Details

sample237.0ms

Algorithm

intervals

Results

140.0ms	22×	body	320	valid
28.0ms	67×	body	10240	exit
20.0ms	46×	body	1280	valid
19.0ms	330×	body	80	valid
12.0ms	47×	body	640	valid
1.0ms	7×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

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

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

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)))
1.8b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

7.0ms	(* (- 1.0 eps) x)
11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
12.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
151.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series297.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (- 1.0 eps) x)
40.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
46.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
178.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	684	1993
1	2176	1881
2	5002	1880

prune423.0ms

Filtered

150 candidates to 107 candidates (71.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
8.4b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp` `unswap-sqr`
7×	`add-cbrt-cube`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`cube-mult` `sub-neg` `flip3--` `unpow3` `associate--l+` `sum-log` `flip--`

Counts

3 → 72

Calls

3 calls:

5.0ms	(* 0.5 (pow x 2))
6.0ms	(* 0.33333333333333337 (pow x 3))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series103.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 0.5 (pow x 2))
39.0ms	(* 0.33333333333333337 (pow x 3))
39.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	281	376
1	1249	330
2	5002	323

prune157.0ms

Filtered

81 candidates to 48 candidates (59.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

5.9b	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
5.9b	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
8.4b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
8.4b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `diff-log` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate--l+` `sum-log`

Counts

4 → 58

Calls

4 calls:

7.0ms	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
55.0ms	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
41.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
39.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify106.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	171	688
1	611	636
2	3106	618
3	5003	616

prune211.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x)))
0.0b	(/ 1.0 (exp (* (+ 1.0 eps) x)))
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
1.8b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
123×	`add-sqr-sqrt`
112×	`*-un-lft-identity`
69×	`add-cube-cbrt`
20×	`associate-/l*`
13×	`add-cbrt-cube`
12×	`difference-of-squares`
10×	`distribute-lft-out--`
9×	`add-exp-log` `associate-/r*` `div-inv`
7×	`distribute-lft-out`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `flip3-+` `diff-log` `frac-sub` `flip--` `flip-+` `sub-div`

Counts

4 → 167

Calls

4 calls:

8.0ms	(/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x)))
5.0ms	(/ 1.0 (exp (* (+ 1.0 eps) x)))
11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
255.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

series202.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x)))
25.0ms	(/ 1.0 (exp (* (+ 1.0 eps) x)))
41.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
101.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	792	2363
1	2706	2248
2	5003	2248

prune628.0ms

Filtered

179 candidates to 146 candidates (81.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes72.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.2b

bsearch170.0ms

Steps

Iters	Range		Point
11	1.648961095024041e-05	5.175139968754377e+19	24.802505831063332

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	49
1	50	49

end0.0ms

sample3.0s

Algorithm

intervals

Results

828.0ms	1933×	body	10240	exit
755.0ms	1697×	body	1280	valid
591.0ms	10153×	body	80	valid
345.0ms	1295×	body	640	valid
108.0ms	625×	body	320	valid
35.0ms	306×	body	160	valid