Details

sample79.0ms

Algorithm

intervals

Results

40.0ms	108×	body	1280	valid
15.0ms	18×	body	2560	valid
9.0ms	50×	body	640	valid
4.0ms	29×	body	320	valid
2.0ms	43×	body	80	valid
1.0ms	8×	body	160	valid

simplify7.0ms

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: 35.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (tan (+ x eps)) (tan x))
4.4b	(tan (+ x eps))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
5×	`tan-quot`
4×	`tan-sum` `add-log-exp`
3×	`fma-neg` `frac-sub`
2×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
8.0ms	(tan (+ x eps))

series144.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (tan (+ x eps)) (tan x))
51.0ms	(tan (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	203	445
1	531	344
2	2464	335
3	5001	280

prune100.0ms

Filtered

49 candidates to 33 candidates (67.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	39	10	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	10	50

Merged error: 12.9b

Counts

50 → 10

localize11.0ms

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))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

352×	`*-un-lft-identity`
305×	`add-sqr-sqrt`
181×	`times-frac`
126×	`prod-diff`
122×	`add-cube-cbrt`
90×	`difference-of-squares`
48×	`distribute-lft-out`
45×	`distribute-lft-out--` `unswap-sqr`
42×	`fma-neg`
29×	`tan-quot`
25×	`associate-l`
19×	`frac-sub`
18×	`associate-/r*`
10×	`associate-/r/`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
6×	`pow1` `flip3--` `flip--` `associate-/l/`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `associate-r` `frac-add` `flip-+`
2×	`frac-2neg` `clear-num`
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`

Counts

4 → 313

Calls

4 calls:

14.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
5.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan eps) (tan x))
36.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series798.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
101.0ms	(+ (tan x) (tan eps))
101.0ms	(* (tan eps) (tan x))
376.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify129.0ms

Algorithm

egg-herbie

Counts

325 → 325

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	857	6288
1	3288	5037
2	5003	4966

prune471.0ms

Filtered

325 candidates to 150 candidates (46.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	312	13	325
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	320	15	335

Merged error: 12.8b

Counts

335 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ 1 (- 1 (* (tan eps) (tan x))))
0.2b	(* (tan eps) (tan x))
2.8b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan eps) (tan x)))) (- (tan x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`times-frac`
21×	`add-cube-cbrt`
16×	`difference-of-squares`
10×	`add-exp-log`
9×	`associate-/r*` `unswap-sqr`
8×	`add-cbrt-cube` `distribute-lft-out--`
7×	`pow1` `associate-l`
6×	`tan-quot` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-/l*`
2×	`div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `flip3--` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `inv-pow`

Counts

4 → 110

Calls

4 calls:

5.0ms	(+ (tan x) (tan eps))
9.0ms	(/ 1 (- 1 (* (tan eps) (tan x))))
5.0ms	(* (tan eps) (tan x))
1.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan eps) (tan x)))) (- (tan x)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (tan x) (tan eps))
135.0ms	(/ 1 (- 1 (* (tan eps) (tan x))))
97.0ms	(* (tan eps) (tan x))
311.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan eps) (tan x)))) (- (tan x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	416	1017
1	1595	883
2	5001	883

prune270.0ms

Filtered

122 candidates to 77 candidates (63.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	123	14	137

Merged error: 12.8b

Counts

137 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan eps) (tan x))
0.2b	(* (tan eps) (tan x))
0.3b	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
2.8b	(- (/ (* (+ (tan x) (tan eps)) (fma (tan eps) (tan x) 1)) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (tan x))

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

3404×	`add-sqr-sqrt`
1681×	`*-un-lft-identity`
1250×	`times-frac`
1172×	`unswap-sqr`
957×	`difference-of-squares`
954×	`prod-diff`
686×	`add-cube-cbrt`
579×	`associate-l`
321×	`associate-r`
318×	`fma-neg`
226×	`swap-sqr`
210×	`*-commutative`
160×	`distribute-lft-out--`
97×	`distribute-lft-out`
85×	`tan-quot`
47×	`pow1`
43×	`frac-sub`
24×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
16×	`associate-*l/`
13×	`associate-r/` `associate-/l`
10×	`prod-exp` `cbrt-unprod`
8×	`associate-/r/`
6×	`add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`pow-plus`
1×	`pow2` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `frac-add` `clear-num` `flip-+`

Counts

4 → 1469

Calls

4 calls:

6.0ms	(* (tan eps) (tan x))
6.0ms	(* (tan eps) (tan x))
21.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
167.0ms	(- (/ (* (+ (tan x) (tan eps)) (fma (tan eps) (tan x) 1)) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (tan eps) (tan x))
95.0ms	(* (tan eps) (tan x))
117.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
790.0ms	(- (/ (* (+ (tan x) (tan eps)) (fma (tan eps) (tan x) 1)) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (tan x))

simplify411.0ms

Algorithm

egg-herbie

Counts

1481 → 1481

Iterations

Useful iterations: 1 (70.0ms)

Iter	Nodes	Cost
0	3030	44189
1	5002	36244

prune1.8s

Filtered

1481 candidates to 362 candidates (24.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	1474	7	1481
Fresh	6	7	13
Picked	0	1	1
Done	0	0	0
Total	1480	15	1495

Merged error: 12.8b

Counts

1495 → 15

regimes166.0ms

Accuracy

88.1% (0.9b remaining)

Error of 15.1b against oracle of 14.2b and baseline of 22.0b

bsearch107.0ms

Steps

Iters	Range		Point
8	4.3316867191426435e-48	2.8908657421656e-45	2.6139865205108016e-45
7	-2.5402615198525885e-31	-1.098374228695933e-32	-1.8570209891564074e-31

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	72
1	52	72

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	3300×	body	1280	valid
506.0ms	603×	body	2560	valid
382.0ms	1864×	body	640	valid
106.0ms	773×	body	320	valid
44.0ms	1113×	body	80	valid
30.0ms	347×	body	160	valid