Details

sample150.0ms

Algorithm

intervals

Results

76.0ms	108×	body	1280	valid
32.0ms	68×	body	640	valid
20.0ms	12×	body	2560	valid
5.0ms	21×	body	320	valid
3.0ms	40×	body	80	valid
1.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
2.5b	(tan (+ x eps))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

18.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series158.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(- (tan (+ x eps)) (tan x))
60.0ms	(tan (+ x eps))

simplify1.7s

Counts

47 → 47

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	94	720
1	194	597
2	457	510
3	1461	450
done	5000	438

prune116.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.4b

localize11.0ms

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

rewrite158.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

30.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
98.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series791.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
95.0ms	(+ (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
377.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.1s

Counts

181 → 181

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	240	4762
1	560	3970
2	1558	3555
done	5000	3149

prune421.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.3b

localize13.0ms

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

rewrite40.0ms

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` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `flip3--` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

10.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series641.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
97.0ms	(+ (tan x) (tan eps))
95.0ms	(* (tan x) (tan eps))
305.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify2.0s

Counts

98 → 98

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	168	1279
1	366	1191
2	902	1085
3	2488	1079
done	5001	1077

prune297.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.7b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (log (exp (* (tan x) (tan eps)))))) (- (tan x)))
3.0b	(log (exp (* (tan x) (tan eps))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`pow1` `add-log-exp`
6×	`tan-quot` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-def` `associate-r` `associate-l` `log-pow`
1×	`+-commutative` `frac-times` `exp-prod` `exp-to-pow` `flip3-+` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `distribute-lft-out` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

9.0ms	(+ (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (log (exp (* (tan x) (tan eps)))))) (- (tan x)))
5.0ms	(log (exp (* (tan x) (tan eps))))

series615.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (tan x) (tan eps))
100.0ms	(* (tan x) (tan eps))
316.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (log (exp (* (tan x) (tan eps)))))) (- (tan x)))
100.0ms	(log (exp (* (tan x) (tan eps))))

simplify1.4s

Counts

79 → 79

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	131	959
1	280	877
2	725	778
3	1833	774
done	5000	773

prune278.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.3b

regimes148.0ms

Accuracy

77.1% (1.6b remaining)

Error of 16.2b against oracle of 14.6b and baseline of 21.8b

bsearch228.0ms

Steps

Iters	Range		Point
9	6.255787448508467e-103	4.277095025588716e-96	7.696293304718232e-100
10	-4.383081831618126e-112	-2.5505156108085874e-123	-4.307211467193249e-112

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	71
1	42	71
done	42	71

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.5s	3272×	body	1280	valid
1.1s	641×	body	2560	valid
961.0ms	1783×	body	640	valid
203.0ms	758×	body	320	valid
118.0ms	1196×	body	80	valid
71.0ms	350×	body	160	valid