Details

sample223.0ms

Algorithm

intervals

Results

126.0ms	109×	body	1280	valid
37.0ms	20×	body	2560	valid
28.0ms	56×	body	640	valid
13.0ms	26×	body	320	valid
4.0ms	37×	body	80	valid
2.0ms	8×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite24.0ms

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:

17.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series177.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(- (tan (+ x eps)) (tan x))
79.0ms	(tan (+ x eps))

simplify75.0ms

Counts: 31 → 31

prune86.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.3b	(* (tan x) (tan eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite407.0ms

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:

8.0ms	(+ (tan x) (tan eps))
32.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
16.0ms	(* (tan x) (tan eps))
347.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series832.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (tan x) (tan eps))
232.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
101.0ms	(* (tan x) (tan eps))
395.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify45.0ms

Counts: 98 → 98

prune296.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
27.7b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`tan-quot`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`cube-div` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

17.0ms	(* (tan x) (tan eps))
12.0ms	(pow (* (tan x) (tan eps)) 3)
155.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
15.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series742.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (tan x) (tan eps))
140.0ms	(pow (* (tan x) (tan eps)) 3)
397.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
102.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify48.0ms

Counts: 94 → 94

prune328.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite345.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

62.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
13.0ms	(* (sin x) (sin eps))
18.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
248.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series838.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
50.0ms	(* (sin x) (sin eps))
110.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
423.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify63.0ms

Counts: 121 → 121

prune395.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.2b

regimes159.0ms

Accuracy

88.2% (0.8b remaining)

Error of 15.7b against oracle of 14.9b and baseline of 22.1b

bsearch225.0ms

Steps

Iters	Range		Point
10	4.950938936375422e-49	1.428063290236237e-30	3.5671412793756766e-32
9	-1.7569643515423198e-39	-6.4004412414421565e-49	-2.5461266251208234e-44

simplify1.0ms

end0.0ms

sample8.3s

Algorithm

intervals

Results

4.3s	3297×	body	1280	valid
1.7s	663×	body	2560	valid
1.3s	1870×	body	640	valid
361.0ms	760×	body	320	valid
161.0ms	332×	body	160	valid
158.0ms	1078×	body	80	valid