Details

sample69.0ms

Algorithm

intervals

Results

30.0ms	72×	body	1280	valid
15.0ms	68×	body	640	valid
7.0ms	26×	body	320	valid
6.0ms	21×	body	2560	valid
2.0ms	53×	body	80	valid
1.0ms	16×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.1b

localize7.0ms

Local error

Found 3 expressions with local error:

1.4b	(+ x (sqrt (+ (* x x) 1.0)))
3.6b	(log (+ x (sqrt (+ (* x x) 1.0))))
11.2b	(sqrt (+ (* x x) 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

8.0ms	(+ x (sqrt (+ (* x x) 1.0)))
8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series282.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ x (sqrt (+ (* x x) 1.0)))
178.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
49.0ms	(sqrt (+ (* x x) 1.0))

simplify157.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	309	393
1	1027	364
2	4764	348
3	5002	347

prune154.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.2b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
182×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
118×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 286

Calls

2 calls:

112.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
71.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series300.0ms

Counts

2 → 6

Calls

2 calls:

162.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
138.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify118.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	854	2089
1	4642	1654
2	5001	1654

prune462.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
16.7b	(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
16.7b	(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
16.7b	(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

rewrite512.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-div`
30×	`associate-*r/`
26×	`frac-sub`
25×	`cbrt-prod`
23×	`add-sqr-sqrt`
16×	`frac-times`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`flip3--` `flip3-+` `flip--` `flip-+`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`associate-*l/` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

366.0ms	(* (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
45.0ms	(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
47.0ms	(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
48.0ms	(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

546.0ms	(* (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
479.0ms	(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
481.0ms	(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
466.0ms	(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

simplify105.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	554	4431
1	2608	4254
2	5001	4131

prune551.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 0.0625) (pow x 5))
0.2b	(/ 0.125 (pow x 3))
14.6b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.0b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
110×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
47×	`unpow-prod-down`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
19×	`associate-/r*`
17×	`sqr-pow`
15×	`add-exp-log`
14×	`cube-prod` `distribute-lft-out--`
13×	`associate-/l*`
12×	`log-prod`
10×	`difference-of-squares`
9×	`add-log-exp`
8×	`neg-mul-1` `frac-sub` `add-cbrt-cube`
6×	`div-exp`
5×	`pow1` `log-div`
4×	`cube-mult` `flip3--` `unpow3` `flip--`
3×	`diff-log` `associate--r+`
2×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `sub-neg` `frac-2neg` `div-sub` `pow-exp` `clear-num` `div-inv` `associate--r-`
1×	`distribute-frac-neg` `rem-log-exp` `log-pow`

Counts

4 → 223

Calls

4 calls:

6.0ms	(/ (- 0.0625) (pow x 5))
4.0ms	(/ 0.125 (pow x 3))
171.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
184.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (- 0.0625) (pow x 5))
35.0ms	(/ 0.125 (pow x 3))
190.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
53.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify102.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	837	1970
1	3817	1891
2	5002	1883

prune620.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 32.7b

bsearch84.0ms

Steps

Iters	Range		Point
10	7.712829756242493e-08	8770343.893451896	0.8919458554924102
9	-1827977.1926269082	-0.00043085380315138777	-1.0384538355180963

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample1.9s

Algorithm

intervals

Results

987.0ms	2382×	body	1280	valid
357.0ms	1513×	body	640	valid
204.0ms	730×	body	2560	valid
106.0ms	769×	body	320	valid
68.0ms	2212×	body	80	valid
31.0ms	394×	body	160	valid