Details

analyze766.0ms

Algorithm: search

sample87.0ms

Algorithm

intervals

Results

39.0ms	102×	body	1280	valid
18.0ms	71×	body	640	valid
16.0ms	18×	body	2560	valid
3.0ms	19×	body	320	valid
1.0ms	36×	body	80	valid
1.0ms	10×	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: 32.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
3.2b	(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))

series41.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(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

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: 12.6b

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))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite30.0ms

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:

4.0ms	(+ (tan x) (tan eps))
8.0ms	(/ (+ (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))

series391.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (tan x) (tan eps))
249.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(* (tan x) (tan eps))
99.0ms	(- (/ (+ (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

prune181.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	14	98
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	90	16	106

Merged error: 12.5b

Counts

106 → 16

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.1b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
10.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
11.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series396.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
31.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
321.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify80.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	599	1352
1	3021	1220
2	5001	1220

prune180.0ms

Filtered

76 candidates to 122 candidates (-60.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	122	16	138

Merged error: 12.4b

Counts

138 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (sin x) 2)
0.3b	(* (tan eps) (tan eps))
2.1b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (pow (sin x) 2) (* (tan eps) (tan eps))) (pow (cos x) 2)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`pow1`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`tan-quot`
8×	`add-exp-log`
6×	`unpow-prod-down` `pow-unpow` `add-cbrt-cube` `add-log-exp`
5×	`frac-sub`
3×	`frac-times` `associate-r/` `swap-sqr` `associate-r` `associate-l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `associate-*l/` `pow-exp` `associate--l+` `flip-+` `unpow2` `sqr-pow`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

2.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
5.0ms	(* (tan eps) (tan eps))
16.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (pow (sin x) 2) (* (tan eps) (tan eps))) (pow (cos x) 2)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series351.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
9.0ms	(* (tan eps) (tan eps))
336.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (pow (sin x) 2) (* (tan eps) (tan eps))) (pow (cos x) 2)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify72.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	535	1106
1	2525	982
2	5002	978

prune143.0ms

Filtered

59 candidates to 95 candidates (-61.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	95	16	111

Merged error: 12.4b

Counts

111 → 16

regimes212.0ms

Accuracy

88.9% (0.8b remaining)

Error of 14.8b against oracle of 14.0b and baseline of 21.4b

bsearch215.0ms

Steps

Iters	Range		Point
9	6.2674200841749714e-40	1.8204733023730324e-31	1.1446738642675772e-39
6	-1.0359344240825382e-48	-8.364471889944184e-50	-1.0169146585760861e-48

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	50
1	45	50

end0.0ms

analyze768.0ms

Algorithm: search

sample2.6s

Algorithm

intervals

Results

1.3s	3295×	body	1280	valid
524.0ms	607×	body	2560	valid
396.0ms	1866×	body	640	valid
111.0ms	763×	body	320	valid
51.0ms	1130×	body	80	valid
32.0ms	339×	body	160	valid

Details

analyze766.0ms

sample87.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series41.0ms

simplify76.0ms

prune62.0ms

localize11.0ms

rewrite30.0ms

series391.0ms

simplify44.0ms

prune181.0ms

localize14.0ms

rewrite35.0ms

series396.0ms

simplify80.0ms

prune180.0ms

localize24.0ms

rewrite31.0ms

series351.0ms

simplify72.0ms

prune143.0ms

regimes212.0ms

bsearch215.0ms

simplify2.0ms

end0.0ms

analyze768.0ms

sample2.6s

Profiling