Details

sample154.0ms

Algorithm

intervals

Results

83.0ms	113×	body	1280	valid
30.0ms	18×	body	2560	valid
19.0ms	47×	body	640	valid
7.0ms	25×	body	320	valid
3.0ms	37×	body	80	valid
3.0ms	16×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
2.6b	(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))
3.0ms	(tan (+ x eps))

series341.0ms

Counts

2 → 6

Calls

2 calls:

287.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

simplify76.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (71.0ms)

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

prune115.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
57×	`prod-diff`
49×	`times-frac`
21×	`fma-neg`
13×	`distribute-lft-out`
10×	`add-log-exp`
8×	`associate-/r/`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 151

Calls

4 calls:

2.0ms	(- 1 (* (tan x) (tan eps)))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
52.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series627.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- 1 (* (tan x) (tan eps)))
93.0ms	(+ (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
340.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify72.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	542	2573
1	1893	2021
2	5002	1996

prune381.0ms

Filtered

163 candidates to 96 candidates (58.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (tan eps))
0.2b	(exp (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
3.8b	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
113×	`times-frac`
112×	`add-sqr-sqrt`
105×	`add-cube-cbrt`
99×	`prod-diff`
64×	`log-pow`
51×	`exp-prod`
32×	`fma-neg`
29×	`distribute-lft-out`
22×	`pow1`
11×	`add-log-exp`
7×	`tan-quot`
6×	`add-exp-log` `add-cbrt-cube`
5×	`exp-sum`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `rem-exp-log` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3--` `flip3-+` `exp-diff` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
5.0ms	(exp (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
88.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

series679.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan x) (tan eps))
139.0ms	(exp (- 1 (* (tan x) (tan eps))))
93.0ms	(* (tan x) (tan eps))
354.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify73.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	623	4254
1	1871	3139
2	5001	3037

prune452.0ms

Filtered

219 candidates to 101 candidates (46.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(pow E (- 1 (* (tan x) (tan eps))))
3.8b	(- (/ (+ (tan x) (tan eps)) (log (pow E (- 1 (* (tan x) (tan eps)))))) (tan x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
65×	`times-frac`
63×	`prod-diff`
20×	`fma-neg`
17×	`distribute-lft-out`
16×	`log-pow`
8×	`add-log-exp`
7×	`tan-quot` `pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unpow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`unpow-prod-down` `pow-unpow` `fma-def` `associate-r` `associate-l`
2×	`sub-neg` `pow-exp` `difference-of-squares`
1×	`+-commutative` `frac-times` `pow-to-exp` `e-exp-1` `flip3--` `pow-pow` `flip3-+` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `pow-sub` `unswap-sqr` `sqr-pow`

Counts

4 → 165

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
3.0ms	(pow E (- 1 (* (tan x) (tan eps))))
37.0ms	(- (/ (+ (tan x) (tan eps)) (log (pow E (- 1 (* (tan x) (tan eps)))))) (tan x))

series785.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
163.0ms	(pow E (- 1 (* (tan x) (tan eps))))
443.0ms	(- (/ (+ (tan x) (tan eps)) (log (pow E (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify79.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	615	3019
1	2069	2265
2	5002	2196

prune403.0ms

Filtered

177 candidates to 99 candidates (55.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.7b

regimes162.0ms

Accuracy

87.6% (0.9b remaining)

Error of 15.2b against oracle of 14.2b and baseline of 21.7b

bsearch131.0ms

Steps

Iters	Range		Point
7	2.5619879438810137e-23	5.215877061287173e-22	4.742281876404587e-23
6	-1.772314194330786e-26	-2.4976135847146302e-27	-5.9719887302803746e-27

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	3326×	body	1280	valid
1.0s	601×	body	2560	valid
803.0ms	1838×	body	640	valid
200.0ms	747×	body	320	valid
105.0ms	1118×	body	80	valid
67.0ms	370×	body	160	valid