Details

sample81.0ms

Algorithm

intervals

Results

44.0ms	109×	body	1280	valid
12.0ms	14×	body	2560	valid
11.0ms	55×	body	640	valid
4.0ms	29×	body	320	valid
1.0ms	36×	body	80	valid
1.0ms	13×	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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 37.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
2.9b	(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))

series141.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (tan (+ x eps)) (tan x))
50.0ms	(tan (+ x eps))

simplify78.0ms

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

prune90.0ms

Filtered

31 candidates to 25 candidates (80.6%)

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: 14.2b

Counts

32 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(- 1 (* (tan x) (tan eps)))
0.2b	(* (tan x) (tan eps))
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(- 1 (* (tan x) (tan eps)))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series839.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
111.0ms	(- 1 (* (tan x) (tan eps)))
96.0ms	(* (tan x) (tan eps))
408.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	401	1066
1	1532	1014
2	5001	1004

prune270.0ms

Filtered

97 candidates to 72 candidates (74.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	85	12	97
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	90	15	105

Merged error: 14.1b

Counts

105 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
27.5b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite38.0ms

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)
22.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
4.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series692.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (tan x) (tan eps))
135.0ms	(pow (* (tan x) (tan eps)) 3)
371.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
92.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	384	791
1	1733	746
2	5002	745

prune261.0ms

Filtered

94 candidates to 67 candidates (71.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	93	16	109

Merged error: 14.1b

Counts

109 → 16

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.3b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
5.4b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite54.0ms

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:

5.0ms	(* (tan x) (tan eps))
8.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
10.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
25.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series990.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (tan x) (tan eps))
283.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
229.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
385.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify82.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	703	2793
1	3294	2509
2	5001	2506

prune303.0ms

Filtered

190 candidates to 103 candidates (54.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	182	8	190
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	188	18	206

Merged error: 14.1b

Counts

206 → 18

regimes195.0ms

Accuracy

86.3% (1.0b remaining)

Error of 15.6b against oracle of 14.6b and baseline of 22.1b

bsearch127.0ms

Steps

Iters	Range		Point
10	2.4207885364210025e-42	1.5859448309362725e-28	6.983508139458444e-29
9	-2.8323207026383242e-99	-1.2649793061547783e-105	-2.7946411682947094e-99

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	23
1	39	23

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	3306×	body	1280	valid
538.0ms	634×	body	2560	valid
377.0ms	1833×	body	640	valid
100.0ms	759×	body	320	valid
44.0ms	1105×	body	80	valid
33.0ms	363×	body	160	valid