Details

sample330.0ms

Algorithm

intervals

Results

258.0ms	113×	body	1280	valid
30.0ms	18×	body	2560	valid
20.0ms	47×	body	640	valid
7.0ms	25×	body	320	valid
3.0ms	37×	body	80	valid
3.0ms	16×	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: 35.5b

localize8.0ms

Local error

Found 2 expressions with local error:

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

series141.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

simplify73.0ms

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

prune84.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

3.0ms	(- 1 (* (tan x) (tan eps)))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series656.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- 1 (* (tan x) (tan eps)))
88.0ms	(+ (tan x) (tan eps))
88.0ms	(* (tan x) (tan eps))
377.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify130.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	343	662
1	1170	624
2	4756	614
3	5001	614

prune235.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (tan eps))
0.2b	(exp (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
3.8b	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot` `add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`exp-prod` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `exp-sum` `rem-exp-log` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3--` `flip3-+` `times-frac` `exp-diff` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
6.0ms	(exp (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
15.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

series670.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan x) (tan eps))
133.0ms	(exp (- 1 (* (tan x) (tan eps))))
90.0ms	(* (tan x) (tan eps))
355.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify101.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	345	719
1	1088	666
2	3871	654
3	5001	654

prune285.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (tan eps))
0.2b	(exp (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
0.3b	(* (tan x) (sin eps))
3.8b	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
11×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `exp-prod` `add-cbrt-cube`
4×	`tan-quot` `difference-of-squares`
3×	`associate-r` `associate-l`
2×	`sub-neg` `diff-log` `exp-sum` `rem-exp-log` `distribute-lft-out--`
1×	`+-commutative` `flip3--` `flip3-+` `times-frac` `exp-diff` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
6.0ms	(exp (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
5.0ms	(* (tan x) (sin eps))
22.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))

series668.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (tan x) (tan eps))
142.0ms	(exp (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
67.0ms	(* (tan x) (sin eps))
364.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))

simplify102.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	359	808
1	1098	744
2	3905	729
3	5001	729

prune286.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.7b

regimes178.0ms

Accuracy

90.2% (0.7b remaining)

Error of 15.0b against oracle of 14.3b and baseline of 21.6b

bsearch128.0ms

Steps

Iters	Range		Point
7	2.5619879438810137e-23	5.215877061287173e-22	2.0534977977042638e-22
6	-1.772314194330786e-26	-2.4976135847146302e-27	-5.9719887302803746e-27

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	23
1	35	23

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	3326×	body	1280	valid
1.0s	601×	body	2560	valid
785.0ms	1838×	body	640	valid
214.0ms	747×	body	320	valid
94.0ms	1118×	body	80	valid
80.0ms	370×	body	160	valid