Details

analyze768.0ms

Algorithm: search

sample92.0ms

Algorithm

intervals

Results

44.0ms	101×	body	1280	valid
20.0ms	21×	body	2560	valid
14.0ms	66×	body	640	valid
3.0ms	19×	body	320	valid
2.0ms	38×	body	80	valid
1.0ms	11×	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: 38.1b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
4.3b	(tan (+ x eps))

rewrite15.0ms

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:

10.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series39.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify78.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (23.0ms)

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: 15.9b

Counts

32 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.4b	(- (/ (+ (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:

6.0ms	(+ (tan x) (tan eps))
7.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series188.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (tan x) (tan eps))
54.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
20.0ms	(* (tan x) (tan eps))
95.0ms	(- (/ (+ (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

prune170.0ms

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: 15.7b

Counts

106 → 18

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

10.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
5.0ms	(/ (* (sin x) (tan eps)) (cos x))
5.0ms	(* (sin x) (tan eps))
18.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series192.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
24.0ms	(/ (* (sin x) (tan eps)) (cos x))
16.0ms	(* (sin x) (tan eps))
97.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify57.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	500	1555
1	1945	1463
2	5001	1462

prune169.0ms

Filtered

82 candidates to 120 candidates (-46.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	120	18	138

Merged error: 15.7b

Counts

138 → 18

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin eps) (cos eps))
0.2b	(/ (sin x) (cos x))
0.2b	(* (tan x) (tan eps))
8.7b	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

4.0ms	(/ (sin eps) (cos eps))
4.0ms	(/ (sin x) (cos x))
5.0ms	(* (tan x) (tan eps))
22.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

series135.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ (sin eps) (cos eps))
5.0ms	(/ (sin x) (cos x))
22.0ms	(* (tan x) (tan eps))
102.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify39.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	410	931
1	1306	863
2	5001	850

prune107.0ms

Filtered

80 candidates to 105 candidates (-31.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	98	7	105
Fresh	7	10	17
Picked	1	0	1
Done	0	0	0
Total	106	17	123

Merged error: 14.0b

Counts

123 → 17

regimes250.0ms

Accuracy

94.1% (0.5b remaining)

Error of 13.7b against oracle of 13.1b and baseline of 22.0b

bsearch248.0ms

Steps

Iters	Range		Point
6	9.96540630748219e-45	1.269177370794961e-43	1.1417540727375646e-43
7	-1.1015942559314249e-20	-6.625125053261104e-22	-8.439240075791184e-22

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	42	24

end0.0ms

analyze938.0ms

Algorithm: search

sample2.6s

Algorithm

intervals

Results

1.3s	3263×	body	1280	valid
546.0ms	632×	body	2560	valid
404.0ms	1883×	body	640	valid
107.0ms	783×	body	320	valid
50.0ms	1113×	body	80	valid
31.0ms	326×	body	160	valid

Details

analyze768.0ms

sample92.0ms

simplify5.0ms

prune3.0ms

localize9.0ms

rewrite15.0ms

series39.0ms

simplify78.0ms

prune62.0ms

localize11.0ms

rewrite31.0ms

series188.0ms

simplify44.0ms

prune170.0ms

localize16.0ms

rewrite41.0ms

series192.0ms

simplify57.0ms

prune169.0ms

localize24.0ms

rewrite37.0ms

series135.0ms

simplify39.0ms

prune107.0ms

regimes250.0ms

bsearch248.0ms

simplify2.0ms

end0.0ms

analyze938.0ms

sample2.6s

Profiling