Details

sample431.0ms

Algorithm

intervals

Results

209.0ms	116×	body	1280	valid
86.0ms	27×	body	2560	valid
61.0ms	54×	body	640	valid
50.0ms	19×	body	320	valid
8.0ms	33×	body	80	valid
4.0ms	7×	body	160	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: 36.4b

localize50.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (tan (+ x eps)) (tan x))
2.7b	(tan (+ x eps))

rewrite33.0ms

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

series214.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(- (tan (+ x eps)) (tan x))
103.0ms	(tan (+ x eps))

simplify3.7s

Counts

33 → 33

Iterations

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

prune327.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize31.0ms

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))
1.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite116.0ms

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:

25.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
7.0ms	(+ (tan x) (tan eps))
20.0ms	(* (tan x) (tan eps))
63.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

275.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
134.0ms	(+ (tan x) (tan eps))
134.0ms	(* (tan x) (tan eps))
472.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
3	3734
2	1101
1	402
0	174

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.1b

localize76.0ms

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)) (* (tan x) (tan eps)))
1.4b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `swap-sqr` `flip--`

Counts

4 → 114

Calls

4 calls:

26.0ms	(* (tan x) (tan eps))
25.0ms	(* (tan x) (tan eps))
106.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
35.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.6s

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (tan x) (tan eps))
124.0ms	(* (tan x) (tan eps))
141.0ms	(* (* (tan x) (tan eps)) (* (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))

simplify838.0ms

Counts

126 → 126

Iterations

Iter	Nodes
2	2628
1	633
0	204

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (tan x) (tan x)) (* (tan eps) (tan eps)))
0.2b	(* (tan x) (tan x))
0.3b	(* (tan eps) (tan eps))
1.4b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt` `pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-l`
6×	`pow-plus` `swap-sqr` `pow-prod-up` `add-log-exp`
5×	`frac-sub`
4×	`pow2` `pow-sqr` `insert-posit16`
3×	`*-commutative` `unswap-sqr`
2×	`flip3-+` `associate--l+` `flip-+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `flip--`

Counts

4 → 123

Calls

4 calls:

75.0ms	(* (* (tan x) (tan x)) (* (tan eps) (tan eps)))
27.0ms	(* (tan x) (tan x))
14.0ms	(* (tan eps) (tan eps))
47.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (* (tan x) (tan x)) (* (tan eps) (tan eps)))
32.0ms	(* (tan x) (tan x))
37.0ms	(* (tan eps) (tan eps))
1.1s	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify860.0ms

Counts

135 → 135

Iterations

Iter	Nodes
2	2914
1	721
0	229

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.0b

regimes319.0ms

Accuracy

90.3% (0.8b remaining)

Error of 15.5b against oracle of 14.7b and baseline of 22.4b

bsearch418.0ms

Steps

Iters	Range		Point
8	4.382036096728738e-39	5.281511530195771e-35	5.153563226205793e-35
10	-4.251253991780348e-17	-8.338193174207716e-34	-8.912746710277703e-18

simplify15.0ms

Iterations

Iter	Nodes
2	57
1	57
0	40

end0.0ms

sample15.5s

Algorithm

intervals

Results

7.6s	3235×	body	1280	valid
3.3s	695×	body	2560	valid
2.6s	1854×	body	640	valid
1.2s	768×	body	320	valid
299.0ms	1095×	body	80	valid
194.0ms	353×	body	160	valid