Details

sample99.0ms

Algorithm

intervals

Results

25.0ms	61×	body	1280	valid
25.0ms	63×	body	10240	exit
19.0ms	287×	body	80	valid
9.0ms	37×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	15×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	305	27
4	1022	27
5	4219	27
done	5001	27

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
2.6b	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

10.0ms	(* (+ 1.0 eps) x)
27.0ms	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
26.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
320.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (+ 1.0 eps) x)
41.0ms	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
43.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
175.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify624.0ms

Counts

131 → 131

Iterations

Useful iterations: done (615.0ms)

Iter	Nodes	Cost
0	245	2879
1	574	2745
2	1518	2586
done	5000	2580

prune361.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (* x x) (- (* 0.6666666666666667 x) 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 25

Calls

1 calls:

15.0ms

(* (* x x) (- (* 0.6666666666666667 x) 1.0))

series75.0ms

Counts

1 → 3

Calls

1 calls:

75.0ms

(* (* x x) (- (* 0.6666666666666667 x) 1.0))

simplify2.1s

Counts

28 → 28

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	57	367
1	163	344
2	671	294
3	3188	294
done	5001	294

prune40.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* x x) (- (* 0.6666666666666667 x) 1.0))
2.8b	(log (exp (* (* x x) (- (* 0.6666666666666667 x) 1.0))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
7×	`add-exp-log` `log-prod` `add-cbrt-cube`
5×	`add-sqr-sqrt`
4×	`distribute-rgt-in` `add-cube-cbrt` `sub-neg` `*-un-lft-identity` `distribute-lft-in` `exp-sum`
3×	`associate-r` `pow-prod-down` `prod-exp` `log-pow` `cbrt-unprod` `add-log-exp`
2×	`associate-*r/`
1×	`exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

2 → 43

Calls

2 calls:

15.0ms	(* (* x x) (- (* 0.6666666666666667 x) 1.0))
2.0ms	(log (exp (* (* x x) (- (* 0.6666666666666667 x) 1.0))))

series150.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(* (* x x) (- (* 0.6666666666666667 x) 1.0))
76.0ms	(log (exp (* (* x x) (- (* 0.6666666666666667 x) 1.0))))

simplify2.3s

Counts

49 → 49

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	82	682
1	196	604
2	740	522
3	3431	522
done	5001	522

prune94.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* x x) (- (* 0.6666666666666667 x) 1.0))
0.0b	(* (* x x) (- (* 0.6666666666666667 x) 1.0))
2.8b	(log (cbrt (exp (* (* x x) (- (* 0.6666666666666667 x) 1.0)))))
2.8b	(log (cbrt (exp (* (* x x) (- (* 0.6666666666666667 x) 1.0)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

17.0ms	(* (* x x) (- (* 0.6666666666666667 x) 1.0))
15.0ms	(* (* x x) (- (* 0.6666666666666667 x) 1.0))
2.0ms	(log (cbrt (exp (* (* x x) (- (* 0.6666666666666667 x) 1.0)))))
2.0ms	(log (cbrt (exp (* (* x x) (- (* 0.6666666666666667 x) 1.0)))))

series868.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (* x x) (- (* 0.6666666666666667 x) 1.0))
81.0ms	(* (* x x) (- (* 0.6666666666666667 x) 1.0))
362.0ms	(log (cbrt (exp (* (* x x) (- (* 0.6666666666666667 x) 1.0)))))
344.0ms	(log (cbrt (exp (* (* x x) (- (* 0.6666666666666667 x) 1.0)))))

simplify2.4s

Counts

102 → 102

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	111	1586
1	247	1510
2	912	1340
3	3946	1320
done	5001	1320

prune296.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes55.0ms

Accuracy

96.5% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.4b

bsearch137.0ms

Steps

Iters	Range		Point
9	0.006616288801049052	22276.40736340321	179.02536135484516

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	51
1	41	51
2	43	51
done	43	51

end0.0ms

sample2.9s

Algorithm

intervals

Results

773.0ms	1921×	body	10240	exit
755.0ms	1725×	body	1280	valid
551.0ms	9975×	body	80	valid
336.0ms	1296×	body	640	valid
104.0ms	610×	body	320	valid
36.0ms	296×	body	160	valid