Details

sample31.0ms

Algorithm

intervals

Results

13.0ms	75×	body	1280	valid
5.0ms	56×	body	640	valid
3.0ms	180×	body	80	valid
1.0ms	22×	body	320	valid
1.0ms	17×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.9b

localize4.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

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:

23.0ms	(/ (- (exp x) 1.0) x)
9.0ms	(- (exp x) 1.0)

series53.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2739	309
3	5001	309

prune116.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.2b	(* 1/6 (pow x 2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log` `add-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp` `sum-log`
2×	`pow1` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 40

Calls

2 calls:

21.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
13.0ms	(* 1/6 (pow x 2))

series46.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
25.0ms	(* 1/6 (pow x 2))

simplify34.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	201	222
1	825	201
2	5001	198

prune80.0ms

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	(+ (log (exp (* 1/6 (pow x 2)))) (+ (* 1/2 x) 1))
0.0b	(exp (* 1/6 (pow x 2)))
0.2b	(* 1/6 (pow x 2))
1.7b	(log (exp (* 1/6 (pow x 2))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cube-cbrt`
8×	`associate-r`
6×	`pow1` `log-prod` `add-cbrt-cube`
4×	`unpow-prod-down` `log-pow` `unswap-sqr`
3×	`associate-+l+` `associate-l` `prod-exp` `sum-log`
2×	`exp-prod` `exp-to-pow` `distribute-lft-out` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `rem-log-exp` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+` `rem-exp-log`

Counts

4 → 69

Calls

4 calls:

23.0ms	(+ (log (exp (* 1/6 (pow x 2)))) (+ (* 1/2 x) 1))
5.0ms	(exp (* 1/6 (pow x 2)))
13.0ms	(* 1/6 (pow x 2))
3.0ms	(log (exp (* 1/6 (pow x 2))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (log (exp (* 1/6 (pow x 2)))) (+ (* 1/2 x) 1))
11.0ms	(exp (* 1/6 (pow x 2)))
27.0ms	(* 1/6 (pow x 2))
24.0ms	(log (exp (* 1/6 (pow x 2))))

simplify36.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	248	405
1	989	343
2	5002	342

prune166.0ms

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
50.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
17.0ms	(* (exp x) (exp x))
18.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series91.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (exp x) 1.0)
44.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
15.0ms	(* (exp x) (exp x))
24.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	376	823
1	1712	737
2	5001	719

prune207.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes18.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.9b

bsearch33.0ms

Steps

Iters	Range		Point
9	-0.04331797882383785	-1.989428328455626e-07	-0.00010696052970747946

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	27	12

end0.0ms

sample891.0ms

Algorithm

intervals

Results

379.0ms	2235×	body	1280	valid
174.0ms	1724×	body	640	valid
98.0ms	5401×	body	80	valid
53.0ms	810×	body	320	valid
18.0ms	411×	body	160	valid