Details

sample83.0ms

Algorithm

intervals

Results

33.0ms	92×	body	1280	valid
19.0ms	22×	body	2560	valid
13.0ms	61×	body	640	valid
4.0ms	27×	body	320	valid
2.0ms	42×	body	80	valid
1.0ms	12×	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: 35.9b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (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))
4.0ms	(tan (+ x eps))

series39.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (tan (+ x eps)) (tan x))
15.0ms	(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

prune98.0ms

Filtered

31 candidates to 25 candidates (19.4%)

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: 12.9b

Counts

32 → 7

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))
1.8b	(- (/ (+ (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:

53.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(+ (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
96.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

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

prune719.0ms

Filtered

98 candidates to 74 candidates (24.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	86	12	98
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	89	16	105

Merged error: 12.8b

Counts

105 → 16

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
1.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
27.8b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`tan-quot`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`cube-div` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(pow (* (tan x) (tan eps)) 3)
24.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
4.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series175.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (tan x) (tan eps))
34.0ms	(pow (* (tan x) (tan eps)) 3)
97.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
21.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify48.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	384	787
1	1733	744
2	5002	743

prune632.0ms

Filtered

94 candidates to 67 candidates (28.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	93	17	110

Merged error: 12.8b

Counts

110 → 17

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.2b	(* (tan x) (tan eps))
0.3b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
4.0b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

8.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
5.0ms	(* (tan x) (tan eps))
10.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
27.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series232.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
21.0ms	(* (tan x) (tan eps))
55.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
97.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify80.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	703	2791
1	3290	2506
2	5001	2503

prune891.0ms

Filtered

190 candidates to 105 candidates (44.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	184	6	190
Fresh	3	12	15
Picked	1	0	1
Done	1	0	1
Total	189	18	207

Merged error: 12.7b

Counts

207 → 18

regimes268.0ms

Accuracy

88.1% (0.9b remaining)

Error of 15.3b against oracle of 14.4b and baseline of 21.6b

bsearch131.0ms

Steps

Iters	Range		Point
8	1.2611993664769552e-51	8.184221022877953e-47	2.1810641200666502e-48
9	-3.5765709940581744e-43	-3.2744036193920184e-48	-3.8779512210660823e-44

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	47
1	53	47
2	53	47

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3400×	body	1280	valid
508.0ms	596×	body	2560	valid
383.0ms	1817×	body	640	valid
96.0ms	701×	body	320	valid
46.0ms	1136×	body	80	valid
32.0ms	350×	body	160	valid

Details

sample83.0ms

simplify4.0ms

prune3.0ms

localize12.0ms

rewrite10.0ms

series39.0ms

simplify73.0ms

prune98.0ms

localize11.0ms

rewrite29.0ms

series192.0ms

simplify44.0ms

prune719.0ms

localize14.0ms

rewrite40.0ms

series175.0ms

simplify48.0ms

prune632.0ms

localize12.0ms

rewrite56.0ms

series232.0ms

simplify80.0ms

prune891.0ms

regimes268.0ms

bsearch131.0ms

simplify2.0ms

end0.0ms

sample2.6s

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