Details

sample159.0ms

Algorithm

intervals

Results

75.0ms	106×	body	1280	valid
41.0ms	25×	body	2560	valid
24.0ms	61×	body	640	valid
5.0ms	20×	body	320	valid
3.0ms	32×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
3.5b	(tan (+ x eps))

rewrite12.0ms

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:

8.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series144.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
57.0ms	(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

prune84.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.5b

localize14.0ms

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))
1.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite61.0ms

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:

11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
39.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series727.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
87.0ms	(+ (tan x) (tan eps))
88.0ms	(* (tan x) (tan eps))
345.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

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

prune288.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
1.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
5.0ms	(/ (* (tan x) (sin eps)) (cos eps))
4.0ms	(* (tan x) (sin eps))
81.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series618.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan x) (tan eps))
94.0ms	(/ (* (tan x) (sin eps)) (cos eps))
68.0ms	(* (tan x) (sin eps))
364.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	385	785
1	1424	712
2	5001	700

prune283.0ms

Filtered

82 candidates to 59 candidates (72.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin eps))
0.2b	(/ (cos eps) (* (tan x) (sin eps)))
0.5b	(/ 1 (/ (cos eps) (* (tan x) (sin eps))))
1.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ 1 (/ (cos eps) (* (tan x) (sin eps)))))) (tan x))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
32×	`add-exp-log` `add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
20×	`add-cbrt-cube`
14×	`div-exp`
9×	`associate-/r*`
7×	`tan-quot` `pow1` `cbrt-undiv`
6×	`associate-l/` `associate-/r/` `div-inv` `associate-/l` `add-log-exp`
5×	`prod-exp`
3×	`rec-exp` `1-exp` `associate-r` `associate-l` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--` `inv-pow` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

4.0ms	(* (tan x) (sin eps))
5.0ms	(/ (cos eps) (* (tan x) (sin eps)))
9.0ms	(/ 1 (/ (cos eps) (* (tan x) (sin eps))))
241.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ 1 (/ (cos eps) (* (tan x) (sin eps)))))) (tan x))

series636.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (tan x) (sin eps))
103.0ms	(/ (cos eps) (* (tan x) (sin eps)))
101.0ms	(/ 1 (/ (cos eps) (* (tan x) (sin eps))))
364.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ 1 (/ (cos eps) (* (tan x) (sin eps)))))) (tan x))

simplify58.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	520	1303
1	2173	1160
2	5002	1116

prune324.0ms

Filtered

129 candidates to 77 candidates (59.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.3b

regimes129.0ms

Accuracy

73.8% (1.9b remaining)

Error of 15.8b against oracle of 13.8b and baseline of 21.1b

bsearch232.0ms

Steps

Iters	Range		Point
9	4.017695445394683e-173	5.816336440788529e-167	5.748527172026931e-167
10	-2.3022776580077488e-90	-1.7535355178555737e-102	-2.2637252434053613e-90

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	40
1	49	40
2	49	40

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.4s	3292×	body	1280	valid
1.1s	636×	body	2560	valid
723.0ms	1787×	body	640	valid
224.0ms	805×	body	320	valid
90.0ms	1118×	body	80	valid
63.0ms	362×	body	160	valid