Details

sample301.0ms

Algorithm

intervals

Results

162.0ms	112×	body	1280	valid
61.0ms	22×	body	2560	valid
39.0ms	50×	body	640	valid
14.0ms	21×	body	320	valid
7.0ms	48×	body	80	valid
1.0ms	3×	body	160	valid

simplify20.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize14.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
4.0b	(tan (+ x eps))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

74.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series217.0ms

Counts

2 → 6

Calls

2 calls:

139.0ms	(- (tan (+ x eps)) (tan x))
78.0ms	(tan (+ x eps))

simplify1.2s

Counts: 31 → 31

prune161.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.7b

localize28.0ms

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))
0.3b	(* (tan x) (tan eps))
1.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite232.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `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` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

59.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(+ (tan x) (tan eps))
30.0ms	(* (tan x) (tan eps))
124.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

340.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
108.0ms	(+ (tan x) (tan eps))
146.0ms	(* (tan x) (tan eps))
580.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.6s

Counts: 98 → 98

prune432.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
1.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`tan-quot`
4×	`times-frac`
3×	`associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `frac-sub` `flip--` `flip-+` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

16.0ms	(+ (tan x) (tan eps))
16.0ms	(/ (* (sin x) (tan eps)) (cos x))
16.0ms	(* (sin x) (tan eps))
197.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series992.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(+ (tan x) (tan eps))
169.0ms	(/ (* (sin x) (tan eps)) (cos x))
110.0ms	(* (sin x) (tan eps))
584.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify837.0ms

Counts: 82 → 82

prune424.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.6b

localize56.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (/ (* (sin x) (tan eps)) (cos x))) (cbrt (/ (* (sin x) (tan eps)) (cos x)))) (cbrt (/ (* (sin x) (tan eps)) (cos x)))))) (tan x))
6.8b	(cbrt (/ (* (sin x) (tan eps)) (cos x)))
6.8b	(cbrt (/ (* (sin x) (tan eps)) (cos x)))
6.8b	(cbrt (/ (* (sin x) (tan eps)) (cos x)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `times-frac`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`difference-of-squares`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

123.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (/ (* (sin x) (tan eps)) (cos x))) (cbrt (/ (* (sin x) (tan eps)) (cos x)))) (cbrt (/ (* (sin x) (tan eps)) (cos x)))))) (tan x))
4.0ms	(cbrt (/ (* (sin x) (tan eps)) (cos x)))
4.0ms	(cbrt (/ (* (sin x) (tan eps)) (cos x)))
5.0ms	(cbrt (/ (* (sin x) (tan eps)) (cos x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

612.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (/ (* (sin x) (tan eps)) (cos x))) (cbrt (/ (* (sin x) (tan eps)) (cos x)))) (cbrt (/ (* (sin x) (tan eps)) (cos x)))))) (tan x))
223.0ms	(cbrt (/ (* (sin x) (tan eps)) (cos x)))
240.0ms	(cbrt (/ (* (sin x) (tan eps)) (cos x)))
229.0ms	(cbrt (/ (* (sin x) (tan eps)) (cos x)))

simplify855.0ms

Counts: 76 → 76

prune497.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.2b

regimes222.0ms

Accuracy

64.1% (2.6b remaining)

Error of 16.2b against oracle of 13.6b and baseline of 20.8b

bsearch371.0ms

Steps

Iters	Range		Point
5	2.232909102710953e-118	5.383721289433789e-118	5.307417583108514e-118
8	-5.326142386021628e-164	-1.4724282309499112e-167	-5.246119333473003e-164

simplify723.0ms

end0.0ms

sample10.9s

Algorithm

intervals

Results

4.8s	3404×	body	1280	valid
2.6s	1806×	body	640	valid
2.0s	641×	body	2560	valid
522.0ms	306×	body	160	valid
446.0ms	739×	body	320	valid
160.0ms	1104×	body	80	valid