Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	54×	body	1280	valid
3.0ms	136×	body	80	valid
3.0ms	37×	body	640	valid
1.0ms	18×	body	320	valid
0.0ms	11×	body	160	valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

25.0ms	(/ (+ x 1.0) (- x 1.0))
10.0ms	(/ x (+ x 1.0))
115.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (+ x 1.0) (- x 1.0))
30.0ms	(/ x (+ x 1.0))
120.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify215.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	1208	18366
1	3687	13388
2	5001	13292

prune725.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
3.3b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite804.0ms

Algorithm

rewrite-expression-head

Rules

4459×	`*-un-lft-identity`
3312×	`times-frac`
2747×	`add-sqr-sqrt`
2436×	`prod-diff`
2258×	`unpow-prod-down` `cube-prod`
1963×	`add-cube-cbrt`
840×	`distribute-lft-out`
420×	`associate-/r/`
397×	`distribute-lft-out--`
380×	`difference-of-squares`
210×	`div-inv`
124×	`flip3-+` `flip-+`
115×	`sqr-pow`
103×	`cube-mult` `unpow3`
87×	`flip3--` `flip--`
42×	`fma-neg`
24×	`swap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
13×	`pow1`
6×	`cbrt-undiv` `pow-unpow` `div-exp` `add-log-exp`
4×	`cube-div` `expm1-log1p-u` `pow-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `rem-cube-cbrt` `unswap-sqr`
2×	`pow-to-exp` `pow-pow`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub`

Counts

4 → 2789

Calls

4 calls:

22.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
49.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
15.0ms	(pow (/ x (+ x 1.0)) 3)
342.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series412.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
41.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
50.0ms	(pow (/ x (+ x 1.0)) 3)
267.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify922.0ms

Algorithm

egg-herbie

Counts

2801 → 2801

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2426	103769
1	5003	93457

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
28.9b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`add-exp-log` `associate-/r*`
7×	`add-cbrt-cube` `associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `associate-/r/`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l/`
1×	`rec-exp` `flip3--` `pow-flip` `1-exp` `flip--` `fma-udef` `inv-pow`

Counts

3 → 96

Calls

3 calls:

11.0ms	(/ 1 (+ x 1.0))
27.0ms	(/ (+ x 1.0) (- x 1.0))
0.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series188.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ 1 (+ x 1.0))
41.0ms	(/ (+ x 1.0) (- x 1.0))
126.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify101.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	352	622
1	1159	566
2	4375	539
3	5001	535

prune191.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

20.7b	(* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3))
20.7b	(* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3))
29.3b	(fma (pow (/ x (- (* x x) (* 1.0 1.0))) 3) (pow (- x 1.0) 3) (- (* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3))))
32.2b	(fma (- (pow (/ 1 (- x 1.0)) 3)) (pow (+ x 1.0) 3) (* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
96×	`-un-lft-identity` `associate-l*`
92×	`times-frac`
90×	`unpow-prod-down` `cube-prod`
64×	`add-exp-log` `unswap-sqr`
48×	`add-cube-cbrt`
36×	`pow-exp` `prod-exp`
28×	`associate-r` `sqr-pow`
18×	`pow-to-exp`
14×	`cube-div`
12×	`div-exp` `distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-cbrt-cube`
6×	`rec-exp` `1-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `frac-times` `flip3--` `flip3-+` `unpow3` `associate-*r/` `flip--` `flip-+` `log1p-expm1-u` `div-inv` `distribute-lft-out` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 278

Calls

4 calls:

99.0ms	(* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3))
100.0ms	(* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3))
0.0ms	(fma (pow (/ x (- (* x x) (* 1.0 1.0))) 3) (pow (- x 1.0) 3) (- (* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3))))
0.0ms	(fma (- (pow (/ 1 (- x 1.0)) 3)) (pow (+ x 1.0) 3) (* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3)))

series891.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3))
74.0ms	(* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3))
317.0ms	(fma (pow (/ x (- (* x x) (* 1.0 1.0))) 3) (pow (- x 1.0) 3) (- (* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3))))
430.0ms	(fma (- (pow (/ 1 (- x 1.0)) 3)) (pow (+ x 1.0) 3) (* (pow (/ 1 (- x 1.0)) 3) (pow (+ x 1.0) 3)))

simplify124.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	581	2792
1	3168	2491
2	5001	2436

prune961.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes56.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.7b

bsearch122.0ms

Steps

Iters	Range		Point
10	18189.836774986274	3039113653047454.0	18487.752119395096
7	-598248.8181308185	-11413.0783357711	-29617.572649619902

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	82
1	93	82
2	107	82
3	109	82
4	109	82

end0.0ms

sample557.0ms

Algorithm

intervals

Results

178.0ms	1682×	body	1280	valid
108.0ms	1257×	body	640	valid
89.0ms	4111×	body	80	valid
43.0ms	642×	body	320	valid
13.0ms	308×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6