Details

sample111.0ms

Algorithm

intervals

Results

35.0ms	69×	body	1280	valid
27.0ms	66×	body	10240	exit
18.0ms	323×	body	80	valid
10.0ms	38×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	7×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
1.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
32×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out`

Counts

4 → 173

Calls

4 calls:

9.0ms	(* (- 1.0 eps) x)
29.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
37.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
27.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (- 1.0 eps) x)
46.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
56.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
196.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify155.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	1253	4065
1	4712	3787
2	5001	3778

prune456.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
4.6b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 45

Calls

2 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
25.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series78.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* 0.6666666666666667 (pow x 3))
43.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify35.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	207	270
1	894	242
2	5002	238

prune110.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(/ (exp (- (* x eps) (* 1.0 x))) eps)
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
2.4b	(- (* 1.0 (+ (/ (exp (- (* x eps) (* 1.0 x))) eps) (exp (- (* x eps) (* 1.0 x))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

35×	`associate-*r/`
27×	`add-sqr-sqrt` `frac-sub`
22×	`*-un-lft-identity` `exp-diff`
18×	`add-cube-cbrt`
16×	`exp-neg` `frac-times` `times-frac`
13×	`flip3--` `flip--`
12×	`neg-sub0`
10×	`flip3-+` `associate-l` `associate-*l/` `add-cbrt-cube` `flip-+`
9×	`frac-add`
8×	`pow1` `add-exp-log` `exp-sum`
6×	`associate-r` `add-log-exp`
5×	`sub-neg` `associate-/l*`
4×	`un-div-inv`
3×	`associate-/r*`
2×	`pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `diff-log` `div-exp` `clear-num` `div-inv` `associate-/l/` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 128

Calls

4 calls:

9.0ms	(* (+ 1.0 eps) x)
11.0ms	(/ (exp (- (* x eps) (* 1.0 x))) eps)
40.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
41.0ms	(- (* 1.0 (+ (/ (exp (- (* x eps) (* 1.0 x))) eps) (exp (- (* x eps) (* 1.0 x))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (+ 1.0 eps) x)
35.0ms	(/ (exp (- (* x eps) (* 1.0 x))) eps)
49.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
175.0ms	(- (* 1.0 (+ (/ (exp (- (* x eps) (* 1.0 x))) eps) (exp (- (* x eps) (* 1.0 x))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify124.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	910	2903
1	3746	2773
2	5002	2772

prune415.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes52.0ms

Accuracy

95.8% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.9b

bsearch153.0ms

Steps

Iters	Range		Point
10	3.9524390088012255e-07	7103758.057079569	130.4040333957902

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	27
1	53	27
2	53	27

end0.0ms

sample2.9s

Algorithm

intervals

Results

781.0ms	1902×	body	10240	exit
762.0ms	1689×	body	1280	valid
575.0ms	10213×	body	80	valid
336.0ms	1265×	body	640	valid
105.0ms	617×	body	320	valid
37.0ms	326×	body	160	valid