Details

sample182.0ms

Algorithm

intervals

Results

86.0ms	118×	body	1280	valid
48.0ms	28×	body	2560	valid
22.0ms	51×	body	640	valid
11.0ms	19×	body	320	valid
3.0ms	15×	body	160	valid
2.0ms	25×	body	80	valid

simplify5.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize9.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.5b	(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:

8.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series145.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (tan (+ x eps)) (tan x))
52.0ms	(tan (+ x eps))

simplify84.0ms

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

prune127.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.6b

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))))
0.3b	(* (tan x) (tan eps))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite78.0ms

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:

6.0ms	(+ (tan x) (tan eps))
11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
49.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series774.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(+ (tan x) (tan eps))
205.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(* (tan x) (tan eps))
351.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify113.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (78.0ms)

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

prune468.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 17.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
3.5b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`tan-quot` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `flip3--` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

4.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
89.0ms	(+ (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
283.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify40.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	367	754
1	1426	679
2	5001	679

prune295.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 17.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
3.5b	(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)))

rewrite16.0ms

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))
4.0ms	(pow (* (tan x) (tan eps)) 3)
0.0ms	(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))
95.0ms	(* (tan x) (tan eps))
127.0ms	(pow (* (tan x) (tan eps)) 3)
884.0ms	(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)))

simplify76.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (66.0ms)

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

prune430.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes171.0ms

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	118
1	64	118

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.4s	3207×	body	1280	valid
1.3s	668×	body	2560	valid
803.0ms	1848×	body	640	valid
230.0ms	777×	body	320	valid
109.0ms	1128×	body	80	valid
81.0ms	372×	body	160	valid