Details

sample155.0ms

Algorithm

intervals

Results

63.0ms	87×	body	1280	valid
40.0ms	24×	body	2560	valid
29.0ms	77×	body	640	valid
7.0ms	28×	body	320	valid
2.0ms	30×	body	80	valid
2.0ms	10×	body	160	valid

simplify4.0ms

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: 35.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite29.0ms

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:

17.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series145.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (tan (+ x eps)) (tan x))
51.0ms	(tan (+ x eps))

simplify70.0ms

Counts

47 → 47

Iterations

Useful iterations: 3 (66.0ms)

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

prune109.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.1b

localize11.0ms

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))
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite152.0ms

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:

9.0ms	(+ (tan x) (tan eps))
27.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
17.0ms	(* (tan x) (tan eps))
92.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series786.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (tan x) (tan eps))
230.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
95.0ms	(* (tan x) (tan eps))
365.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify69.0ms

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

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.9b

localize16.0ms

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)))
2.4b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite100.0ms

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:

15.0ms	(* (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
67.0ms	(* (* (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)))

series933.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (tan x) (tan eps))
99.0ms	(* (tan x) (tan eps))
120.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
614.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify56.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	432	1098
1	1952	917
2	5001	864
done	5001	864

prune373.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (tan x) (tan x)) (* (tan eps) (tan eps)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan eps) (tan eps))
2.4b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

68.0ms	(* (* (tan x) (tan x)) (* (tan eps) (tan eps)))
17.0ms	(* (tan x) (tan x))
15.0ms	(* (tan eps) (tan eps))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series822.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (* (tan x) (tan x)) (* (tan eps) (tan eps)))
33.0ms	(* (tan x) (tan x))
34.0ms	(* (tan eps) (tan eps))
626.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify63.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	485	1132
1	2210	926
2	5001	909
done	5001	909

prune323.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 14.9b

regimes188.0ms

Accuracy

86.3% (1.0b remaining)

Error of 15.4b against oracle of 14.5b and baseline of 21.4b

bsearch99.0ms

Steps

Iters	Range		Point
9	4.790029874967855e-71	1.4938963809151437e-62	1.4671055856340722e-62
1	-4.770358420029441e-23	-4.590456568991035e-23	-4.72538295726984e-23

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	48
1	53	48
2	53	48
done	53	48

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	3360×	body	1280	valid
1.1s	646×	body	2560	valid
756.0ms	1815×	body	640	valid
194.0ms	746×	body	320	valid
96.0ms	1092×	body	80	valid
59.0ms	341×	body	160	valid