Details

sample188.0ms

Algorithm

intervals

Results

93.0ms	109×	body	1280	valid
47.0ms	26×	body	2560	valid
26.0ms	52×	body	640	valid
5.0ms	19×	body	320	valid
4.0ms	42×	body	80	valid
2.0ms	8×	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: 35.6b

localize9.0ms

Local error

Found 2 expressions with local error:

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

17.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series136.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(- (tan (+ x eps)) (tan x))
53.0ms	(tan (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (68.0ms)

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

prune109.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.8b

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))
2.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite158.0ms

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:

10.0ms	(+ (tan x) (tan eps))
27.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
16.0ms	(* (tan x) (tan eps))
91.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series708.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ (tan x) (tan eps))
195.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
86.0ms	(* (tan x) (tan eps))
343.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify74.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (54.0ms)

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

prune418.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
2.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

221×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
124×	`times-frac`
94×	`add-cube-cbrt`
90×	`prod-diff`
44×	`difference-of-squares`
31×	`distribute-lft-out`
30×	`fma-neg`
22×	`distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`pow1` `flip3--` `flip--` `div-inv` `add-log-exp`
5×	`tan-quot` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`frac-2neg` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 236

Calls

4 calls:

42.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
14.0ms	(/ (* (sin x) (tan eps)) (cos x))
13.0ms	(* (sin x) (tan eps))
178.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series715.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
93.0ms	(/ (* (sin x) (tan eps)) (cos x))
72.0ms	(* (sin x) (tan eps))
346.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify96.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	707	4967
1	2760	4039
2	5002	3999

prune590.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 13.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (* (sin x) (tan eps)) (/ 1 (cos x)))))
0.2b	(* (sin x) (tan eps))
0.2b	(* (* (sin x) (tan eps)) (/ 1 (cos x)))
2.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (sin x) (tan eps)) (/ 1 (cos x))))) (tan x))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
79×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
70×	`times-frac`
54×	`prod-diff`
30×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`fma-neg`
16×	`associate-r` `distribute-lft-out`
13×	`prod-exp`
11×	`pow1`
10×	`associate-/r/`
7×	`cbrt-unprod`
6×	`tan-quot` `flip3--` `flip--` `div-inv` `add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `associate-r/` `associate-l` `pow-prod-down` `log1p-expm1-u` `associate-/l`
3×	`cbrt-undiv` `associate-/r*` `associate-/l/`
2×	`rec-exp` `1-exp` `*-commutative` `difference-of-squares`
1×	`frac-times` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `associate-*l/` `frac-add` `clear-num` `un-div-inv` `frac-sub` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 191

Calls

4 calls:

29.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (* (sin x) (tan eps)) (/ 1 (cos x)))))
13.0ms	(* (sin x) (tan eps))
36.0ms	(* (* (sin x) (tan eps)) (/ 1 (cos x)))
94.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (sin x) (tan eps)) (/ 1 (cos x))))) (tan x))

series727.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (* (sin x) (tan eps)) (/ 1 (cos x)))))
67.0ms	(* (sin x) (tan eps))
92.0ms	(* (* (sin x) (tan eps)) (/ 1 (cos x)))
355.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (sin x) (tan eps)) (/ 1 (cos x))))) (tan x))

simplify96.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	772	3746
1	3582	3072
2	5001	3049

prune492.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.7b

regimes183.0ms

Accuracy

77.4% (1.7b remaining)

Error of 15.8b against oracle of 14.1b and baseline of 21.6b

bsearch176.0ms

Steps

Iters	Range		Point
8	4.199934233506477e-84	1.3088573146631599e-80	1.213878359842028e-80
6	-2.695503673017005e-139	-3.24490854001114e-140	-2.6553631736288533e-139

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	43
1	40	43

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	3280×	body	1280	valid
1.1s	627×	body	2560	valid
810.0ms	1854×	body	640	valid
203.0ms	751×	body	320	valid
110.0ms	1137×	body	80	valid
65.0ms	351×	body	160	valid