Details

sample297.0ms

Algorithm

intervals

Results

168.0ms	111×	body	1280	valid
45.0ms	20×	body	2560	valid
40.0ms	56×	body	640	valid
18.0ms	23×	body	320	valid
5.0ms	36×	body	80	valid
3.0ms	10×	body	160	valid

simplify7.0ms

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: 34.5b

localize24.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
2.4b	(tan (+ x eps))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

26.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series264.0ms

Counts

2 → 6

Calls

2 calls:

136.0ms	(- (tan (+ x eps)) (tan x))
127.0ms	(tan (+ x eps))

simplify962.0ms

Counts

31 → 31

Iterations

Useful iterations: done (960.0ms)

Iter	Nodes	Cost
0	68	11636
1	137	10793
2	355	10793
3	1176	10753
done	5000	10711

prune210.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`tan-quot`
6×	`pow1`
4×	`distribute-lft-out` `associate-/l*`
3×	`associate-/r` `flip3--` `associate-r` `associate-l*` `flip--` `associate-/l/`
2×	`sub-neg` `diff-log` `associate-/r/` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

4.0ms	(- 1 (* (tan x) (tan eps)))
29.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
23.0ms	(* (tan x) (tan eps))
124.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

170.0ms	(- 1 (* (tan x) (tan eps)))
348.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
113.0ms	(* (tan x) (tan eps))
556.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.9s

Counts

97 → 97

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	171	46691
1	431	44120
2	2002	43880
done	5000	43840

prune665.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
0.1b	(/ (* (sin x) (tan eps)) (cos x))
0.3b	(* (sin x) (tan eps))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
28×	`times-frac`
20×	`add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`difference-of-squares`
9×	`associate-/r*`
7×	`distribute-lft-out`
6×	`pow1` `distribute-lft-out--` `add-log-exp`
5×	`tan-quot` `associate-/l*`
4×	`associate-/l/`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `div-inv` `flip--`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 108

Calls

4 calls:

40.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
22.0ms	(/ (* (sin x) (tan eps)) (cos x))
21.0ms	(* (sin x) (tan eps))
148.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

296.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
158.0ms	(/ (* (sin x) (tan eps)) (cos x))
125.0ms	(* (sin x) (tan eps))
599.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify1.8s

Counts

120 → 120

Iterations

Useful iterations: 2 (796.0ms)

Iter	Nodes	Cost
0	218	70819
1	510	67754
2	2227	67314
done	5001	67314

prune797.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.9b

localize95.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.1b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

84×	`pow1`
73×	`tan-quot`
37×	`frac-times`
35×	`pow-prod-down`
30×	`add-cbrt-cube` `add-exp-log`
25×	`associate-*r/`
24×	`associate-*l/`
17×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `pow-sqr` `pow-prod-up`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`associate-r` `associate-l` `frac-sub`
4×	`pow-plus`
3×	`*-commutative`
2×	`pow2` `flip3-+` `swap-sqr` `associate--l+` `flip-+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `flip--` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

23.0ms	(* (tan x) (tan eps))
77.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
90.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
93.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series2.7s

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (tan x) (tan eps))
166.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
136.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.3s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify2.0s

Counts

150 → 150

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	223	71517
1	762	58471
done	5000	56391

prune984.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.9b

regimes418.0ms

Accuracy

85.5% (1.0b remaining)

Error of 15.6b against oracle of 14.6b and baseline of 21.5b

bsearch398.0ms

Steps

Iters	Range		Point
8	2.0514026188518955e-26	3.4507352230645513e-22	3.290261811358081e-26
9	-1.0921450650867151e-76	-9.281782166033958e-82	-1.0354031092861841e-76

simplify35.0ms

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	37	1575
1	59	1495
2	63	1495
done	63	1495

end0.0ms

sample11.6s

Algorithm

intervals

Results

4.9s	3324×	body	1280	valid
3.5s	1870×	body	640	valid
2.1s	637×	body	2560	valid
521.0ms	731×	body	320	valid
177.0ms	1103×	body	80	valid
156.0ms	335×	body	160	valid