Details

sample326.0ms

Algorithm

intervals

Results

157.0ms	106×	body	1280	valid
82.0ms	58×	body	640	valid
46.0ms	16×	body	2560	valid
15.0ms	25×	body	320	valid
7.0ms	36×	body	80	valid
5.0ms	15×	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: 38.2b

localize10.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite78.0ms

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:

67.0ms	(- (tan (+ x eps)) (tan x))
9.0ms	(tan (+ x eps))

series565.0ms

Counts

2 → 6

Calls

2 calls:

486.0ms	(- (tan (+ x eps)) (tan x))
79.0ms	(tan (+ x eps))

simplify2.5s

Counts

47 → 47

Iterations

Useful iterations: done (2.5s)

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

prune149.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize13.0ms

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))

rewrite241.0ms

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:

61.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
18.0ms	(+ (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
118.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

367.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
134.0ms	(+ (tan x) (tan eps))
150.0ms	(* (tan x) (tan eps))
611.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.6s

Counts

181 → 181

Iterations

Useful iterations: done (1.6s)

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

prune627.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.8b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

20.0ms	(* (tan x) (tan eps))
32.0ms	(* (tan x) (tan eps))
88.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (tan x) (tan eps))
147.0ms	(* (tan x) (tan eps))
153.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
882.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify1.5s

Counts

119 → 119

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	158	1871
1	428	1759
2	1476	1476
done	5000	1399

prune519.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.4b	(pow (* (tan x) (tan eps)) (* 2 3))
2.8b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (cbrt (pow (* (tan x) (tan eps)) (* 2 3))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
10.7b	(cbrt (pow (* (tan x) (tan eps)) (* 2 3)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

17.0ms	(* (tan x) (tan eps))
13.0ms	(pow (* (tan x) (tan eps)) (* 2 3))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (cbrt (pow (* (tan x) (tan eps)) (* 2 3))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
9.0ms	(cbrt (pow (* (tan x) (tan eps)) (* 2 3)))

series1.4s

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (tan x) (tan eps))
199.0ms	(pow (* (tan x) (tan eps)) (* 2 3))
885.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (cbrt (pow (* (tan x) (tan eps)) (* 2 3))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
166.0ms	(cbrt (pow (* (tan x) (tan eps)) (* 2 3)))

simplify1.1s

Counts

77 → 77

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	168	1481
1	420	1305
2	1297	1138
done	5001	1078

prune544.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.1b

regimes181.0ms

Accuracy

87.7% (0.9b remaining)

Error of 15.2b against oracle of 14.3b and baseline of 21.8b

bsearch306.0ms

Steps

Iters	Range		Point
9	1.7638441963605991e-34	9.114405519066242e-29	5.858392615759789e-32
6	-1.0258849894178107e-80	-9.969104774869095e-82	-8.360406307762017e-81

simplify10.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	43	83
1	58	79
done	58	79

end0.0ms

sample11.2s

Algorithm

intervals

Results

4.8s	3225×	body	1280	valid
3.1s	633×	body	2560	valid
1.8s	1918×	body	640	valid
827.0ms	737×	body	320	valid
179.0ms	1136×	body	80	valid
152.0ms	351×	body	160	valid