Details

sample322.0ms

Algorithm

intervals

Results

151.0ms	105×	body	1280	valid
76.0ms	17×	body	2560	valid
51.0ms	59×	body	640	valid
14.0ms	24×	body	320	valid
8.0ms	42×	body	80	valid
3.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

72.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series229.0ms

Counts

2 → 6

Calls

2 calls:

170.0ms	(- (tan (+ x eps)) (tan x))
59.0ms	(tan (+ x eps))

simplify2.6s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
4	4117
3	1335
2	453
1	203
0	94

prune303.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.2b

localize26.0ms

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))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite211.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

46.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(+ (tan x) (tan eps))
13.0ms	(* (tan x) (tan eps))
125.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

359.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
156.0ms	(+ (tan x) (tan eps))
151.0ms	(* (tan x) (tan eps))
587.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.3s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	1645
1	576
0	238

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.1b

localize60.0ms

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)))
2.1b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-cbrt-cube` `add-exp-log`
19×	`frac-times` `pow-prod-down`
13×	`associate-l/` `associate-r/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
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:

33.0ms	(* (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
70.0ms	(* (* (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)))

series1.3s

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (tan x) (tan eps))
142.0ms	(* (tan x) (tan eps))
194.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
867.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify1.6s

Counts

119 → 119

Iterations

Iter	Nodes
done	5001
2	1594
1	443
0	157

prune896.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.1b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (- (tan x)))
27.1b	(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

rewrite407.0ms

Algorithm

rewrite-expression-head

Rules

256×	`tan-quot`
163×	`frac-times`
97×	`associate-*l/`
85×	`associate-*r/`
82×	`pow1`
63×	`cbrt-div`
34×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `pow-plus` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube` `fma-udef`

Counts

4 → 187

Calls

4 calls:

102.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
66.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (- (tan x)))
218.0ms	(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

series1.5s

Counts

4 → 12

Calls

4 calls:

213.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
183.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
939.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (- (tan x)))
124.0ms	(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

simplify2.0s

Counts

199 → 199

Iterations

Iter	Nodes
done	5001
2	2568
1	795
0	336

prune1.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 15.1b

regimes365.0ms

Accuracy

89% (0.8b remaining)

Error of 15.4b against oracle of 14.6b and baseline of 21.8b

bsearch127.0ms

Steps

Iters	Range		Point
1	3.282886774816453e-26	3.4817375791661903e-26	3.4320248780787555e-26
9	-1.2142195303351722e-24	-5.149820411924956e-30	-5.5478192972833355e-27

simplify12.0ms

Iterations

Iter	Nodes
done	46
1	46
0	36

end0.0ms

sample9.9s

Algorithm

intervals

Results

4.5s	3251×	body	1280	valid
2.5s	1865×	body	640	valid
1.7s	650×	body	2560	valid
412.0ms	772×	body	320	valid
320.0ms	1137×	body	80	valid
96.0ms	325×	body	160	valid