Details

sample500.0ms

Algorithm

intervals

Results

275.0ms	112×	body	1280	valid
106.0ms	49×	body	640	valid
62.0ms	17×	body	2560	valid
18.0ms	21×	body	320	valid
12.0ms	22×	body	160	valid
10.0ms	35×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize27.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.3b	(tan (+ x eps))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `tan-quot` `add-log-exp`
2×	`pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 27

Calls

2 calls:

26.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series233.0ms

Counts

2 → 6

Calls

2 calls:

134.0ms	(- (tan (+ x eps)) (tan x))
100.0ms	(tan (+ x eps))

simplify1.5s

Counts

33 → 33

Iterations

Iter	Nodes
5	3439
4	1447
3	676
2	287
1	139
0	70

prune348.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`insert-posit16`
3×	`associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`frac-times` `+-commutative` `sum-log` `flip3-+` `times-frac` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

4.0ms	(- 1 (* (tan x) (tan eps)))
7.0ms	(+ (tan x) (tan eps))
27.0ms	(* (tan x) (tan eps))
57.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series940.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(- 1 (* (tan x) (tan eps)))
149.0ms	(+ (tan x) (tan eps))
106.0ms	(* (tan x) (tan eps))
503.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.4s

Counts

78 → 78

Iterations

Iter	Nodes
3	3007
2	950
1	358
0	149

prune918.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`add-cbrt-cube` `add-exp-log`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`tan-quot`
4×	`times-frac` `insert-posit16`
3×	`associate-/r` `associate-r` `associate-l*`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `diff-log` `pow-prod-down` `frac-add` `-commutative` `frac-sub` `flip-+` `div-inv` `flip--` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `unswap-sqr` `associate-/l/`

Counts

4 → 74

Calls

4 calls:

16.0ms	(+ (tan x) (tan eps))
31.0ms	(/ (* (tan x) (sin eps)) (cos eps))
26.0ms	(* (tan x) (sin eps))
167.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series905.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(+ (tan x) (tan eps))
131.0ms	(/ (* (tan x) (sin eps)) (cos eps))
92.0ms	(* (tan x) (sin eps))
541.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
3	4832
2	1185
1	399
0	166

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (/ (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
13×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
4×	`insert-posit16`
3×	`frac-times` `times-frac` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 84

Calls

4 calls:

24.0ms	(* (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
330.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

series1.7s

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (tan x) (tan eps))
138.0ms	(* (tan x) (tan eps))
162.0ms	(* (tan x) (tan eps))
1.3s	(- (/ (+ (tan x) (tan eps)) (/ (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

simplify1.7s

Counts

96 → 96

Iterations

Iter	Nodes
3	4659
2	1110
1	330
0	130

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.5b

regimes274.0ms

Accuracy

88.9% (0.8b remaining)

Error of 15.4b against oracle of 14.6b and baseline of 22.1b

bsearch437.0ms

Steps

Iters	Range		Point
9	2.8247475806395485e-77	4.478245262004958e-68	3.143523747535153e-69
11	-511.55301347613675	-1.7758424453292816e-19	-8.29565067036897e-18

simplify16.0ms

Iterations

Iter	Nodes
2	46
1	46
0	34

end0.0ms

sample14.6s

Algorithm

intervals

Results

7.5s	3310×	body	1280	valid
2.9s	1902×	body	640	valid
2.7s	630×	body	2560	valid
783.0ms	755×	body	320	valid
241.0ms	1053×	body	80	valid
215.0ms	350×	body	160	valid