Details

sample369.0ms

Algorithm

intervals

Results

193.0ms	98×	body	1280	valid
76.0ms	24×	body	2560	valid
58.0ms	56×	body	640	valid
14.0ms	22×	body	320	valid
8.0ms	44×	body	80	valid
4.0ms	12×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize13.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.9b	(tan (+ x eps))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

36.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series219.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(- (tan (+ x eps)) (tan x))
94.0ms	(tan (+ x eps))

simplify3.0s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
4	4082
3	1357
2	454
1	205
0	96

prune256.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize44.0ms

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))
2.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite242.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `frac-add` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

43.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(+ (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
154.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

282.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
135.0ms	(+ (tan x) (tan eps))
140.0ms	(* (tan x) (tan eps))
488.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.5s

Counts

185 → 185

Iterations

Iter	Nodes
done	5001
2	1631
1	580
0	242

prune788.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.0b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`tan-quot` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `associate-r` `associate-l` `associate-/l`
2×	`div-exp` `associate-/r/`
1×	`frac-times` `cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `pow-flip` `flip--` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

10.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
12.0ms	(+ (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series865.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
156.0ms	(+ (tan x) (tan eps))
149.0ms	(* (tan x) (tan eps))
378.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify2.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5002
3	2563
2	960
1	366
0	170

prune789.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 14.4b

localize73.0ms

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)))
2.9b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-cbrt-cube` `add-exp-log`
19×	`frac-times` `pow-prod-down`
13×	`associate-l/` `associate-r/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 111

Calls

4 calls:

26.0ms	(* (tan x) (tan eps))
35.0ms	(* (tan x) (tan eps))
121.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series1.4s

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (tan x) (tan eps))
156.0ms	(* (tan x) (tan eps))
190.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
852.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify1.4s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	1621
1	449
0	160

prune750.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 14.4b

regimes348.0ms

Accuracy

88% (0.9b remaining)

Error of 15.5b against oracle of 14.6b and baseline of 21.7b

bsearch306.0ms

Steps

Iters	Range		Point
10	3.302217848673879e-63	5.871316347800174e-52	5.810306508670788e-52
9	-5.469986621237647e-61	-8.278077243234882e-66	-5.421325500005225e-61

simplify14.0ms

Iterations

Iter	Nodes
done	39
1	39
0	30

end0.0ms

sample11.4s

Algorithm

intervals

Results

5.6s	3269×	body	1280	valid
2.5s	1897×	body	640	valid
1.7s	649×	body	2560	valid
961.0ms	761×	body	320	valid
174.0ms	341×	body	160	valid
167.0ms	1083×	body	80	valid