Details

sample271.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0%

Results

48.0ms	114×	body	1280	valid
18.0ms	21×	body	2560	valid
13.0ms	63×	body	640	valid
3.0ms	19×	body	320	valid
2.0ms	37×	body	80	valid
0.0ms	2×	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

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: 35.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (tan (+ x eps)) (tan x))
3.8b	(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))

simplify76.0ms

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

prune64.0ms

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: 15.0b

Counts

32 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

3.0ms	(- 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))

series165.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(- 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))

simplify121.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	343	662
1	1170	624
2	4756	614
3	5001	614

prune128.0ms

Filtered

56 candidates to 74 candidates (-32.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	65	9	74
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	69	13	82

Merged error: 14.9b

Counts

82 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
0.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
6.0ms	(/ (* (tan x) (sin eps)) (cos eps))
5.0ms	(* (tan x) (sin eps))
20.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series156.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan x) (tan eps))
22.0ms	(/ (* (tan x) (sin eps)) (cos eps))
15.0ms	(* (tan x) (sin eps))
99.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	385	785
1	1424	711
2	5001	699

prune116.0ms

Filtered

61 candidates to 82 candidates (-34.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	82	13	95

Merged error: 14.9b

Counts

95 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (- 1 (* (tan x) (tan eps))) 3))
0.2b	(pow (- 1 (* (tan x) (tan eps))) 3)
0.3b	(* (tan x) (tan eps))
0.9b	(- (/ (+ (tan x) (tan eps)) (cbrt (pow (- 1 (* (tan x) (tan eps))) 3))) (tan x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

3.0ms	(cbrt (pow (- 1 (* (tan x) (tan eps))) 3))
4.0ms	(pow (- 1 (* (tan x) (tan eps))) 3)
5.0ms	(* (tan x) (tan eps))
27.0ms	(- (/ (+ (tan x) (tan eps)) (cbrt (pow (- 1 (* (tan x) (tan eps))) 3))) (tan x))

series183.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt (pow (- 1 (* (tan x) (tan eps))) 3))
37.0ms	(pow (- 1 (* (tan x) (tan eps))) 3)
23.0ms	(* (tan x) (tan eps))
98.0ms	(- (/ (+ (tan x) (tan eps)) (cbrt (pow (- 1 (* (tan x) (tan eps))) 3))) (tan x))

simplify57.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	411	1066
1	1644	1001
2	5001	989

prune113.0ms

Filtered

63 candidates to 101 candidates (-60.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	100	14	114

Merged error: 14.9b

Counts

114 → 14

regimes200.0ms

Accuracy

88.8% (0.8b remaining)

Error of 15.6b against oracle of 14.8b and baseline of 22.0b

bsearch76.0ms

Steps

Iters	Range		Point
8	2.204477728256459e-48	4.345194051043022e-45	1.6277682026229048e-45
9	-1.7456715723823598e-53	-4.089749456738131e-62	-3.0916808970742654e-54

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample2.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0%

Results

1.3s	3284×	body	1280	valid
573.0ms	660×	body	2560	valid
380.0ms	1778×	body	640	valid
114.0ms	766×	body	320	valid
56.0ms	1139×	body	80	valid
36.0ms	373×	body	160	valid

Details

sample271.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series39.0ms

simplify76.0ms

prune64.0ms

localize13.0ms

rewrite25.0ms

series165.0ms

simplify121.0ms

prune128.0ms

localize16.0ms

rewrite37.0ms

series156.0ms

simplify45.0ms

prune116.0ms

localize14.0ms

rewrite42.0ms

series183.0ms

simplify57.0ms

prune113.0ms

regimes200.0ms

bsearch76.0ms

simplify1.0ms

end0.0ms

sample2.9s

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