Details

sample454.0ms

Algorithm

intervals

Results

252.0ms	101×	body	1280	valid
95.0ms	28×	body	2560	valid
59.0ms	55×	body	640	valid
23.0ms	32×	body	320	valid
6.0ms	30×	body	80	valid
5.0ms	10×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize28.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
4.4b	(tan (+ x eps))

rewrite36.0ms

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` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 27

Calls

2 calls:

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

series191.0ms

Counts

2 → 6

Calls

2 calls:

132.0ms	(- (tan (+ x eps)) (tan x))
59.0ms	(tan (+ x eps))

simplify1.5s

Counts

33 → 33

Iterations

Iter	Nodes
5	3439
4	1447
3	676
2	287
1	139
0	70

prune383.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
2.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite134.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`insert-posit16` `associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `flip3--` `frac-add` `associate-/r/` `flip-+` `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` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

38.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
10.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
70.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

313.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
132.0ms	(+ (tan x) (tan eps))
123.0ms	(* (tan x) (tan eps))
477.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
3	3786
2	1110
1	404
0	174

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.0b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `swap-sqr` `flip--`

Counts

4 → 114

Calls

4 calls:

32.0ms	(* (tan x) (tan eps))
27.0ms	(* (tan x) (tan eps))
129.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
45.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.6s

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (tan x) (tan eps))
136.0ms	(* (tan x) (tan eps))
169.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.2s	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify969.0ms

Counts

126 → 126

Iterations

Iter	Nodes
2	2595
1	633
0	204

prune1.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
2.0b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (tan eps))) (cos x)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`tan-quot`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`associate-*r/` `frac-sub`
4×	`frac-times` `insert-posit16`
3×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `associate--l+` `flip-+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `flip--`

Counts

4 → 84

Calls

4 calls:

17.0ms	(* (sin x) (tan eps))
16.0ms	(* (tan x) (tan eps))
22.0ms	(* (tan x) (tan eps))
77.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (tan eps))) (cos x)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.9s

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (sin x) (tan eps))
146.0ms	(* (tan x) (tan eps))
160.0ms	(* (tan x) (tan eps))
1.5s	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (tan eps))) (cos x)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify839.0ms

Counts

96 → 96

Iterations

Iter	Nodes
2	2025
1	523
0	179

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

regimes238.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
2	35
1	35
0	26

end0.0ms

sample14.1s

Algorithm

intervals

Results

7.2s	3298×	body	1280	valid
2.7s	1761×	body	640	valid
2.7s	660×	body	2560	valid
680.0ms	806×	body	320	valid
284.0ms	1103×	body	80	valid
184.0ms	372×	body	160	valid