Details

sample438.0ms

Algorithm

intervals

Results

177.0ms	95×	body	1280	valid
109.0ms	29×	body	2560	valid
102.0ms	55×	body	640	valid
22.0ms	27×	body	320	valid
12.0ms	44×	body	80	valid
3.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize21.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
4.3b	(tan (+ x eps))

rewrite485.0ms

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:

474.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series206.0ms

Counts

2 → 6

Calls

2 calls:

133.0ms	(- (tan (+ x eps)) (tan x))
73.0ms	(tan (+ x eps))

simplify3.7s

Counts

33 → 33

Iterations

Iter	Nodes
5	3750
4	1478
3	672
2	285
1	137
0	70

prune203.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize40.0ms

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))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

27.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
7.0ms	(+ (tan x) (tan eps))
27.0ms	(* (tan x) (tan eps))
79.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

319.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
156.0ms	(+ (tan x) (tan eps))
147.0ms	(* (tan x) (tan eps))
516.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
3	3734
2	1101
1	402
0	174

prune696.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (sin x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite145.0ms

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` `prod-exp` `associate-*r/` `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:

8.0ms	(+ (tan x) (tan eps))
13.0ms	(* (sin x) (tan eps))
15.0ms	(/ (* (sin x) (tan eps)) (cos x))
108.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series868.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (tan x) (tan eps))
105.0ms	(* (sin x) (tan eps))
144.0ms	(/ (* (sin x) (tan eps)) (cos x))
496.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify2.2s

Counts

86 → 86

Iterations

Iter	Nodes
3	4391
2	1131
1	391
0	167

prune569.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.4b

localize65.0ms

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))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite195.0ms

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:

13.0ms	(+ (tan x) (tan eps))
29.0ms	(/ (* (tan x) (sin eps)) (cos eps))
25.0ms	(* (tan x) (sin eps))
126.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series840.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(+ (tan x) (tan eps))
138.0ms	(/ (* (tan x) (sin eps)) (cos eps))
96.0ms	(* (tan x) (sin eps))
490.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify3.1s

Counts

86 → 86

Iterations

Iter	Nodes
3	4552
2	1185
1	397
0	166

prune558.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.4b

regimes192.0ms

Accuracy

0% (0.3b remaining)

Error of 12.7b against oracle of 12.4b and baseline of 12.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	17
1	17
0	15

end0.0ms

sample14.7s

Algorithm

intervals

Results

8.1s	3248×	body	1280	valid
2.7s	1886×	body	640	valid
2.4s	640×	body	2560	valid
734.0ms	759×	body	320	valid
305.0ms	1093×	body	80	valid
236.0ms	374×	body	160	valid