Details

sample348.0ms

Algorithm

intervals

Results

173.0ms	106×	body	1280	valid
85.0ms	28×	body	2560	valid
49.0ms	58×	body	640	valid
13.0ms	23×	body	320	valid
5.0ms	31×	body	80	valid
4.0ms	10×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize20.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (tan (+ x eps)) (tan x))
4.5b	(tan (+ x eps))

rewrite524.0ms

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:

40.0ms	(- (tan (+ x eps)) (tan x))
482.0ms	(tan (+ x eps))

series235.0ms

Counts

2 → 6

Calls

2 calls:

137.0ms	(- (tan (+ x eps)) (tan x))
98.0ms	(tan (+ x eps))

simplify2.6s

Counts

47 → 47

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	94	720
1	194	597
2	457	510
3	1461	450
done	5000	438

prune170.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.4b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite226.0ms

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:

38.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
153.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

350.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
147.0ms	(+ (tan x) (tan eps))
146.0ms	(* (tan x) (tan eps))
548.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.6s

Counts

181 → 181

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	240	4762
1	560	3970
2	1558	3555
done	5000	3149

prune574.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.3b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
61×	`times-frac`
48×	`prod-diff`
17×	`distribute-lft-out`
16×	`fma-neg`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`tan-quot` `div-inv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip--` `fma-udef` `distribute-lft-out--`

Counts

4 → 146

Calls

4 calls:

0.0ms	(fma (tan x) (- (tan eps)) 1)
26.0ms	(/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1))
14.0ms	(+ (tan eps) (tan x))
92.0ms	(- (/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1)) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

159.0ms	(fma (tan x) (- (tan eps)) 1)
334.0ms	(/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1))
132.0ms	(+ (tan eps) (tan x))
602.0ms	(- (/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1)) (tan x))

simplify2.8s

Counts

158 → 158

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	197	4292
1	442	3635
2	1141	3246
3	3979	2811
done	5000	2811

prune630.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b	(pow (* (tan x) (tan eps)) 3)
2.9b	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

48×	`pow1`
40×	`tan-quot`
21×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
10×	`prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `associate-r` `associate-l` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `pow-unpow`
2×	`pow-pow` `pow-plus` `pow-exp` `*-commutative` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `swap-sqr` `fma-udef` `unswap-sqr` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

16.0ms	(* (tan x) (tan eps))
108.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
36.0ms	(pow (* (tan x) (tan eps)) 3)
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

series2.0s

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (tan x) (tan eps))
161.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
209.0ms	(pow (* (tan x) (tan eps)) 3)
1.5s	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

simplify2.0s

Counts

123 → 123

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	234	2288
1	658	1831
2	2963	1614
done	5002	1583

prune679.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.0b

regimes261.0ms

Accuracy

75.5% (1.8b remaining)

Error of 14.2b against oracle of 12.3b and baseline of 19.9b

bsearch379.0ms

Steps

Iters	Range		Point
4	8.374626897052483e-75	1.4393546628418213e-74	9.730491097206055e-75
8	-2.286418009881596e-145	-4.6651284413305015e-148	-2.0348245825395098e-145

simplify13.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	51	329
1	62	174
done	62	174

end0.0ms

sample10.1s

Algorithm

intervals

Results

5.5s	3328×	body	1280	valid
1.9s	1824×	body	640	valid
1.7s	625×	body	2560	valid
341.0ms	817×	body	320	valid
158.0ms	354×	body	160	valid
143.0ms	1052×	body	80	valid