Details

sample422.0ms

Algorithm

intervals

Results

201.0ms	116×	body	1280	valid
119.0ms	27×	body	2560	valid
62.0ms	54×	body	640	valid
16.0ms	19×	body	320	valid
7.0ms	33×	body	80	valid
3.0ms	7×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize64.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (tan (+ x eps)) (tan x))
2.7b	(tan (+ x eps))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

14.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series204.0ms

Counts

2 → 6

Calls

2 calls:

141.0ms	(- (tan (+ x eps)) (tan x))
62.0ms	(tan (+ x eps))

simplify3.0s

Counts

49 → 49

Iterations

Iter	Nodes
4	3889
3	1289
2	437
1	203
0	96

prune502.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize34.0ms

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))

rewrite178.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

34.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(+ (tan x) (tan eps))
25.0ms	(* (tan x) (tan eps))
100.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

326.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
135.0ms	(+ (tan x) (tan eps))
130.0ms	(* (tan x) (tan eps))
507.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify3.5s

Counts

185 → 185

Iterations

Iter	Nodes
3	5442
2	1570
1	577
0	242

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.1b

localize55.0ms

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)))
1.5b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-cbrt-cube` `add-exp-log`
19×	`frac-times` `pow-prod-down`
13×	`associate-l/` `associate-r/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 111

Calls

4 calls:

28.0ms	(* (tan x) (tan eps))
30.0ms	(* (tan x) (tan eps))
87.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (tan x) (tan eps))
149.0ms	(* (tan x) (tan eps))
177.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
731.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify6.0s

Counts

123 → 123

Iterations

Iter	Nodes
3	8117
2	1650
1	428
0	160

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize132.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
0.3b	(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
0.3b	(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
2.4b	(- (/ (/ (sin x) (- 1 (* (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (cos x)) (/ (sin x) (cos x)))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

2172×	`times-frac`
1348×	`add-sqr-sqrt`
1323×	`*-un-lft-identity`
1189×	`add-cube-cbrt`
871×	`prod-diff`
258×	`difference-of-squares`
131×	`div-inv`
86×	`associate-/r/`
67×	`fma-neg`
43×	`flip3--` `flip--`
40×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
11×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `unswap-sqr`
2×	`clear-num` `associate-/r` `frac-2neg` `cos-mult` `sin-mult` `associate-/l` `associate-/l/`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `distribute-rgt-out--` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub` `sub-div`

Counts

4 → 1088

Calls

4 calls:

17.0ms	(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
34.0ms	(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
42.0ms	(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
103.0ms	(- (/ (/ (sin x) (- 1 (* (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (cos x)) (/ (sin x) (cos x)))

series705.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
162.0ms	(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
55.0ms	(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
321.0ms	(- (/ (/ (sin x) (- 1 (* (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (cos x)) (/ (sin x) (cos x)))

simplify2.8s

Counts

1100 → 1100

Iterations

Iter	Nodes
1	3159
0	1361

prune24.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

regimes235.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	28
1	28
0	24

end0.0ms

sample9.9s

Algorithm

intervals

Results

4.7s	3235×	body	1280	valid
2.5s	695×	body	2560	valid
1.6s	1854×	body	640	valid
542.0ms	768×	body	320	valid
221.0ms	1095×	body	80	valid
144.0ms	353×	body	160	valid