Details

sample10.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.993896%

Results

42.0ms	106×	body	1280	valid
16.0ms	19×	body	2560	valid
12.0ms	55×	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: 33.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
2.9b	(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))

series42.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- (tan (+ x eps)) (tan x))
15.0ms	(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

prune60.0ms

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: 11.8b

Counts

32 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (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))

rewrite28.0ms

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:

3.0ms	(- 1 (* (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))

series200.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(- 1 (* (tan x) (tan eps)))
53.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
23.0ms	(* (tan x) (tan eps))
98.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	401	1066
1	1532	1014
2	5001	1003

prune176.0ms

Filtered

72 candidates to 97 candidates (-34.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	82	15	97
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	88	17	105

Merged error: 11.7b

Counts

105 → 17

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))
0.3b	(* (sin x) (tan eps))
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite42.0ms

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))))
7.0ms	(/ (* (sin x) (tan eps)) (cos x))
5.0ms	(* (sin x) (tan eps))
16.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series195.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
22.0ms	(/ (* (sin x) (tan eps)) (cos x))
16.0ms	(* (sin x) (tan eps))
100.0ms	(- (/ (+ (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	1557
1	1945	1465
2	5001	1463

prune159.0ms

Filtered

82 candidates to 120 candidates (-46.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	120	17	137

Merged error: 11.7b

Counts

137 → 17

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.2b	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
0.2b	(* (tan x) (tan eps))
5.1b	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
14.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
5.0ms	(* (tan x) (tan eps))
14.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos x) (sin eps))
68.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
21.0ms	(* (tan x) (tan eps))
99.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

simplify70.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	586	1415
1	2535	1261
2	5001	1261

prune98.0ms

Filtered

70 candidates to 96 candidates (-37.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	85	11	96
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	92	21	113

Merged error: 11.6b

Counts

113 → 21

regimes285.0ms

Accuracy

87.3% (1.0b remaining)

Error of 16.0b against oracle of 15.1b and baseline of 22.7b

bsearch98.0ms

Steps

Iters	Range		Point
10	3.051267008860385e-20	1.97186230971332e-10	8.9070814780451e-18
7	-2.16426469178295e-60	-6.725490013111577e-62	-2.1399087419179173e-60

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	42
1	52	42

end0.0ms

sample12.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.993896%

Results

1.3s	3353×	body	1280	valid
557.0ms	681×	body	2560	valid
363.0ms	1762×	body	640	valid
108.0ms	800×	body	320	valid
44.0ms	1064×	body	80	valid
31.0ms	340×	body	160	valid

Details

sample10.3s

simplify5.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series42.0ms

simplify78.0ms

prune60.0ms

localize11.0ms

rewrite28.0ms

series200.0ms

simplify49.0ms

prune176.0ms

localize16.0ms

rewrite42.0ms

series195.0ms

simplify57.0ms

prune159.0ms

localize24.0ms

rewrite39.0ms

series197.0ms

simplify70.0ms

prune98.0ms

regimes285.0ms

bsearch98.0ms

simplify2.0ms

end0.0ms

sample12.7s

Profiling