Details

sample165.0ms

Algorithm

intervals

Results

77.0ms	109×	body	1280	valid
43.0ms	26×	body	2560	valid
24.0ms	52×	body	640	valid
5.0ms	19×	body	320	valid
3.0ms	42×	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: 35.6b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

20.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series131.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(- (tan (+ x eps)) (tan x))
47.0ms	(tan (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune82.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.8b

localize15.0ms

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))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `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` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

8.0ms	(+ (tan x) (tan eps))
28.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(* (tan x) (tan eps))
75.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series689.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ (tan x) (tan eps))
193.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
84.0ms	(* (tan x) (tan eps))
328.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune279.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.7b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
26×	`times-frac`
20×	`add-exp-log` `add-cbrt-cube`
18×	`add-cube-cbrt`
12×	`difference-of-squares`
7×	`associate-/r*` `distribute-lft-out`
6×	`pow1` `distribute-lft-out--` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
4×	`associate-/l/`
3×	`tan-quot` `associate-r` `associate-l` `associate-/r/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `div-inv` `sin-mult`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `cos-mult` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

58.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))))
12.0ms	(* (sin x) (sin eps))
17.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
233.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

series687.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))))
47.0ms	(* (sin x) (sin eps))
90.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
345.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

simplify64.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	546	1825
1	2409	1688
2	5002	1688

prune415.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.7b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
41×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
13×	`associate-r` `associate-l`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r` `associate-/l` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`tan-quot` `frac-times` `sub-neg` `flip3--` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 120

Calls

4 calls:

8.0ms	(/ (sin x) (cos eps))
9.0ms	(/ (sin eps) (cos x))
27.0ms	(* (/ (sin x) (cos eps)) (/ (sin eps) (cos x)))
75.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (/ (sin x) (cos eps)) (/ (sin eps) (cos x))))) (tan x))

series524.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (sin x) (cos eps))
38.0ms	(/ (sin eps) (cos x))
94.0ms	(* (/ (sin x) (cos eps)) (/ (sin eps) (cos x)))
349.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (/ (sin x) (cos eps)) (/ (sin eps) (cos x))))) (tan x))

simplify62.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	559	1358
1	2322	1226
2	5001	1212

prune474.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.7b

regimes141.0ms

Accuracy

84.2% (1.2b remaining)

Error of 15.3b against oracle of 14.1b and baseline of 21.7b

bsearch173.0ms

Steps

Iters	Range		Point
8	4.199934233506477e-84	1.3088573146631599e-80	1.1378951959851225e-80
7	-2.0882778719170116e-105	-1.015544434114402e-106	-4.418632866442672e-106

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	32	15

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3280×	body	1280	valid
1.1s	627×	body	2560	valid
778.0ms	1854×	body	640	valid
211.0ms	751×	body	320	valid
95.0ms	1137×	body	80	valid
63.0ms	351×	body	160	valid