Details

sample112.0ms

Algorithm

intervals

Results

30.0ms	70×	body	1280	valid
28.0ms	70×	body	10240	exit
20.0ms	304×	body	80	valid
11.0ms	47×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	10×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (36.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(* (- 1.0 eps) x)
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
2.7b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

6.0ms	(* (+ 1.0 eps) x)
6.0ms	(* (- 1.0 eps) x)
10.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
133.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series285.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (+ 1.0 eps) x)
33.0ms	(* (- 1.0 eps) x)
40.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
185.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	573	1558
1	1984	1475
2	5001	1475

prune364.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
5.0b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite20.0ms

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)))

series108.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 0.5 (pow x 2))
38.0ms	(* 0.33333333333333337 (pow x 3))
44.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify49.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	281	367
1	1210	327
2	5001	314

prune163.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))) 3)
0.1b	(* 0.33333333333333337 (pow x 3))
4.5b	(cbrt (pow (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))) 3))
5.0b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

8.0ms	(pow (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))) 3)
6.0ms	(* 0.33333333333333337 (pow x 3))
8.0ms	(cbrt (pow (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))) 3))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))) 3)
43.0ms	(* 0.33333333333333337 (pow x 3))
39.0ms	(cbrt (pow (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))) 3))
43.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	346	862
1	1520	806
2	5001	799

prune236.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1.5 (pow x 2))
5.0b	(- (+ (* 1.0 (pow x 3)) 1.0) (* 1.5 (pow x 2)))
9.0b	(cbrt (- (+ (* 1.0 (pow x 3)) 1.0) (* 1.5 (pow x 2))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

5.0ms	(* 1.5 (pow x 2))
7.0ms	(- (+ (* 1.0 (pow x 3)) 1.0) (* 1.5 (pow x 2)))
6.0ms	(cbrt (- (+ (* 1.0 (pow x 3)) 1.0) (* 1.5 (pow x 2))))

series225.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 1.5 (pow x 2))
45.0ms	(- (+ (* 1.0 (pow x 3)) 1.0) (* 1.5 (pow x 2)))
154.0ms	(cbrt (- (+ (* 1.0 (pow x 3)) 1.0) (* 1.5 (pow x 2))))

simplify41.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	330	528
1	1200	489
2	5002	454

prune164.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

regimes50.0ms

Accuracy

96.8% (0.5b remaining)

Error of 1.1b against oracle of 0.6b and baseline of 16.9b

bsearch139.0ms

Steps

Iters	Range		Point
9	0.22405535791780642	2068602.189562926	46.924791671462984

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	31
1	40	31

end0.0ms

sample2.8s

Algorithm

intervals

Results

753.0ms	1875×	body	10240	exit
724.0ms	1692×	body	1280	valid
537.0ms	9878×	body	80	valid
328.0ms	1296×	body	640	valid
103.0ms	625×	body	320	valid
33.0ms	313×	body	160	valid