Details

sample347.0ms

Algorithm

intervals

Results

139.0ms	97×	body	1280	valid
84.0ms	21×	body	2560	valid
54.0ms	59×	body	640	valid
38.0ms	42×	body	80	valid
15.0ms	24×	body	320	valid
6.0ms	13×	body	160	valid

simplify8.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize18.0ms

Local error

Found 2 expressions with local error:

2.7b	(tan (+ x eps))
1.5b	(- (tan (+ x eps)) (tan x))

rewrite39.0ms

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:

Slowest

33.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series188.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

121.0ms	(- (tan (+ x eps)) (tan x))
67.0ms	(tan (+ x eps))

simplify533.0ms

Counts: 65 → 49

prune562.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.7b

localize32.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b	(* (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))

rewrite146.0ms

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:

Slowest

76.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
30.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
28.0ms	(* (tan x) (tan eps))
8.0ms	(+ (tan x) (tan eps))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

474.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
344.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
144.0ms	(* (tan x) (tan eps))
119.0ms	(+ (tan x) (tan eps))

simplify778.0ms

Counts: 257 → 185

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.7b

localize57.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(/ (sin x) (cos x))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

1393×	`times-frac`
890×	`add-sqr-sqrt`
851×	`*-un-lft-identity`
845×	`add-cube-cbrt`
585×	`prod-diff`
106×	`div-inv`
45×	`fma-neg`
30×	`add-cbrt-cube` `add-exp-log`
28×	`associate-/r/`
26×	`associate-r` `associate-l`
15×	`flip3--` `flip--`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `distribute-lft-out--`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `frac-sub`

Counts

4 → 791

Calls

4 calls:

Slowest

111.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
37.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
26.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
8.0ms	(/ (sin x) (cos x))

series589.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

301.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
144.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
113.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
30.0ms	(/ (sin x) (cos x))

simplify2.1s

Counts: 1414 → 803

prune14.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.6b

localize76.0ms

Local error

Found 4 expressions with local error:

27.5b	(cbrt (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))
3.2b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
0.3b	(* (sin x) (sin x))
0.3b	(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

1380×	`times-frac`
876×	`add-sqr-sqrt`
847×	`*-un-lft-identity`
841×	`add-cube-cbrt`
585×	`prod-diff`
105×	`div-inv`
45×	`fma-neg`
28×	`associate-/r/`
18×	`frac-times` `pow1` `add-cbrt-cube` `add-exp-log`
16×	`swap-sqr` `associate-r` `associate-l`
15×	`cbrt-div` `flip3--` `flip--`
14×	`associate-*r/`
12×	`associate-*l/`
6×	`add-log-exp` `difference-of-squares`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `distribute-lft-out--`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `frac-sub` `sqr-sin` `sin-mult`

Counts

4 → 781

Calls

4 calls:

Slowest

160.0ms	(cbrt (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))
53.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
18.0ms	(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
12.0ms	(* (sin x) (sin x))

series420.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

241.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
110.0ms	(cbrt (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))
49.0ms	(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
19.0ms	(* (sin x) (sin x))

simplify1.8s

Counts: 1420 → 793

prune13.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.6b

regimes216.0ms

Accuracy

0% (0.4b remaining)

Error of 13.0b against oracle of 12.6b and baseline of 13.0b

bsearch863.0ms

end0.0ms

sample9.5s

Algorithm

intervals

Results

4.4s	3336×	body	1280	valid
2.2s	1860×	body	640	valid
1.7s	622×	body	2560	valid
727.0ms	782×	body	320	valid
180.0ms	330×	body	160	valid
163.0ms	1070×	body	80	valid