Details

sample83.0ms

Algorithm

intervals

Results

40.0ms	112×	body	1280	valid
17.0ms	21×	body	2560	valid
12.0ms	59×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	35×	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

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: 37.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
3.8b	(tan (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series138.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
52.0ms	(tan (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	192	420
1	538	319
2	2593	310
3	5001	255

prune105.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	37	10	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	10	48

Merged error: 14.6b

Counts

48 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

9.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
17.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series728.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(+ (tan x) (tan eps))
93.0ms	(* (tan x) (tan eps))
345.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify79.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	559	2915
1	2054	2366
2	5001	2345

prune378.0ms

Filtered

181 candidates to 110 candidates (60.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	166	15	181
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	174	17	191

Merged error: 14.4b

Counts

191 → 17

localize16.0ms

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))
2.3b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`tan-quot`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 79

Calls

4 calls:

6.0ms	(* (tan x) (tan eps))
6.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series853.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
585.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify35.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	259	837
1	1059	718
2	5002	684

prune469.0ms

Filtered

91 candidates to 71 candidates (78.0%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	16	16
Picked	1	0	1
Done	0	0	0
Total	91	17	108

Merged error: 14.4b

Counts

108 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (tan eps))
0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

181×	`*-un-lft-identity`
136×	`add-sqr-sqrt`
98×	`times-frac`
90×	`prod-diff`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
30×	`fma-neg`
25×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
17×	`distribute-lft-out--`
9×	`associate-/r/`
8×	`add-log-exp`
6×	`pow1`
5×	`flip3--` `prod-exp` `flip--` `cbrt-unprod` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`tan-quot` `fma-def` `associate-r` `associate-l`
2×	`sin-mult`
1×	`+-commutative` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `clear-num` `associate-/r` `sum-log` `cos-mult` `-commutative` `frac-sub` `flip-+` `associate-/l/` `associate-/l*` `unswap-sqr`

Counts

4 → 202

Calls

4 calls:

5.0ms	(+ (tan x) (tan eps))
5.0ms	(* (sin x) (sin eps))
8.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
21.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series596.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ (tan x) (tan eps))
42.0ms	(* (sin x) (sin eps))
111.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
360.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify101.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	715	4655
1	2931	3696
2	5002	3657

prune416.0ms

Filtered

214 candidates to 105 candidates (49.1%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	212	2	214
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	213	18	231

Merged error: 14.4b

Counts

231 → 18

regimes153.0ms

Accuracy

76.2% (1.7b remaining)

Error of 15.8b against oracle of 14.0b and baseline of 21.4b

bsearch67.0ms

Steps

Iters	Range		Point
6	1.6562438629286766e-161	2.3198190621330934e-160	2.2779433490070854e-160
3	-1.6831681745849877e-31	-1.3783358247051904e-31	-1.5879080652475512e-31

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	18
1	35	18

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	3237×	body	1280	valid
511.0ms	620×	body	2560	valid
376.0ms	1872×	body	640	valid
109.0ms	779×	body	320	valid
46.0ms	1133×	body	80	valid
31.0ms	359×	body	160	valid