Details

sample152.0ms

Algorithm

intervals

Results

76.0ms	113×	body	1280	valid
30.0ms	18×	body	2560	valid
25.0ms	60×	body	640	valid
6.0ms	23×	body	320	valid
2.0ms	32×	body	80	valid
2.0ms	10×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
3.2b	(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))

series148.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(- (tan (+ x eps)) (tan x))
57.0ms	(tan (+ x eps))

simplify71.0ms

Counts

47 → 47

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	192	420
1	538	319
2	2593	310
3	5001	255
done	5001	255

prune112.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

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))
0.3b	(* (tan x) (tan eps))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite154.0ms

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:

29.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
95.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series781.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
95.0ms	(+ (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
376.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify70.0ms

Counts

181 → 181

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	559	2915
1	2054	2366
2	5001	2345
done	5001	2345

prune401.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
3.1b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`tan-quot`
21×	`*-un-lft-identity`
18×	`associate-r`
16×	`add-cube-cbrt`
15×	`add-exp-log`
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×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `associate-*r/` `prod-diff` `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` `fma-neg` `diff-log` `1-exp` `sum-log` `div-inv`

Counts

4 → 114

Calls

4 calls:

46.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
9.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
31.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series758.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
92.0ms	(+ (tan x) (tan eps))
92.0ms	(* (tan x) (tan eps))
357.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify77.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	621	1405
1	2833	1269
2	5001	1264
done	5001	1264

prune360.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.4b

localize16.0ms

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`tan-quot`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 79

Calls

4 calls:

14.0ms	(* (tan x) (tan eps))
17.0ms	(* (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
0.0ms	(fma (/ 1 (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (/ (+ (tan x) (tan eps)) (cbrt (- 1 (* (tan x) (tan eps))))) (- (tan x)))

series780.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
498.0ms	(fma (/ 1 (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (/ (+ (tan x) (tan eps)) (cbrt (- 1 (* (tan x) (tan eps))))) (- (tan x)))

simplify66.0ms

Counts

91 → 91

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	199	781
1	625	688
2	2402	687
3	5001	683
done	5001	683

prune314.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.4b

regimes156.0ms

Accuracy

89.2% (0.8b remaining)

Error of 15.6b against oracle of 14.9b and baseline of 22.0b

bsearch142.0ms

Steps

Iters	Range		Point
11	3.560853546224578e-32	4.11075536510938e-11	1.1330226692906078e-17
7	-5.197023235810444e-30	-1.5925208387961846e-31	-5.846838523325571e-31

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14
done	30	14

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3329×	body	1280	valid
1.1s	673×	body	2560	valid
763.0ms	1885×	body	640	valid
193.0ms	711×	body	320	valid
97.0ms	1071×	body	80	valid
56.0ms	331×	body	160	valid