Details

sample92.0ms

Algorithm

intervals

Results

43.0ms	99×	body	1280	valid
18.0ms	20×	body	2560	valid
13.0ms	61×	body	640	valid
3.0ms	22×	body	320	valid
2.0ms	46×	body	80	valid
1.0ms	8×	body	160	valid

simplify5.0ms

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

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: 38.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (tan (+ x eps)) (tan x))
3.3b	(tan (+ x eps))

rewrite11.0ms

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

series43.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (22.0ms)

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

prune62.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	23	8	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 14.3b

Counts

32 → 8

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

rewrite31.0ms

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:

8.0ms	(/ (+ (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))

series197.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(+ (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
100.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	397	1052
1	1432	1007
2	5001	995

prune183.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	83	15	98
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	88	18	106

Merged error: 14.1b

Counts

106 → 18

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
10.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
11.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series392.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
31.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
317.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify79.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	599	1352
1	3021	1220
2	5001	1220

prune182.0ms

Filtered

76 candidates to 122 candidates (-60.5%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	120	20	140

Merged error: 14.1b

Counts

140 → 20

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 2)
2.8b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

13×	`tan-quot` `add-sqr-sqrt`
11×	`pow1` `add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`frac-sub`
4×	`frac-times` `associate-*r/`
3×	`pow-unpow` `pow-prod-down` `associate-*l/` `prod-exp`
2×	`pow-pow` `flip3-+` `pow-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `unpow-prod-down` `flip3--` `distribute-lft-in` `diff-log` `flip--` `unpow2` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
5.0ms	(pow (* (tan x) (tan eps)) 2)
17.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series392.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
29.0ms	(pow (* (tan x) (tan eps)) 2)
318.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify69.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	518	1048
1	2493	958
2	5002	958

prune123.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	6	13	19
Picked	0	1	1
Done	0	0	0
Total	92	19	111

Merged error: 14.1b

Counts

111 → 19

regimes275.0ms

Accuracy

88% (0.9b remaining)

Error of 15.1b against oracle of 14.2b and baseline of 21.7b

bsearch75.0ms

Steps

Iters	Range		Point
7	2.1181145555577212e-29	3.981426531127762e-27	1.0191077428645162e-28
9	-3.094896026434978e-75	-1.8293544552739442e-83	-9.21724289424432e-76

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	62
1	61	62
2	62	62
3	62	62

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3264×	body	1280	valid
559.0ms	647×	body	2560	valid
395.0ms	1819×	body	640	valid
108.0ms	757×	body	320	valid
52.0ms	1152×	body	80	valid
36.0ms	361×	body	160	valid

Details

sample92.0ms

simplify5.0ms

prune3.0ms

localize9.0ms

rewrite11.0ms

series43.0ms

simplify77.0ms

prune62.0ms

localize11.0ms

rewrite31.0ms

series197.0ms

simplify46.0ms

prune183.0ms

localize15.0ms

rewrite38.0ms

series392.0ms

simplify79.0ms

prune182.0ms

localize15.0ms

rewrite35.0ms

series392.0ms

simplify69.0ms

prune123.0ms

regimes275.0ms

bsearch75.0ms

simplify3.0ms

end0.0ms

sample2.7s

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