Details

sample78.0ms

Algorithm

intervals

Results

40.0ms	113×	body	1280	valid
11.0ms	49×	body	640	valid
10.0ms	12×	body	2560	valid
4.0ms	30×	body	320	valid
2.0ms	43×	body	80	valid
1.0ms	9×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

prune3.0ms

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: 38.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (tan (+ x eps)) (tan x))
4.1b	(tan (+ x eps))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

6.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series42.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- (tan (+ x eps)) (tan x))
19.0ms	(tan (+ x eps))

simplify61.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4947	335
1	4947	335

prune59.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 15.8b

Counts

32 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

7.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series192.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
20.0ms	(+ (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
97.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5281	1555

prune158.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	92	13	105

Merged error: 15.6b

Counts

105 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (tan x))
0.2b	(pow (exp (tan x)) (tan eps))
3.0b	(log (pow (exp (tan x)) (tan eps)))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
7×	`log-prod` `add-log-exp`
6×	`unpow-prod-down` `exp-prod`
5×	`pow1` `add-exp-log`
4×	`pow-pow` `add-cbrt-cube`
3×	`pow-unpow` `rem-log-exp`
2×	`pow-to-exp` `pow-exp` `difference-of-squares` `sqr-pow`
1×	`tan-quot` `sub-neg` `flip3--` `times-frac` `diff-log` `log-pow` `frac-sub` `flip--` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 65

Calls

4 calls:

2.0ms	(exp (tan x))
4.0ms	(pow (exp (tan x)) (tan eps))
2.0ms	(log (pow (exp (tan x)) (tan eps)))
15.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

series200.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(exp (tan x))
32.0ms	(pow (exp (tan x)) (tan eps))
37.0ms	(log (pow (exp (tan x)) (tan eps)))
122.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5002	923

prune113.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	80	10	90

Merged error: 13.4b

Counts

90 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
10.3b	(+ (* (+ (tan x) (tan eps)) (cos x)) (* (sin x) (+ (* (tan x) (tan eps)) -1)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
11×	`associate-*l/`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
9×	`associate-r` `frac-add`
8×	`associate-*r/`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `sum-log` `distribute-lft-out`

Counts

4 → 83

Calls

4 calls:

7.0ms	(* (+ (tan x) (tan eps)) (cos x))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
10.0ms	(+ (* (+ (tan x) (tan eps)) (cos x)) (* (sin x) (+ (* (tan x) (tan eps)) -1)))

series119.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ (tan x) (tan eps)) (cos x))
21.0ms	(* (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
51.0ms	(+ (* (+ (tan x) (tan eps)) (cos x)) (* (sin x) (+ (* (tan x) (tan eps)) -1)))

simplify41.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5088	1412

prune113.0ms

Filtered

74 candidates to 95 candidates (-28.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	97	8	105

Merged error: 0.2b

Counts

105 → 8

regimes131.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	27
1	24	27

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3359×	body	1280	valid
543.0ms	613×	body	2560	valid
398.0ms	1836×	body	640	valid
105.0ms	752×	body	320	valid
48.0ms	1093×	body	80	valid
33.0ms	347×	body	160	valid

Details

sample78.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series42.0ms

simplify61.0ms

prune59.0ms

localize10.0ms

rewrite29.0ms

series192.0ms

simplify48.0ms

prune158.0ms

localize15.0ms

rewrite24.0ms

series200.0ms

simplify52.0ms

prune113.0ms

localize19.0ms

rewrite30.0ms

series119.0ms

simplify41.0ms

prune113.0ms

regimes131.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

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