Details

sample172.0ms

Algorithm

intervals

Results

81.0ms	111×	body	1280	valid
40.0ms	24×	body	2560	valid
29.0ms	55×	body	640	valid
9.0ms	32×	body	320	valid
2.0ms	26×	body	80	valid
1.0ms	8×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize9.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
4.0b	(tan (+ x eps))

rewrite13.0ms

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:

8.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series142.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (tan (+ x eps)) (tan x))
50.0ms	(tan (+ x eps))

simplify1.1s

Counts

47 → 47

Iterations

Useful iterations: 3 (293.0ms)

Iter	Nodes	Cost
0	94	720
1	190	597
2	473	510
3	1662	450
done	5000	450

prune120.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.2b

localize12.0ms

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))))
0.2b	(* (tan x) (tan eps))
2.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite78.0ms

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:

4.0ms	(+ (tan x) (tan eps))
11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
51.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series737.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (tan x) (tan eps))
211.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(* (tan x) (tan eps))
346.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify794.0ms

Counts

181 → 181

Iterations

Useful iterations: done (788.0ms)

Iter	Nodes	Cost
0	240	4762
1	537	3970
2	1548	3555
done	5001	3549

prune405.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.1b

localize18.0ms

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	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
21.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series863.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
117.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
564.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify834.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (153.0ms)

Iter	Nodes	Cost
0	158	1871
1	427	1759
2	1647	1476
done	5000	1476

prune352.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.1b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`fma-udef`

Counts

4 → 93

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
7.0ms	(* (tan x) (tan x))
5.0ms	(* (tan eps) (tan eps))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series717.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (tan x) (tan eps))
35.0ms	(* (tan x) (tan x))
31.0ms	(* (tan eps) (tan eps))
561.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify630.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (132.0ms)

Iter	Nodes	Cost
0	167	1441
1	383	1325
2	1378	1120
done	5001	1120

prune273.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.1b

regimes177.0ms

Accuracy

87.8% (0.9b remaining)

Error of 15.6b against oracle of 14.6b and baseline of 22.2b

bsearch211.0ms

Steps

Iters	Range		Point
11	2.28145452431431e-18	2231369.5462890854	2.855628566329288e-18
10	-4.161461817671002e-38	-2.4684106388071866e-48	-1.9500134694671836e-38

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	88
1	41	52
done	41	52

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	3341×	body	1280	valid
1.1s	666×	body	2560	valid
753.0ms	1788×	body	640	valid
231.0ms	779×	body	320	valid
95.0ms	1078×	body	80	valid
69.0ms	348×	body	160	valid