Details

sample347.0ms

Algorithm

intervals

Results

164.0ms	97×	body	1280	valid
77.0ms	26×	body	2560	valid
57.0ms	63×	body	640	valid
16.0ms	25×	body	320	valid
7.0ms	38×	body	80	valid
3.0ms	7×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize60.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
3.1b	(tan (+ x eps))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

36.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

series233.0ms

Counts

2 → 6

Calls

2 calls:

144.0ms	(- (tan (+ x eps)) (tan x))
88.0ms	(tan (+ x eps))

simplify885.0ms

Counts

47 → 47

Iterations

Useful iterations: done (884.0ms)

Iter	Nodes	Cost
0	94	720
1	202	600
2	741	510
done	5001	450

prune218.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.5b

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))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite216.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

17.0ms	(+ (tan x) (tan eps))
31.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(* (tan x) (tan eps))
135.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

155.0ms	(+ (tan x) (tan eps))
268.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
118.0ms	(* (tan x) (tan eps))
531.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.3s

Counts

181 → 181

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	240	4762
1	596	3988
2	2892	3557
done	5000	3556

prune720.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

221×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
124×	`times-frac`
94×	`add-cube-cbrt`
90×	`prod-diff`
44×	`difference-of-squares`
31×	`distribute-lft-out`
30×	`fma-neg`
22×	`distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`pow1` `flip3--` `flip--` `div-inv` `add-log-exp`
5×	`tan-quot` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 236

Calls

4 calls:

86.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
24.0ms	(/ (* (tan x) (sin eps)) (cos eps))
14.0ms	(* (tan x) (sin eps))
275.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

316.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
168.0ms	(/ (* (tan x) (sin eps)) (cos eps))
72.0ms	(* (tan x) (sin eps))
566.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify2.5s

Counts

248 → 248

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	303	7980
1	735	6699
2	3585	6012
done	5000	6003

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
2.8b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `flip-+` `fma-udef` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

14.0ms	(+ (tan x) (tan eps))
22.0ms	(/ (* (tan x) (sin eps)) (cos eps))
28.0ms	(* (tan x) (sin eps))
1.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

series822.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(+ (tan x) (tan eps))
154.0ms	(/ (* (tan x) (sin eps)) (cos eps))
94.0ms	(* (tan x) (sin eps))
419.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

simplify1.8s

Counts

85 → 85

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	150	1069
1	363	1040
2	1677	911
done	5000	900

prune518.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.3b

regimes470.0ms

Accuracy

85.2% (1.1b remaining)

Error of 15.1b against oracle of 13.9b and baseline of 21.6b

bsearch348.0ms

Steps

Iters	Range		Point
9	1.666090664139391e-91	7.120530906151667e-84	6.814433610919413e-84
9	-4.325919977650215e-09	-2.58561076839667e-15	-2.6215293643417535e-15

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	76
1	39	76
done	39	76

end0.0ms

sample10.9s

Algorithm

intervals

Results

5.6s	3245×	body	1280	valid
1.9s	635×	body	2560	valid
1.4s	1842×	body	640	valid
967.0ms	1131×	body	80	valid
454.0ms	792×	body	320	valid
117.0ms	355×	body	160	valid