Details

sample88.0ms

Algorithm

intervals

Results

42.0ms	110×	body	1280	valid
13.0ms	16×	body	2560	valid
12.0ms	56×	body	640	valid
6.0ms	18×	body	320	valid
2.0ms	43×	body	80	valid
1.0ms	13×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 34.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (tan (+ x eps)) (tan x))
3.0b	(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))

series43.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (21.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune52.0ms

Filtered

31 candidates to 25 candidates (19.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	25	6	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	6	32

Merged error: 12.9b

Counts

32 → 6

localize11.0ms

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))
1.7b	(- (/ (+ (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))

series190.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms	(+ (tan x) (tan eps))
20.0ms	(* (tan x) (tan eps))
95.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	994

prune143.0ms

Filtered

98 candidates to 74 candidates (24.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	89	9	98
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	93	11	104

Merged error: 12.8b

Counts

104 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (* (tan x) (tan eps)))
0.2b	(* (tan x) (tan eps))
1.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
2.7b	(log (exp (* (tan x) (tan eps))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`tan-quot`
3×	`log-prod` `associate-r` `associate-l` `log-pow`
2×	`exp-prod` `exp-to-pow` `difference-of-squares`
1×	`frac-times` `sub-neg` `flip3--` `times-frac` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

6.0ms	(exp (* (tan x) (tan eps)))
7.0ms	(* (tan x) (tan eps))
18.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
2.0ms	(log (exp (* (tan x) (tan eps))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(exp (* (tan x) (tan eps)))
21.0ms	(* (tan x) (tan eps))
133.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
37.0ms	(log (exp (* (tan x) (tan eps))))

simplify73.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	271	685
1	808	627
2	2809	613
3	5001	613

prune110.0ms

Filtered

73 candidates to 53 candidates (27.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	73	11	84

Merged error: 12.8b

Counts

84 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (tan x) (tan eps)) (cos x))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
8.0b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

7.0ms	(* (+ (tan x) (tan eps)) (cos x))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
9.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

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)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	527	955
1	2405	907
2	5002	907

prune120.0ms

Filtered

94 candidates to 72 candidates (23.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	87	7	94
Fresh	6	3	9
Picked	1	0	1
Done	0	1	1
Total	94	11	105

Merged error: 0.1b

Counts

105 → 11

regimes155.0ms

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	29	21
1	29	21

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3285×	body	1280	valid
537.0ms	621×	body	2560	valid
385.0ms	1805×	body	640	valid
109.0ms	804×	body	320	valid
48.0ms	1103×	body	80	valid
35.0ms	382×	body	160	valid

Details

sample88.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series43.0ms

simplify73.0ms

prune52.0ms

localize11.0ms

rewrite29.0ms

series190.0ms

simplify42.0ms

prune143.0ms

localize13.0ms

rewrite35.0ms

series221.0ms

simplify73.0ms

prune110.0ms

localize19.0ms

rewrite28.0ms

series119.0ms

simplify68.0ms

prune120.0ms

regimes155.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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