Details

sample160.0ms

Algorithm

intervals

Results

82.0ms	103×	body	1280	valid
32.0ms	66×	body	640	valid
23.0ms	13×	body	2560	valid
7.0ms	22×	body	320	valid
5.0ms	44×	body	80	valid
2.0ms	8×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
3.0b	(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))

series142.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (70.0ms)

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

prune114.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize11.0ms

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))
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite77.0ms

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:

3.0ms	(+ (tan x) (tan eps))
11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
50.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series730.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (tan x) (tan eps))
203.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(* (tan x) (tan eps))
347.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify77.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (52.0ms)

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

prune400.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.4b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
21.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series844.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (tan x) (tan eps))
86.0ms	(* (tan x) (tan eps))
105.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
567.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	432	1098
1	1952	917
2	5001	864

prune332.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.0b

localize12.0ms

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))
2.4b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite14.0ms

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)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
85.0ms	(+ (tan x) (tan eps))
86.0ms	(* (tan x) (tan eps))
278.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	367	756
1	1426	681
2	5002	680

prune247.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.0b

regimes135.0ms

Accuracy

83.8% (1.2b remaining)

Error of 15.9b against oracle of 14.8b and baseline of 21.9b

bsearch182.0ms

Steps

Iters	Range		Point
6	4.762716230442895e-61	3.0568216683503453e-60	1.855047695958225e-60
10	-3.439603128940124e-97	-3.096018323033091e-109	-2.1355630045751297e-97

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	43
1	42	43

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.7s	3310×	body	1280	valid
1.2s	663×	body	2560	valid
869.0ms	1817×	body	640	valid
243.0ms	748×	body	320	valid
122.0ms	1133×	body	80	valid
75.0ms	329×	body	160	valid