Details

sample328.0ms

Algorithm

intervals

Results

172.0ms	96×	body	1280	valid
60.0ms	24×	body	2560	valid
44.0ms	56×	body	640	valid
19.0ms	39×	body	320	valid
5.0ms	31×	body	80	valid
3.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize19.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
6.3b	(tan (+ x eps))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

35.0ms	(- (tan (+ x eps)) (tan x))
14.0ms	(tan (+ x eps))

series234.0ms

Counts

2 → 6

Calls

2 calls:

150.0ms	(- (tan (+ x eps)) (tan x))
83.0ms	(tan (+ x eps))

simplify2.6s

Counts

31 → 31

Iterations

Useful iterations: 4 (403.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	278	341
3	528	337
4	1109	335
5	2471	335
done	5000	335

prune127.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize18.0ms

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))
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

33.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
25.0ms	(* (tan x) (tan eps))
127.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

304.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
178.0ms	(+ (tan x) (tan eps))
112.0ms	(* (tan x) (tan eps))
511.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.3s

Counts

98 → 98

Iterations

Useful iterations: 3 (913.0ms)

Iter	Nodes	Cost
0	172	1724
1	397	1649
2	1095	1579
3	2939	1563
done	5000	1563

prune377.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.2b	(* (tan x) (tan eps))
2.4b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`tan-quot`
19×	`*-un-lft-identity`
18×	`associate-r`
15×	`add-exp-log`
14×	`add-cube-cbrt`
11×	`times-frac` `add-cbrt-cube`
8×	`pow1` `frac-sub` `add-log-exp`
7×	`frac-times` `associate-l` `associate-*l/`
5×	`flip3-+` `frac-add` `prod-exp` `flip-+`
4×	`unswap-sqr`
3×	`associate-*r/` `cbrt-unprod`
2×	`flip3--` `div-exp` `pow-prod-down` `associate-/r/` `un-div-inv` `*-commutative` `flip--` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rec-exp` `diff-log` `1-exp` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

14.0ms	(+ (tan x) (tan eps))
63.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
15.0ms	(* (tan x) (tan eps))
38.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

150.0ms	(+ (tan x) (tan eps))
278.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
121.0ms	(* (tan x) (tan eps))
562.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify1.8s

Counts

111 → 111

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	225	2170
1	550	1939
2	1651	1820
done	5000	1796

prune490.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cos x) (- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))) (* (* (cos x) (cos eps)) (cos x)))
0.2b	(* (tan x) (tan eps))
0.2b	(* (* (cos x) (cos eps)) (cos x))
2.4b	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-undiv` `div-exp` `associate-r` `add-log-exp`
4×	`tan-quot` `associate-r/` `associate-l*` `pow-prod-down`
3×	`associate-*l/` `associate-/l/`
2×	`flip3--` `cos-mult` `*-commutative` `frac-sub` `sin-cos-mult` `flip--`
1×	`frac-times` `sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `associate-/r/` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

242.0ms	(/ (* (cos x) (- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))) (* (* (cos x) (cos eps)) (cos x)))
19.0ms	(* (tan x) (tan eps))
39.0ms	(* (* (cos x) (cos eps)) (cos x))
154.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))

series1.2s

Counts

4 → 12

Calls

4 calls:

536.0ms	(/ (* (cos x) (- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))) (* (* (cos x) (cos eps)) (cos x)))
102.0ms	(* (tan x) (tan eps))
51.0ms	(* (* (cos x) (cos eps)) (cos x))
481.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))

simplify2.0s

Counts

94 → 94

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	187	2861
1	550	2801
2	2411	2069
done	5000	2061

prune503.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.9b

regimes263.0ms

Accuracy

86% (1.0b remaining)

Error of 15.5b against oracle of 14.4b and baseline of 21.9b

bsearch268.0ms

Steps

Iters	Range		Point
9	5.252562429305735e-86	4.785952250071044e-79	1.7602505446838355e-79
9	-6.683415139468467e-26	-6.664835066811297e-31	-1.757922927393182e-27

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	24	117
1	36	68
done	36	68

end0.0ms

sample10.8s

Algorithm

intervals

Results

5.7s	3277×	body	1280	valid
1.9s	640×	body	2560	valid
1.5s	1781×	body	640	valid
640.0ms	364×	body	160	valid
495.0ms	834×	body	320	valid
165.0ms	1104×	body	80	valid