x) 1.0))
81.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
14.0ms	(* (exp x) (exp x))
26.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify728.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (233.0ms)

Iter	Nodes	Cost
0	160	1376
1	418	1216
2	1585	1053
done	5001	1053

prune214.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 1.0) x)
0.0b	(/ (* 1.0 1.0) (* x (+ (exp x) 1.0)))
0.0b	(/ (exp (* 2 x)) (* (+ (exp x) 1.0) x))
3.4b	(- (/ (exp (* 2 x)) (* (+ (exp x) 1.0) x)) (/ (* 1.0 1.0) (* x (+ (exp x) 1.0))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube`
21×	`add-exp-log`
12×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `associate-/r/`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`times-frac` `associate-r/` `associate-l` `associate-/l`
3×	`associate-r`
2×	`distribute-rgt-out--` `frac-2neg` `clear-num` `associate-/r*` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

14.0ms	(* (+ (exp x) 1.0) x)
7.0ms	(/ (* 1.0 1.0) (* x (+ (exp x) 1.0)))
7.0ms	(/ (exp (* 2 x)) (* (+ (exp x) 1.0) x))
22.0ms	(- (/ (exp (* 2 x)) (* (+ (exp x) 1.0) x)) (/ (* 1.0 1.0) (* x (+ (exp x) 1.0))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (+ (exp x) 1.0) x)
47.0ms	(/ (* 1.0 1.0) (* x (+ (exp x) 1.0)))
44.0ms	(/ (exp (* 2 x)) (* (+ (exp x) 1.0) x))
108.0ms	(- (/ (exp (* 2 x)) (* (+ (exp x) 1.0) x)) (/ (* 1.0 1.0) (* x (+ (exp x) 1.0))))

simplify804.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (242.0ms)

Iter	Nodes	Cost
0	175	1675
1	474	1575
2	2018	1381
done	5000	1381

prune221.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes21.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.6b

bsearch31.0ms

Steps

Iters	Range		Point
8	-0.04390830018224924	-1.7961213486546931e-06	-0.00016134030061260165

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	52
1	34	52
done	34	52

end0.0ms

sample892.0ms

Algorithm

intervals

Results

392.0ms	2235×	body	1280	valid
180.0ms	1635×	body	640	valid
107.0ms	5418×	body	80	valid
59.0ms	846×	body	320	valid
19.0ms	430×	body	160	valid