Details

sample85.0ms

Algorithm

intervals

Results

41.0ms	100×	body	1280	valid
18.0ms	22×	body	2560	valid
12.0ms	57×	body	640	valid
2.0ms	17×	body	320	valid
2.0ms	45×	body	80	valid
1.0ms	15×	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: 34.0b

localize8.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
3.5b	(tan (+ x eps))

rewrite10.0ms

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:

6.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series137.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
51.0ms	(tan (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (21.0ms)

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

prune86.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.0b

localize11.0ms

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))
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite34.0ms

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))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series744.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(+ (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
352.0ms	(- (/ (+ (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

prune290.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.5b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

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

series1.2s

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
113.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
897.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify79.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	599	1352
1	3021	1220
2	5001	1220

prune361.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (* (tan x) (tan eps)) (* (sin x) (tan eps)))
2.5b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (* (tan x) (tan eps)) (* (sin x) (tan eps))) (cos x)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

25×	`tan-quot`
20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
11×	`associate-*r/`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`frac-times`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
3×	`*-commutative`
2×	`flip3-+` `associate--l+` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `flip--`

Counts

4 → 90

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
10.0ms	(* (* (tan x) (tan eps)) (* (sin x) (tan eps)))
19.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (* (tan x) (tan eps)) (* (sin x) (tan eps))) (cos x)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
129.0ms	(* (* (tan x) (tan eps)) (* (sin x) (tan eps)))
1.0s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (* (tan x) (tan eps)) (* (sin x) (tan eps))) (cos x)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify78.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	588	1376
1	2944	1232
2	5002	1232

prune334.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.9b

regimes144.0ms

Accuracy

87.6% (0.9b remaining)

Error of 15.4b against oracle of 14.5b and baseline of 22.0b

bsearch129.0ms

Steps

Iters	Range		Point
8	2.7379472383092327e-72	1.7149841608833565e-68	7.60268013552436e-69
11	-1.5073415317839904e-10	-5.397704668065765e-30	-6.425365041334478e-20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	46
1	51	46

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3283×	body	1280	valid
574.0ms	663×	body	2560	valid
381.0ms	1812×	body	640	valid
102.0ms	755×	body	320	valid
47.0ms	1105×	body	80	valid
35.0ms	382×	body	160	valid