Details

sample157.0ms

Algorithm

intervals

Results

69.0ms	96×	body	1280	valid
37.0ms	19×	body	2560	valid
28.0ms	67×	body	640	valid
9.0ms	32×	body	320	valid
3.0ms	33×	body	80	valid
2.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite13.0ms

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:

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

series151.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(- (tan (+ x eps)) (tan x))
57.0ms	(tan (+ x eps))

simplify1.3s

Counts

47 → 47

Iterations

Useful iterations: 3 (330.0ms)

Iter	Nodes	Cost
0	94	720
1	194	597
2	478	510
3	1669	450
done	5000	450

prune130.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.2b

localize12.0ms

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))
2.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite83.0ms

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:

14.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
52.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series788.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
97.0ms	(+ (tan x) (tan eps))
97.0ms	(* (tan x) (tan eps))
378.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify874.0ms

Counts

181 → 181

Iterations

Useful iterations: done (869.0ms)

Iter	Nodes	Cost
0	240	4762
1	552	3970
2	1567	3555
done	5000	3549

prune430.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
2.7b	(fma (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan x) (tan eps)) 3))) (fma (* (tan x) (tan eps)) (fma (tan eps) (tan x) 1) 1) (- (tan x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`tan-quot`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `frac-times` `pow-unpow` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod`
2×	`pow-pow` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `fma-udef` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
4.0ms	(pow (* (tan x) (tan eps)) 3)
0.0ms	(fma (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan x) (tan eps)) 3))) (fma (* (tan x) (tan eps)) (fma (tan eps) (tan x) 1) 1) (- (tan x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (tan x) (tan eps))
92.0ms	(* (tan x) (tan eps))
125.0ms	(pow (* (tan x) (tan eps)) 3)
917.0ms	(fma (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan x) (tan eps)) 3))) (fma (* (tan x) (tan eps)) (fma (tan eps) (tan x) 1) 1) (- (tan x)))

simplify783.0ms

Counts

95 → 95

Iterations

Useful iterations: 2 (217.0ms)

Iter	Nodes	Cost
0	173	1612
1	472	1474
2	2350	1328
done	5000	1328

prune424.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.1b

localize18.0ms

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)))
2.7b	(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (fma (tan eps) (tan x) 1) (- (tan x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
22.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (fma (tan eps) (tan x) 1) (- (tan x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (tan x) (tan eps))
98.0ms	(* (tan x) (tan eps))
120.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
598.0ms	(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (fma (tan eps) (tan x) 1) (- (tan x)))

simplify736.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (174.0ms)

Iter	Nodes	Cost
0	157	1832
1	417	1746
2	1633	1476
done	5001	1476

prune334.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes86.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	115
1	43	115
done	43	115

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	3276×	body	1280	valid
1.1s	646×	body	2560	valid
789.0ms	1863×	body	640	valid
215.0ms	766×	body	320	valid
90.0ms	1085×	body	80	valid
68.0ms	364×	body	160	valid