Details

sample88.0ms

Algorithm

intervals

Results

44.0ms	110×	body	1280	valid
16.0ms	19×	body	2560	valid
12.0ms	53×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	29×	body	80	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: 39.6b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (tan (+ x eps)) (tan x))
5.2b	(tan (+ x eps))

rewrite16.0ms

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:

11.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series141.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(- (tan (+ x eps)) (tan x))
49.0ms	(tan (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (72.0ms)

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

prune122.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	36	11	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	11	48

Merged error: 14.2b

Counts

48 → 11

localize12.0ms

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))
3.6b	(- (/ (+ (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:

5.0ms	(+ (tan x) (tan eps))
8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
14.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series776.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(+ (tan x) (tan eps))
226.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
96.0ms	(* (tan x) (tan eps))
361.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify78.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (57.0ms)

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

prune402.0ms

Filtered

181 candidates to 110 candidates (60.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	168	13	181
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	173	19	192

Merged error: 14.0b

Counts

192 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
3.7b	(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`tan-quot`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `frac-times` `pow-unpow` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod`
2×	`pow-pow` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `fma-udef` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
5.0ms	(pow (* (tan x) (tan eps)) 3)
1.0ms	(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (tan x) (tan eps))
93.0ms	(* (tan x) (tan eps))
123.0ms	(pow (* (tan x) (tan eps)) 3)
892.0ms	(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	483	922
1	2591	827
2	5002	826

prune426.0ms

Filtered

95 candidates to 73 candidates (76.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	9	9	18
Picked	1	0	1
Done	0	0	0
Total	102	12	114

Merged error: 0.2b

Counts

114 → 12

localize72.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos eps) 3)
0.4b	(pow (cos eps) 3)
0.4b	(pow (cos eps) 3)
3.5b	(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

131×	`times-frac`
117×	`prod-diff`
113×	`*-un-lft-identity`
111×	`add-sqr-sqrt`
106×	`add-cube-cbrt`
28×	`associate-*l/` `associate-/r/`
25×	`div-inv`
15×	`flip3--` `flip--`
9×	`unpow-prod-down` `pow-unpow` `fma-neg` `cube-prod`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `distribute-rgt-out--` `log1p-expm1-u`
3×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
2×	`distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

4 → 224

Calls

4 calls:

3.0ms	(pow (cos eps) 3)
3.0ms	(pow (cos eps) 3)
3.0ms	(pow (cos eps) 3)
20.0ms	(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (cos eps) 3)
34.0ms	(pow (cos eps) 3)
29.0ms	(pow (cos eps) 3)
248.0ms	(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

simplify135.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	738	8220
1	2873	6202
2	5001	5728

prune1.4s

Filtered

236 candidates to 88 candidates (37.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	233	3	236
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	235	13	248

Merged error: 0.2b

Counts

248 → 13

regimes217.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	116
1	64	116

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	3346×	body	1280	valid
547.0ms	613×	body	2560	valid
402.0ms	1786×	body	640	valid
112.0ms	735×	body	320	valid
52.0ms	1149×	body	80	valid
37.0ms	371×	body	160	valid

Details

sample88.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite16.0ms

series141.0ms

simplify77.0ms

prune122.0ms

localize12.0ms

rewrite44.0ms

series776.0ms

simplify78.0ms

prune402.0ms

localize22.0ms

rewrite19.0ms

series1.2s

simplify73.0ms

prune426.0ms

localize72.0ms

rewrite41.0ms

series340.0ms

simplify135.0ms

prune1.4s

regimes217.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling