Details

sample477.0ms

Algorithm

intervals

Results

274.0ms	116×	body	1280	valid
84.0ms	53×	body	640	valid
70.0ms	20×	body	2560	valid
18.0ms	14×	body	320	valid
12.0ms	43×	body	80	valid
7.0ms	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))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

Slowest

14.0ms	(- (tan (+ x eps)) (tan x))
8.0ms	(tan (+ x eps))

series206.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

139.0ms	(- (tan (+ x eps)) (tan x))
67.0ms	(tan (+ x eps))

simplify1.3s

Counts: 33 → 33

prune366.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.5b

localize29.0ms

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))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`insert-posit16` `associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `flip3--` `frac-add` `associate-/r/` `flip-+` `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` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

Slowest

79.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
27.0ms	(* (tan x) (tan eps))
23.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
7.0ms	(+ (tan x) (tan eps))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

491.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
291.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
139.0ms	(+ (tan x) (tan eps))
113.0ms	(* (tan x) (tan eps))

simplify1.3s

Counts: 102 → 102

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.4b

localize43.0ms

Local error

Found 4 expressions with local error:

5.8b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
0.3b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.2b	(* (tan x) (tan eps))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
104×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
23×	`associate-/r*`
19×	`add-exp-log`
16×	`associate-/r/` `distribute-lft-out`
15×	`tan-quot`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1` `div-inv`
6×	`associate-/l*` `add-log-exp`
5×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
4×	`cbrt-undiv` `insert-posit16`
3×	`associate-r` `associate-l`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3--` `1-exp` `flip--` `distribute-lft-out--` `associate-/l/`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `pow-flip` `inv-pow` `unswap-sqr`

Counts

4 → 182

Calls

4 calls:

Slowest

115.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
23.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
22.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
13.0ms	(* (tan x) (tan eps))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

392.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
377.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
354.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
132.0ms	(* (tan x) (tan eps))

simplify1.5s

Counts: 194 → 194

prune2.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.4b

localize77.0ms

Local error

Found 4 expressions with local error:

6.2b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (+ (tan x) (tan eps)) (cos x))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `insert-posit16` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

Slowest

69.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
44.0ms	(* (+ (tan x) (tan eps)) (cos x))
27.0ms	(* (tan x) (tan eps))
27.0ms	(* (tan x) (tan eps))

series716.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

288.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
150.0ms	(* (+ (tan x) (tan eps)) (cos x))
141.0ms	(* (tan x) (tan eps))
137.0ms	(* (tan x) (tan eps))

simplify888.0ms

Counts: 98 → 98

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes184.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch7.0ms

end0.0ms

sample14.8s

Algorithm

intervals

Results

7.4s	3331×	body	1280	valid
2.9s	628×	body	2560	valid
2.5s	1837×	body	640	valid
1.3s	751×	body	320	valid
328.0ms	1096×	body	80	valid
217.0ms	357×	body	160	valid