Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	66×	body	1280	valid
3.0ms	132×	body	80	valid
3.0ms	33×	body	640	valid
1.0ms	19×	body	320	valid
0.0ms	6×	body	160	valid

simplify21.0ms

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

prune1.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite108.0ms

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:

5.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
40.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ x (+ x 1.0))
36.0ms	(/ (+ x 1.0) (- x 1.0))
131.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify216.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (72.0ms)

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

prune731.0ms

Filtered

605 candidates to 217 candidates (35.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (+ x 1.0) (- x 1.0))))
0.0b	(/ (+ x 1.0) (- x 1.0))
0.5b	(expm1 (/ (+ x 1.0) (- x 1.0)))
2.1b	(- (/ x (+ x 1.0)) (log1p (expm1 (/ (+ x 1.0) (- x 1.0)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

113×	`*-un-lft-identity`
80×	`add-sqr-sqrt`
69×	`times-frac`
65×	`add-cube-cbrt`
54×	`prod-diff`
18×	`fma-neg` `distribute-lft-out`
10×	`associate-/r/`
7×	`add-log-exp` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
5×	`flip3-+` `associate-/r*` `flip-+` `log1p-expm1-u` `div-inv`
4×	`pow1` `expm1-log1p-u` `associate-/l*`
2×	`log1p-udef` `flip3--` `diff-log` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `expm1-log1p` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `expm1-udef`

Counts

4 → 159

Calls

4 calls:

1.0ms	(log1p (expm1 (/ (+ x 1.0) (- x 1.0))))
8.0ms	(/ (+ x 1.0) (- x 1.0))
1.0ms	(expm1 (/ (+ x 1.0) (- x 1.0)))
16.0ms	(- (/ x (+ x 1.0)) (log1p (expm1 (/ (+ x 1.0) (- x 1.0)))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(log1p (expm1 (/ (+ x 1.0) (- x 1.0))))
42.0ms	(/ (+ x 1.0) (- x 1.0))
89.0ms	(expm1 (/ (+ x 1.0) (- x 1.0)))
255.0ms	(- (/ x (+ x 1.0)) (log1p (expm1 (/ (+ x 1.0) (- x 1.0)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	550	3056
1	1750	1635
2	5001	1598

prune278.0ms

Filtered

171 candidates to 99 candidates (57.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0))))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.1b	(fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

452×	`*-un-lft-identity`
248×	`times-frac`
142×	`add-sqr-sqrt`
112×	`distribute-lft-out`
80×	`add-cube-cbrt`
53×	`distribute-lft-out--`
48×	`swap-sqr`
26×	`associate-r` `associate-l`
25×	`difference-of-squares`
20×	`add-exp-log` `add-cbrt-cube`
17×	`associate-/r*`
13×	`associate-/r/`
11×	`pow1`
7×	`associate-/l*`
6×	`cbrt-undiv` `div-exp` `div-inv`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `pow-sqr` `*-commutative` `pow-prod-up` `fma-udef`

Counts

4 → 255

Calls

4 calls:

11.0ms	(/ (+ x 1.0) (- x 1.0))
31.0ms	(/ (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0))))
27.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
1.0ms	(fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

series938.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (+ x 1.0) (- x 1.0))
598.0ms	(/ (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0))))
57.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
247.0ms	(fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

simplify120.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	827	3968
1	4005	3729
2	5003	3664

prune413.0ms

Filtered

267 candidates to 138 candidates (51.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(cbrt (pow (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3))
0.1b	(pow (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3)
2.1b	(fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

224×	`*-un-lft-identity`
128×	`times-frac`
110×	`add-sqr-sqrt`
58×	`add-cube-cbrt`
48×	`swap-sqr`
38×	`distribute-lft-out`
32×	`distribute-lft-out--`
26×	`associate-r` `associate-l`
20×	`difference-of-squares`
17×	`add-exp-log` `add-cbrt-cube`
12×	`pow1` `cbrt-prod`
8×	`associate-/r/`
6×	`unpow-prod-down` `cube-prod`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow2` `frac-times` `pow-to-exp` `pow-pow` `pow-plus` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 188

Calls

4 calls:

28.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.0ms	(cbrt (pow (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3))
2.0ms	(pow (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3)
1.0ms	(fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

series873.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
259.0ms	(cbrt (pow (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3))
316.0ms	(pow (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3)
246.0ms	(fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	730	2671
1	3678	2442
2	5002	2379

prune379.0ms

Filtered

200 candidates to 107 candidates (53.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes46.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 29.3b

bsearch75.0ms

Steps

Iters	Range		Point
8	136.14768989527596	4873390.516357292	12465.73071789302
8	-21754618.13974568	-2693.2368339428763	-19335.42983839344

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	31
1	56	31
2	61	31
3	61	31

end0.0ms

sample536.0ms

Algorithm

intervals

Results

182.0ms	1725×	body	1280	valid
103.0ms	1273×	body	640	valid
94.0ms	4100×	body	80	valid
43.0ms	602×	body	320	valid
13.0ms	300×	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