Details

sample335.0ms

Algorithm

intervals

Results

172.0ms	115×	body	1280	valid
72.0ms	50×	body	640	valid
40.0ms	14×	body	2560	valid
19.0ms	28×	body	320	valid
8.0ms	15×	body	160	valid
7.0ms	34×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize27.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.0b	(tan (+ x eps))

rewrite21.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

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

series176.0ms

Counts

2 → 6

Calls

2 calls:

108.0ms	(- (tan (+ x eps)) (tan x))
68.0ms	(tan (+ x eps))

simplify2.5s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
4	4489
3	1451
2	479
1	205
0	96

prune278.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.1b

localize41.0ms

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))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite178.0ms

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` `insert-posit16` `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 → 173

Calls

4 calls:

9.0ms	(+ (tan x) (tan eps))
24.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(* (tan x) (tan eps))
125.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

138.0ms	(+ (tan x) (tan eps))
313.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
125.0ms	(* (tan x) (tan eps))
541.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.1s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
2	1720
1	580
0	242

prune864.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.2b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`tan-quot` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `associate-r` `associate-l` `associate-/l`
2×	`div-exp` `associate-/r/`
1×	`frac-times` `cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `pow-flip` `flip--` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

8.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
29.0ms	(* (tan x) (tan eps))
1.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series801.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
116.0ms	(+ (tan x) (tan eps))
129.0ms	(* (tan x) (tan eps))
405.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify2.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
3	2995
2	1032
1	366
0	170

prune750.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(log (exp (/ 1 (- 1 (* (tan x) (tan eps))))))
0.2b	(* (tan x) (tan eps))
3.2b	(fma (+ (tan x) (tan eps)) (log (exp (/ 1 (- 1 (* (tan x) (tan eps)))))) (- (tan x)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`log-pow`
15×	`exp-prod` `add-cube-cbrt`
9×	`times-frac`
7×	`pow1`
6×	`add-cbrt-cube` `tan-quot` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `fma-def` `associate-r` `associate-l`
2×	`associate-/r/`
1×	`frac-times` `+-commutative` `sum-log` `flip3-+` `flip3--` `rem-log-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `flip--` `distribute-lft-out` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

13.0ms	(+ (tan x) (tan eps))
15.0ms	(log (exp (/ 1 (- 1 (* (tan x) (tan eps))))))
29.0ms	(* (tan x) (tan eps))
1.0ms	(fma (+ (tan x) (tan eps)) (log (exp (/ 1 (- 1 (* (tan x) (tan eps)))))) (- (tan x)))

series888.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ (tan x) (tan eps))
221.0ms	(log (exp (/ 1 (- 1 (* (tan x) (tan eps))))))
140.0ms	(* (tan x) (tan eps))
385.0ms	(fma (+ (tan x) (tan eps)) (log (exp (/ 1 (- 1 (* (tan x) (tan eps)))))) (- (tan x)))

simplify3.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5004
3	2927
2	970
1	368
0	189

prune567.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.2b

regimes219.0ms

Accuracy

0% (0.4b remaining)

Error of 12.7b against oracle of 12.4b and baseline of 12.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample14.2s

Algorithm

intervals

Results

7.3s	3317×	body	1280	valid
2.5s	1856×	body	640	valid
2.5s	618×	body	2560	valid
1.1s	765×	body	320	valid
338.0ms	1108×	body	80	valid
216.0ms	336×	body	160	valid