Details

sample360.0ms

Algorithm

intervals

Results

157.0ms	115×	body	1280	valid
61.0ms	11×	body	160	valid
54.0ms	17×	body	2560	valid
52.0ms	64×	body	640	valid
11.0ms	20×	body	320	valid
6.0ms	29×	body	80	valid

simplify25.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize20.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
2.8b	(tan (+ x eps))

rewrite28.0ms

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:

19.0ms	(- (tan (+ x eps)) (tan x))
8.0ms	(tan (+ x eps))

series212.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(- (tan (+ x eps)) (tan x))
93.0ms	(tan (+ x eps))

simplify1.2s

Counts: 31 → 31

prune166.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.4b

localize32.0ms

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))
0.2b	(* (tan x) (tan eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite199.0ms

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:

48.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
22.0ms	(* (tan x) (tan eps))
115.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

361.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
135.0ms	(+ (tan x) (tan eps))
124.0ms	(* (tan x) (tan eps))
590.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.4s

Counts: 98 → 98

prune451.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.3b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

26.0ms	(* (tan x) (tan eps))
19.0ms	(* (tan x) (tan eps))
87.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
47.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.7s

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (tan x) (tan eps))
108.0ms	(* (tan x) (tan eps))
163.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.3s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts: 122 → 122

prune452.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.3b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite272.0ms

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:

9.0ms	(+ (tan x) (tan eps))
18.0ms	(/ (* (sin x) (tan eps)) (cos x))
14.0ms	(* (sin x) (tan eps))
228.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series907.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ (tan x) (tan eps))
143.0ms	(/ (* (sin x) (tan eps)) (cos x))
100.0ms	(* (sin x) (tan eps))
523.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify641.0ms

Counts: 82 → 82

prune422.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

regimes285.0ms

Accuracy

89.5% (0.8b remaining)

Error of 15.2b against oracle of 14.4b and baseline of 22.0b

bsearch317.0ms

Steps

Iters	Range		Point
9	6.234436350971775e-49	1.1561517521963542e-41	2.462633582693938e-42
10	-0.0006576197608759923	-8.63582207798018e-19	-3.607294612619752e-18

simplify1.2s

end0.0ms

sample11.0s

Algorithm

intervals

Results

5.3s	3355×	body	1280	valid
2.6s	631×	body	2560	valid
2.0s	1809×	body	640	valid
464.0ms	771×	body	320	valid
171.0ms	1104×	body	80	valid
108.0ms	330×	body	160	valid