Details

sample342.0ms

Algorithm

intervals

Results

198.0ms	109×	body	1280	valid
55.0ms	20×	body	2560	valid
46.0ms	56×	body	640	valid
15.0ms	26×	body	320	valid
6.0ms	37×	body	80	valid
3.0ms	8×	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: 37.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite56.0ms

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:

48.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series211.0ms

Counts

2 → 6

Calls

2 calls:

134.0ms	(- (tan (+ x eps)) (tan x))
76.0ms	(tan (+ x eps))

simplify2.7s

Counts

31 → 31

Iterations

Useful iterations: 4 (438.0ms)

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

prune123.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.4b

localize17.0ms

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))))
0.3b	(* (tan x) (tan eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite189.0ms

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:

9.0ms	(+ (tan x) (tan eps))
32.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
23.0ms	(* (tan x) (tan eps))
122.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series945.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (tan x) (tan eps))
231.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
114.0ms	(* (tan x) (tan eps))
501.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.1s

Counts

98 → 98

Iterations

Useful iterations: 3 (773.0ms)

Iter	Nodes	Cost
0	172	1724
1	397	1649
2	1091	1579
3	2924	1563
done	5001	1563

prune377.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
27.7b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`tan-quot`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`cube-div` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

34.0ms	(* (tan x) (tan eps))
26.0ms	(pow (* (tan x) (tan eps)) 3)
201.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
9.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series812.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (tan x) (tan eps))
151.0ms	(pow (* (tan x) (tan eps)) 3)
434.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
115.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify695.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (241.0ms)

Iter	Nodes	Cost
0	163	1405
1	385	1180
2	1457	1110
done	5000	1110

prune544.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 15.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite533.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

104.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
27.0ms	(* (sin x) (sin eps))
39.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
352.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

305.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
52.0ms	(* (sin x) (sin eps))
160.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
524.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify1.2s

Counts

121 → 121

Iterations

Useful iterations: 2 (414.0ms)

Iter	Nodes	Cost
0	221	2922
1	529	2810
2	1890	2618
done	5000	2618

prune640.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 15.2b

regimes223.0ms

Accuracy

88.7% (0.8b remaining)

Error of 15.7b against oracle of 14.9b and baseline of 21.9b

bsearch296.0ms

Steps

Iters	Range		Point
10	4.950938936375422e-49	1.428063290236237e-30	3.5671412793756766e-32
9	-1.7569643515423198e-39	-6.4004412414421565e-49	-7.287696018930272e-45

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	55
1	34	37
done	34	37

end0.0ms

sample12.1s

Algorithm

intervals

Results

6.0s	3297×	body	1280	valid
2.6s	663×	body	2560	valid
2.2s	1870×	body	640	valid
518.0ms	760×	body	320	valid
281.0ms	1078×	body	80	valid
125.0ms	332×	body	160	valid