Details

sample315.0ms

Algorithm

intervals

Results

192.0ms	121×	body	1280	valid
51.0ms	17×	body	2560	valid
42.0ms	57×	body	640	valid
7.0ms	15×	body	320	valid
5.0ms	36×	body	80	valid
3.0ms	10×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	272
1	9	272
2	10	272
done	10	272

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize16.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
4.6b	(tan (+ x eps))

rewrite22.0ms

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:

15.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series260.0ms

Counts

2 → 6

Calls

2 calls:

156.0ms	(- (tan (+ x eps)) (tan x))
103.0ms	(tan (+ x eps))

simplify4.0s

Counts

47 → 47

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	94	20012
1	203	18282
2	453	16535
3	1335	16386
4	4117	14630
done	5000	14566

prune309.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.8b

localize23.0ms

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

rewrite186.0ms

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:

6.0ms	(+ (tan x) (tan eps))
29.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
24.0ms	(* (tan x) (tan eps))
120.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

141.0ms	(+ (tan x) (tan eps))
286.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
160.0ms	(* (tan x) (tan eps))
520.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.7s

Counts

181 → 181

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	238	103743
1	576	94109
2	1626	85105
done	5001	83671

prune835.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.6b

localize45.0ms

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

rewrite95.0ms

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:

15.0ms	(* (tan x) (tan eps))
11.0ms	(* (tan x) (tan eps))
66.0ms	(* (* (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:

147.0ms	(* (tan x) (tan eps))
150.0ms	(* (tan x) (tan eps))
180.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
869.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify2.5s

Counts

119 → 119

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	157	46237
1	443	40097
2	1594	38992
done	5001	38077

prune769.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.6b

localize107.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin eps))
0.3b	(* (cos eps) (cos eps))
0.3b	(* (* (tan x) (sin eps)) (* (tan x) (sin eps)))
2.8b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (cos eps) (cos eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

16.0ms	(* (tan x) (sin eps))
9.0ms	(* (cos eps) (cos eps))
42.0ms	(* (* (tan x) (sin eps)) (* (tan x) (sin eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (cos eps) (cos eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (tan x) (sin eps))
18.0ms	(* (cos eps) (cos eps))
104.0ms	(* (* (tan x) (sin eps)) (* (tan x) (sin eps)))
971.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (cos eps) (cos eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify2.7s

Counts

111 → 111

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	175	37482
1	472	30583
2	1541	29223
done	5000	28863

prune698.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 14.6b

regimes493.0ms

Accuracy

86.7% (1.0b remaining)

Error of 15.5b against oracle of 14.5b and baseline of 21.8b

bsearch314.0ms

Steps

Iters	Range		Point
9	8.491318493822432e-78	1.4984895451995754e-70	3.4964004687602118e-74
8	-6.358562521077362e-50	-7.09086929250311e-54	-6.248907778173893e-50

simplify21.0ms

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	28	1205
1	39	1165
done	39	1165

end0.0ms

sample11.8s

Algorithm

intervals

Results

5.4s	3279×	body	1280	valid
2.7s	1836×	body	640	valid
2.6s	675×	body	2560	valid
394.0ms	760×	body	320	valid
353.0ms	1117×	body	80	valid
114.0ms	333×	body	160	valid