Details

sample152.0ms

Algorithm

intervals

Results

69.0ms	95×	body	1280	valid
37.0ms	22×	body	2560	valid
24.0ms	58×	body	640	valid
6.0ms	25×	body	320	valid
3.0ms	18×	body	160	valid
3.0ms	38×	body	80	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: 34.0b

localize16.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (tan (+ x eps)) (tan x))
3.9b	(tan (+ x eps))

rewrite12.0ms

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))

series138.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (tan (+ x eps)) (tan x))
49.0ms	(tan (+ x eps))

simplify1.1s

Counts

47 → 47

Iterations

Useful iterations: 3 (454.0ms)

Iter	Nodes	Cost
0	94	720
1	190	597
2	484	510
3	1960	450
done	5000	450

prune122.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.3b

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))
4.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite76.0ms

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:

11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
49.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series737.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
88.0ms	(+ (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
352.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify782.0ms

Counts

181 → 181

Iterations

Useful iterations: done (776.0ms)

Iter	Nodes	Cost
0	240	4762
1	537	3970
2	1701	3549
done	5000	3525

prune421.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
4.0b	(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (fma (tan eps) (tan x) 1) (- (tan x)))

rewrite34.0ms

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))
20.0ms	(* (* (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)))

series825.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (tan x) (tan eps))
87.0ms	(* (tan x) (tan eps))
107.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
544.0ms	(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (fma (tan eps) (tan x) 1) (- (tan x)))

simplify484.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (136.0ms)

Iter	Nodes	Cost
0	157	1832
1	417	1746
2	1659	1476
done	5000	1476

prune371.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin eps) 2)
0.3b	(pow (sin eps) 2)
0.3b	(pow (sin eps) 2)
1.3b	(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))) (cos x))) (/ (sin x) (cos x)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

131×	`times-frac`
117×	`prod-diff`
110×	`*-un-lft-identity`
108×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
28×	`associate-*l/` `associate-/r/`
25×	`div-inv`
15×	`flip3--` `flip--`
9×	`unpow-prod-down` `pow-unpow` `fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `distribute-rgt-out--` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `unpow2` `sqr-pow`
2×	`distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

4 → 209

Calls

4 calls:

1.0ms	(pow (sin eps) 2)
1.0ms	(pow (sin eps) 2)
1.0ms	(pow (sin eps) 2)
43.0ms	(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))) (cos x))) (/ (sin x) (cos x)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin eps) 2)
18.0ms	(pow (sin eps) 2)
22.0ms	(pow (sin eps) 2)
225.0ms	(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))) (cos x))) (/ (sin x) (cos x)))

simplify808.0ms

Counts

221 → 221

Iterations

Useful iterations: done (798.0ms)

Iter	Nodes	Cost
0	310	13038
1	709	11830
2	2199	9353
done	5000	9326

prune939.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

regimes134.0ms

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	35	117
1	45	117
done	45	117

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3289×	body	1280	valid
1.2s	686×	body	2560	valid
779.0ms	1815×	body	640	valid
207.0ms	736×	body	320	valid
96.0ms	1115×	body	80	valid
64.0ms	359×	body	160	valid