Details

sample148.0ms

Algorithm

intervals

Results

73.0ms	105×	body	1280	valid
28.0ms	13×	body	2560	valid
25.0ms	61×	body	640	valid
6.0ms	24×	body	320	valid
3.0ms	40×	body	80	valid
2.0ms	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
4.4b	(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))

series140.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
52.0ms	(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

prune121.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.0b

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))

rewrite76.0ms

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:

13.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
47.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series763.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
104.0ms	(+ (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
356.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (55.0ms)

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

prune414.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.9b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 201

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
4.0ms	(/ (* (sin x) (tan eps)) (cos x))
5.0ms	(* (sin x) (tan eps))
96.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series644.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (tan x) (tan eps))
102.0ms	(/ (* (sin x) (tan eps)) (cos x))
75.0ms	(* (sin x) (tan eps))
375.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify91.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	678	4171
1	2545	3274
2	5002	3234

prune506.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.1b	(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)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
94.0ms	(+ (tan x) (tan eps))
96.0ms	(* (tan x) (tan eps))
295.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (12.0ms)

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

prune276.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.9b

regimes164.0ms

Accuracy

81.8% (1.3b remaining)

Error of 16.0b against oracle of 14.8b and baseline of 21.8b

bsearch217.0ms

Steps

Iters	Range		Point
9	1.3415957068562499e-74	3.3780603822421874e-67	7.895037822047127e-70
10	-1.8709674672778204e-72	-1.3251169945525502e-86	-1.429298289274309e-72

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	27
1	37	27

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	3328×	body	1280	valid
1.1s	632×	body	2560	valid
783.0ms	1821×	body	640	valid
201.0ms	769×	body	320	valid
98.0ms	1120×	body	80	valid
66.0ms	330×	body	160	valid