Details

sample337.0ms

Algorithm

intervals

Results

174.0ms	101×	body	1280	valid
54.0ms	61×	body	640	valid
52.0ms	17×	body	2560	valid
20.0ms	32×	body	320	valid
7.0ms	36×	body	80	valid
3.0ms	9×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize25.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
3.0b	(tan (+ x eps))

rewrite106.0ms

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:

43.0ms	(- (tan (+ x eps)) (tan x))
61.0ms	(tan (+ x eps))

series694.0ms

Counts

2 → 6

Calls

2 calls:

606.0ms	(- (tan (+ x eps)) (tan x))
87.0ms	(tan (+ x eps))

simplify1.1s

Counts

47 → 47

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	94	720
1	202	600
2	741	510
done	5001	450

prune332.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.8b

localize33.0ms

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))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite305.0ms

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:

67.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
18.0ms	(+ (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
177.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

380.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
158.0ms	(+ (tan x) (tan eps))
174.0ms	(* (tan x) (tan eps))
622.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify3.0s

Counts

181 → 181

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	240	4762
1	596	3988
2	2892	3557
done	5000	3556

prune1.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.6b

localize39.0ms

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))
2.8b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite78.0ms

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:

19.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
25.0ms	(+ (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
1.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
183.0ms	(+ (tan x) (tan eps))
188.0ms	(* (tan x) (tan eps))
544.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	168	1279
1	390	1191
2	1477	1085
done	5001	1081

prune845.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.8b	(expm1 (/ 1 (- 1 (* (tan x) (tan eps)))))
2.8b	(fma (+ (tan x) (tan eps)) (log1p (expm1 (/ 1 (- 1 (* (tan x) (tan eps)))))) (- (tan x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

18.0ms	(+ (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
1.0ms	(expm1 (/ 1 (- 1 (* (tan x) (tan eps)))))
1.0ms	(fma (+ (tan x) (tan eps)) (log1p (expm1 (/ 1 (- 1 (* (tan x) (tan eps)))))) (- (tan x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

161.0ms	(+ (tan x) (tan eps))
167.0ms	(* (tan x) (tan eps))
303.0ms	(expm1 (/ 1 (- 1 (* (tan x) (tan eps)))))
669.0ms	(fma (+ (tan x) (tan eps)) (log1p (expm1 (/ 1 (- 1 (* (tan x) (tan eps)))))) (- (tan x)))

simplify1.1s

Counts

74 → 74

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	135	955
1	313	900
2	1152	820
done	5000	792

prune616.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.6b

regimes451.0ms

Accuracy

83% (1.3b remaining)

Error of 15.7b against oracle of 14.4b and baseline of 21.8b

bsearch399.0ms

Steps

Iters	Range		Point
8	1.8633570208784266e-73	8.362132446925381e-70	6.028701907762214e-70
9	-1.5329575775787027e-96	-2.7753575140769423e-105	-1.5063983278569401e-96

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	78
1	45	78
done	45	78

end0.0ms

sample14.9s

Algorithm

intervals

Results

6.5s	3321×	body	1280	valid
3.3s	1825×	body	640	valid
3.0s	633×	body	2560	valid
1.1s	764×	body	320	valid
225.0ms	1089×	body	80	valid
157.0ms	368×	body	160	valid