Details

sample91.0ms

Algorithm

intervals

Results

42.0ms	106×	body	1280	valid
23.0ms	26×	body	2560	valid
11.0ms	50×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	34×	body	80	valid
1.0ms	13×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 36.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (tan (+ x eps)) (tan x))
4.6b	(tan (+ x eps))

rewrite13.0ms

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:

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

series140.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
53.0ms	(tan (+ x eps))

simplify83.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (74.0ms)

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

prune112.0ms

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))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite44.0ms

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))
18.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series733.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(+ (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
349.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify74.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (53.0ms)

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

prune405.0ms

Filtered

181 candidates to 110 candidates (60.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	166	15	181
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	173	18	191

Merged error: 14.4b

Counts

191 → 18

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 205

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(* (sin x) (sin eps))
8.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
22.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series558.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (cos eps))
50.0ms	(* (sin x) (sin eps))
98.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
369.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify115.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	692	4666
1	2952	3700
2	5001	3660

prune503.0ms

Filtered

217 candidates to 103 candidates (47.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	214	3	217
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	217	18	235

Merged error: 14.4b

Counts

235 → 18

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* (tan x) (tan eps)))
0.2b	(* (tan x) (tan eps))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
3.9b	(log (exp (* (tan x) (tan eps))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

211×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
113×	`times-frac`
102×	`prod-diff`
89×	`add-cube-cbrt`
34×	`fma-neg` `difference-of-squares`
33×	`distribute-lft-out--`
28×	`distribute-lft-out`
23×	`pow1`
19×	`log-pow`
9×	`add-log-exp`
8×	`associate-/r/`
6×	`add-exp-log` `add-cbrt-cube`
5×	`tan-quot` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`log-prod` `associate-r` `associate-l`
2×	`exp-prod` `exp-to-pow`
1×	`frac-times` `sub-neg` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 205

Calls

4 calls:

4.0ms	(exp (* (tan x) (tan eps)))
5.0ms	(* (tan x) (tan eps))
28.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
2.0ms	(log (exp (* (tan x) (tan eps))))

series668.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(exp (* (tan x) (tan eps)))
95.0ms	(* (tan x) (tan eps))
360.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
94.0ms	(log (exp (* (tan x) (tan eps))))

simplify82.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	550	4427
1	1792	3340
2	5002	3281

prune352.0ms

Filtered

217 candidates to 97 candidates (44.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	220	15	235

Merged error: 14.3b

Counts

235 → 15

regimes154.0ms

Accuracy

87.1% (0.9b remaining)

Error of 14.8b against oracle of 13.9b and baseline of 20.8b

bsearch94.0ms

Steps

Iters	Range		Point
7	6.36136280187789e-24	8.2289824352113225e-22	6.649700708263956e-24
7	-5.4036321860508605e-36	-8.669559720866199e-38	-5.183456130247362e-37

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	29	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3319×	body	1280	valid
528.0ms	603×	body	2560	valid
403.0ms	1839×	body	640	valid
113.0ms	771×	body	320	valid
51.0ms	1104×	body	80	valid
36.0ms	364×	body	160	valid