Details

sample225.0ms

Algorithm

intervals

Results

112.0ms	110×	body	1280	valid
44.0ms	22×	body	2560	valid
29.0ms	50×	body	640	valid
18.0ms	30×	body	320	valid
5.0ms	16×	body	160	valid
3.0ms	28×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize16.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite34.0ms

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:

24.0ms	(- (tan (+ x eps)) (tan x))
8.0ms	(tan (+ x eps))

series223.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(- (tan (+ x eps)) (tan x))
77.0ms	(tan (+ x eps))

simplify2.9s

Counts

47 → 47

Iterations

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

prune294.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.5b

localize42.0ms

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))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite188.0ms

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:

26.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
7.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
129.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

341.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
157.0ms	(+ (tan x) (tan eps))
144.0ms	(* (tan x) (tan eps))
583.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.1s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	1645
1	576
0	238

prune951.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.4b

localize74.0ms

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)))
3.3b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite126.0ms

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:

12.0ms	(* (tan x) (tan eps))
13.0ms	(* (tan x) (tan eps))
97.0ms	(* (* (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 (* (tan x) (tan eps))) (- (tan x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (tan x) (tan eps))
128.0ms	(* (tan x) (tan eps))
165.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
917.0ms	(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

prune940.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.4b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.4b	(pow (* (tan x) (tan eps)) 3)
3.3b	(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)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

24.0ms	(* (tan x) (tan eps))
79.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
20.0ms	(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)))

series2.3s

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (tan x) (tan eps))
191.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
176.0ms	(pow (* (tan x) (tan eps)) 3)
1.7s	(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)))

simplify2.7s

Counts

123 → 123

Iterations

Iter	Nodes
done	5573
2	2805
1	699
0	212

prune735.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.4b

regimes244.0ms

Accuracy

88.5% (0.9b remaining)

Error of 15.4b against oracle of 14.6b and baseline of 22.0b

bsearch268.0ms

Steps

Iters	Range		Point
9	2.786526732181471e-40	5.824320714786293e-34	5.041570059440358e-35
10	-1212215.9807367995	-5.980124527132304e-10	-6.095793693328762e-10

simplify7.0ms

Iterations

Iter	Nodes
done	46
1	46
0	36

end0.0ms

sample8.8s

Algorithm

intervals

Results

4.4s	3309×	body	1280	valid
1.8s	1843×	body	640	valid
1.5s	655×	body	2560	valid
436.0ms	775×	body	320	valid
283.0ms	1098×	body	80	valid
118.0ms	320×	body	160	valid