Details

sample463.0ms

Algorithm

intervals

Results

228.0ms	116×	body	1280	valid
119.0ms	20×	body	2560	valid
69.0ms	53×	body	640	valid
12.0ms	14×	body	320	valid
11.0ms	43×	body	80	valid
10.0ms	10×	body	160	valid

simplify9.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize35.0ms

Local error

Found 2 expressions with local error:

3.2b	(tan (+ x eps))
0.6b	(- (tan (+ x eps)) (tan x))

rewrite21.0ms

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

13.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series232.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

146.0ms	(- (tan (+ x eps)) (tan x))
86.0ms	(tan (+ x eps))

simplify1.5s

Counts: 49 → 49

prune453.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.5b

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (/ (+ (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))

rewrite171.0ms

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

88.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
45.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
28.0ms	(* (tan x) (tan eps))
7.0ms	(+ (tan x) (tan eps))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

504.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
337.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
125.0ms	(+ (tan x) (tan eps))
118.0ms	(* (tan x) (tan eps))

simplify803.0ms

Counts: 185 → 185

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.2b

localize58.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (/ (/ (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 eps) (cos eps))

rewrite184.0ms

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

100.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
23.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
18.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
9.0ms	(/ (sin eps) (cos eps))

series655.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

327.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
149.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
139.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
40.0ms	(/ (sin eps) (cos eps))

simplify2.8s

Counts: 803 → 803

prune14.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.2b

localize59.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
3.7b	(log (exp (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

1384×	`times-frac`
883×	`add-sqr-sqrt`
844×	`*-un-lft-identity`
838×	`add-cube-cbrt`
585×	`prod-diff`
105×	`div-inv`
45×	`fma-neg`
28×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
26×	`associate-r` `associate-l`
15×	`flip3--` `flip--`
9×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
7×	`add-log-exp`
6×	`difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `log-pow`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `distribute-lft-out--`
1×	`exp-prod` `sub-neg` `exp-to-pow` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 777

Calls

4 calls:

Slowest

80.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
23.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
21.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
8.0ms	(log (exp (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))

series822.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

341.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
164.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
159.0ms	(log (exp (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))
157.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))

simplify2.3s

Counts: 789 → 789

prune13.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.2b

regimes148.0ms

Accuracy

0% (0.5b remaining)

Error of 13.0b against oracle of 12.5b and baseline of 13.0b

bsearch5.0ms

end0.0ms

sample10.0s

Algorithm

intervals

Results

5.4s	3331×	body	1280	valid
1.9s	1837×	body	640	valid
1.7s	628×	body	2560	valid
486.0ms	751×	body	320	valid
207.0ms	1096×	body	80	valid
147.0ms	357×	body	160	valid