Details

sample222.0ms

Algorithm

intervals

Results

98.0ms	90×	body	1280	valid
53.0ms	23×	body	2560	valid
30.0ms	52×	body	640	valid
19.0ms	42×	body	320	valid
5.0ms	16×	body	160	valid
4.0ms	33×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize16.0ms

Local error

Found 2 expressions with local error:

3.2b	(- (tan (+ x eps)) (tan x))
3.7b	(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:

27.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series656.0ms

Counts

2 → 6

Calls

2 calls:

167.0ms	(- (tan (+ x eps)) (tan x))
487.0ms	(tan (+ x eps))

simplify2.7s

Counts

47 → 47

Iterations

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

prune308.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.9b

localize43.0ms

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))
0.3b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite205.0ms

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:

23.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
10.0ms	(+ (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
137.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

349.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
146.0ms	(+ (tan x) (tan eps))
155.0ms	(* (tan x) (tan eps))
585.0ms	(- (/ (+ (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

prune927.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.7b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.5b	(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)))

rewrite97.0ms

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:

13.0ms	(* (tan x) (tan eps))
10.0ms	(pow (* (tan x) (tan eps)) 3)
70.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(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)))

series1.8s

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (tan x) (tan eps))
163.0ms	(pow (* (tan x) (tan eps)) 3)
191.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.3s	(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)))

simplify2.2s

Counts

123 → 123

Iterations

Iter	Nodes
done	5433
2	2782
1	696
0	212

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.7b

localize122.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin eps) (sin x)) (* (sin eps) (sin x)))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
3.5b	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (/ (* (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (sin eps) (sin x))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps)))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

121×	`pow1`
51×	`pow-prod-down`
40×	`add-cbrt-cube` `add-exp-log`
32×	`tan-quot`
24×	`prod-exp` `cbrt-unprod`
19×	`frac-times`
13×	`associate-l/` `associate-r/`
12×	`pow-sqr` `pow-prod-up`
6×	`pow-plus`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `cos-mult` `add-cube-cbrt` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`fma-udef`

Counts

4 → 139

Calls

4 calls:

70.0ms	(* (* (sin eps) (sin x)) (* (sin eps) (sin x)))
99.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
50.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (/ (* (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (sin eps) (sin x))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps)))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

series1.7s

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (* (sin eps) (sin x)) (* (sin eps) (sin x)))
171.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
102.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
1.3s	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (/ (* (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (sin eps) (sin x))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps)))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

simplify2.4s

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
2	3315
1	697
0	230

prune1.3s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 13.7b

regimes376.0ms

Accuracy

88.7% (0.8b remaining)

Error of 15.2b against oracle of 14.3b and baseline of 21.5b

bsearch308.0ms

Steps

Iters	Range		Point
7	1.198224572307006e-47	2.3800638025231682e-46	2.292531808674074e-46
6	-1.420566845900726e-44	-1.8566375790700655e-45	-1.0260016803855225e-44

simplify37.0ms

Iterations

Iter	Nodes
done	55
1	55
0	40

end0.0ms

sample10.8s

Algorithm

intervals

Results

5.2s	3293×	body	1280	valid
1.8s	1807×	body	640	valid
1.8s	645×	body	2560	valid
970.0ms	816×	body	320	valid
560.0ms	341×	body	160	valid
222.0ms	1098×	body	80	valid