Details

sample157.0ms

Algorithm

intervals

Results

76.0ms	96×	body	1280	valid
29.0ms	17×	body	2560	valid
26.0ms	62×	body	640	valid
10.0ms	35×	body	320	valid
3.0ms	34×	body	80	valid
2.0ms	12×	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: 38.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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:

18.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series155.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(- (tan (+ x eps)) (tan x))
58.0ms	(tan (+ x eps))

simplify72.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (67.0ms)

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

prune119.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.4b

localize12.0ms

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))
4.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite157.0ms

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:

29.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
17.0ms	(* (tan x) (tan eps))
96.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series824.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
100.0ms	(+ (tan x) (tan eps))
100.0ms	(* (tan x) (tan eps))
390.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (51.0ms)

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

prune445.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (sin x) (sin eps))
0.2b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
4.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 202

Calls

4 calls:

8.0ms	(+ (tan x) (tan eps))
12.0ms	(* (sin x) (sin eps))
17.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
296.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

series666.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (tan x) (tan eps))
48.0ms	(* (sin x) (sin eps))
107.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
409.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

simplify96.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	725	4655
1	2944	3696
2	5001	3657

prune614.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
0.2b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
0.3b	(* (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))
4.5b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))))) (+ 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))) (- (tan x)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-exp-log` `add-cbrt-cube`
73×	`prod-exp` `cbrt-unprod`
48×	`cbrt-undiv` `div-exp`
11×	`pow1`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `swap-sqr` `associate-r` `associate-l` `associate-/r/` `cos-mult` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r` `associate-/l/` `sin-mult` `associate-/l`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `fma-udef` `unswap-sqr`

Counts

4 → 147

Calls

4 calls:

19.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
17.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
70.0ms	(* (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))))) (+ 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))) (- (tan x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
108.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
139.0ms	(* (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))
658.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))))) (+ 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))) (- (tan x)))

simplify115.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	685	2978
1	4414	1949
2	5001	1948

prune464.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.2b

regimes224.0ms

Accuracy

87.3% (0.9b remaining)

Error of 15.3b against oracle of 14.3b and baseline of 21.7b

bsearch180.0ms

Steps

Iters	Range		Point
9	4.9236548997223346e-36	6.481252319714892e-31	1.6763362246559567e-31
9	-2.2082264187638084e-10	-1.8774124276059505e-19	-7.65111219922148e-19

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	44
1	45	44

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.5s	3249×	body	1280	valid
1.1s	660×	body	2560	valid
805.0ms	1872×	body	640	valid
217.0ms	764×	body	320	valid
98.0ms	1126×	body	80	valid
68.0ms	329×	body	160	valid