Details

sample88.0ms

Algorithm

intervals

Results

39.0ms	105×	body	1280	valid
21.0ms	25×	body	2560	valid
13.0ms	61×	body	640	valid
4.0ms	29×	body	320	valid
1.0ms	28×	body	80	valid
1.0ms	8×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 37.5b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
3.6b	(tan (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`tan-quot`
4×	`add-sqr-sqrt` `tan-sum` `*-un-lft-identity` `add-log-exp`
3×	`frac-sub`
2×	`pow1` `add-exp-log` `+-commutative` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 27

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series146.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(- (tan (+ x eps)) (tan x))
51.0ms	(tan (+ x eps))

simplify84.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	146	236
1	307	227
2	769	225
3	2494	224
4	5001	224

prune93.0ms

Filtered

33 candidates to 25 candidates (75.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	25	8	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	8	34

Merged error: 16.3b

Counts

34 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan eps) (tan x))
2.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

85×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
37×	`times-frac`
29×	`tan-quot`
26×	`difference-of-squares`
23×	`add-cube-cbrt`
19×	`frac-sub`
18×	`associate-/r*`
13×	`distribute-lft-out--` `unswap-sqr`
12×	`distribute-lft-out`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
6×	`pow1` `associate-/l/`
3×	`flip3-+` `associate-r` `frac-add` `flip-+`
2×	`flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 134

Calls

4 calls:

18.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
5.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan eps) (tan x))
29.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series757.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
91.0ms	(+ (tan x) (tan eps))
95.0ms	(* (tan eps) (tan x))
361.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify68.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	603	2005
1	2335	1933
2	5002	1933

prune398.0ms

Filtered

146 candidates to 96 candidates (65.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	127	19	146
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	135	19	154

Merged error: 16.2b

Counts

154 → 19

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan eps) (tan x))
0.3b	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.3b	(pow (* (tan eps) (tan x)) 3)
2.3b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))))) (tan x))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

126×	`tan-quot` `add-sqr-sqrt`
80×	`frac-sub`
71×	`frac-times`
69×	`*-un-lft-identity`
48×	`pow1` `associate-/r*`
39×	`associate-*l/` `difference-of-squares`
36×	`associate-l`
33×	`associate-r`
31×	`add-cube-cbrt`
30×	`flip3-+` `flip-+`
29×	`unswap-sqr`
24×	`unpow-prod-down` `cube-prod`
21×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`swap-sqr`
12×	`associate-/l*`
10×	`prod-exp` `cbrt-unprod`
9×	`associate-/l/`
8×	`associate--l+` `*-commutative`
7×	`sqr-pow`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`+-commutative` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `pow-sqr` `pow-prod-up`
3×	`cube-div` `pow-unpow` `frac-2neg` `frac-add` `clear-num` `distribute-lft-out`
2×	`pow-pow` `pow-plus` `pow-exp` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `times-frac` `diff-log` `unpow3` `flip--`

Counts

4 → 261

Calls

4 calls:

5.0ms	(* (tan eps) (tan x))
18.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
8.0ms	(pow (* (tan eps) (tan x)) 3)
241.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))))) (tan x))

series1.9s

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan eps) (tan x))
112.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
128.0ms	(pow (* (tan eps) (tan x)) 3)
1.6s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))))) (tan x))

simplify115.0ms

Algorithm

egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2373	8301
1	5002	8084

prune866.0ms

Filtered

273 candidates to 157 candidates (57.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	267	6	273
Fresh	13	5	18
Picked	1	0	1
Done	0	0	0
Total	281	11	292

Merged error: 14.0b

Counts

292 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (tan eps) (tan x)) 3)
0.3b	(pow (* (tan eps) (tan x)) 3)
0.3b	(* (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3))))
2.4b	(- (* 1 (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3)))) (tan x))

rewrite789.0ms

Algorithm

rewrite-expression-head

Rules

4347×	`tan-quot`
3006×	`frac-times`
2565×	`associate-*r/`
1345×	`associate-*l/`
1264×	`frac-add`
1235×	`add-sqr-sqrt`
784×	`associate-/r*`
762×	`*-un-lft-identity`
641×	`difference-of-squares`
236×	`unpow-prod-down` `cube-prod`
224×	`unswap-sqr`
200×	`associate-/l*`
147×	`associate-/l/`
144×	`add-cube-cbrt`
136×	`associate-r`
108×	`sqr-pow`
94×	`associate-l`
86×	`distribute-lft-out`
76×	`flip3-+` `flip-+`
67×	`times-frac`
56×	`distribute-lft-out--`
51×	`clear-num`
49×	`frac-2neg`
29×	`frac-sub`
24×	`distribute-rgt-out`
15×	`add-exp-log` `add-cbrt-cube`
13×	`*-commutative`
12×	`pow1`
8×	`swap-sqr`
6×	`cube-div` `pow-unpow` `un-div-inv` `add-log-exp`
4×	`pow-pow` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
3×	`pow-prod-down`
2×	`cube-mult` `pow-to-exp` `flip3--` `unpow3` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `div-inv`

Counts

4 → 1572

Calls

4 calls:

8.0ms	(pow (* (tan eps) (tan x)) 3)
8.0ms	(pow (* (tan eps) (tan x)) 3)
175.0ms	(* (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3))))
67.0ms	(- (* 1 (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

124.0ms	(pow (* (tan eps) (tan x)) 3)
121.0ms	(pow (* (tan eps) (tan x)) 3)
483.0ms	(* (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3))))
514.0ms	(- (* 1 (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3)))) (tan x))

simplify443.0ms

Algorithm

egg-herbie

Counts

1584 → 1584

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5001	58723

prune7.8s

Filtered

1584 candidates to 1066 candidates (67.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	1577	7	1584
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	1585	10	1595

Merged error: 0.1b

Counts

1595 → 10

regimes169.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 20.2b

bsearch208.0ms

Steps

Iters	Range		Point
8	2.4853599159652707e-08	7.157538394725048e-05	1.0062887731628292e-05
10	-158403.45398835975	-1.2252616440760547e-11	-4.231189509677948e-06

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	109	130
1	143	130
2	148	130
3	148	130

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3264×	body	1280	valid
606.0ms	685×	body	2560	valid
393.0ms	1819×	body	640	valid
109.0ms	777×	body	320	valid
48.0ms	1139×	body	80	valid
29.0ms	316×	body	160	valid