Details

sample317.0ms

Algorithm

intervals

Results

81.0ms	65×	body	10240	exit
64.0ms	35×	body	640	valid
62.0ms	53×	body	1280	valid
56.0ms	333×	body	80	valid
8.0ms	16×	body	320	valid
3.0ms	8×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1391
3	370
2	124
1	47
0	19

prune48.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.4b

localize193.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0))))
0.0b	(exp (* x (+ eps 1.0)))
0.0b	(exp (* x (- eps 1.0)))
3.8b	(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
38×	`exp-sum`
36×	`times-frac`
29×	`add-cube-cbrt`
19×	`distribute-rgt-in` `distribute-lft-in`
18×	`prod-diff`
12×	`difference-of-squares`
8×	`add-log-exp`
6×	`add-cbrt-cube` `associate-/l*` `distribute-lft-out--`
5×	`associate-/r*` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`exp-prod` `sub-neg` `exp-to-pow` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `fma-udef` `div-inv` `flip--`

Counts

4 → 120

Calls

4 calls:

105.0ms	(/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0))))
23.0ms	(exp (* x (+ eps 1.0)))
32.0ms	(exp (* x (- eps 1.0)))
3.0ms	(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0))))
24.0ms	(exp (* x (+ eps 1.0)))
35.0ms	(exp (* x (- eps 1.0)))
220.0ms	(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))))

simplify8.8s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
3	4806
2	1511
1	624
0	274

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize131.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) x)
2.8b	(fma 1.0 (* x x) (* (/ 2.7755575615628914e-17 eps) (* (* x x) x)))
3.5b	(* (/ 2.7755575615628914e-17 eps) (* (* x x) x))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
29×	`add-cbrt-cube` `add-exp-log`
15×	`prod-exp` `cbrt-unprod`
14×	`associate-l`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac` `pow-prod-down`
6×	`pow-plus` `pow-prod-up`
4×	`associate-r`
3×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `*-commutative`
1×	`pow3` `associate-*l/` `fma-udef` `div-inv` `unswap-sqr`

Counts

3 → 83

Calls

3 calls:

56.0ms	(* (* x x) x)
2.0ms	(fma 1.0 (* x x) (* (/ 2.7755575615628914e-17 eps) (* (* x x) x)))
189.0ms	(* (/ 2.7755575615628914e-17 eps) (* (* x x) x))

series279.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* (* x x) x)
95.0ms	(fma 1.0 (* x x) (* (/ 2.7755575615628914e-17 eps) (* (* x x) x)))
126.0ms	(* (/ 2.7755575615628914e-17 eps) (* (* x x) x))

simplify6.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5002
3	3285
2	818
1	304
0	118

prune880.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize170.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 2.7755575615628914e-17 eps) (log (exp (* (* x x) x))))
0.1b	(* (* x x) x)
1.6b	(log (exp (* (* x x) x)))
2.8b	(fma 1.0 (* x x) (* (/ 2.7755575615628914e-17 eps) (log (exp (* (* x x) x)))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1`
22×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
14×	`add-cbrt-cube` `associate-l` `add-exp-log`
10×	`times-frac`
9×	`log-prod` `associate-r`
6×	`pow-plus` `log-pow` `pow-prod-up` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
2×	`pow2` `exp-prod` `exp-to-pow` `pow-sqr` `*-commutative`
1×	`cbrt-undiv` `div-exp` `rem-log-exp` `pow3` `associate-*l/` `fma-udef` `div-inv`

Counts

4 → 103

Calls

4 calls:

50.0ms	(* (/ 2.7755575615628914e-17 eps) (log (exp (* (* x x) x))))
90.0ms	(* (* x x) x)
17.0ms	(log (exp (* (* x x) x)))
1.0ms	(fma 1.0 (* x x) (* (/ 2.7755575615628914e-17 eps) (log (exp (* (* x x) x)))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (/ 2.7755575615628914e-17 eps) (log (exp (* (* x x) x))))
77.0ms	(* (* x x) x)
74.0ms	(log (exp (* (* x x) x)))
121.0ms	(fma 1.0 (* x x) (* (/ 2.7755575615628914e-17 eps) (log (exp (* (* x x) x)))))

simplify6.7s

Counts

115 → 115

Iterations

Iter	Nodes
done	5029
3	3342
2	932
1	343
0	146

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.4b

localize233.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (- eps 1.0)))
0.2b	(sqrt (exp (* x (- eps 1.0))))
0.2b	(sqrt (exp (* x (- eps 1.0))))
4.2b	(fma (* (sqrt (exp (* x (- eps 1.0)))) (sqrt (exp (* x (- eps 1.0))))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

66×	`exp-sum`
54×	`prod-diff`
50×	`sqrt-prod`
44×	`add-sqr-sqrt`
42×	`*-un-lft-identity` `add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
8×	`add-log-exp`
6×	`pow1` `sub-neg` `sqrt-pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod` `exp-to-pow`
2×	`rem-sqrt-square` `pow1/2`
1×	`fma-udef` `rem-exp-log`

Counts

4 → 126

Calls

4 calls:

32.0ms	(exp (* x (- eps 1.0)))
44.0ms	(sqrt (exp (* x (- eps 1.0))))
27.0ms	(sqrt (exp (* x (- eps 1.0))))
1.0ms	(fma (* (sqrt (exp (* x (- eps 1.0)))) (sqrt (exp (* x (- eps 1.0))))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(exp (* x (- eps 1.0)))
65.0ms	(sqrt (exp (* x (- eps 1.0))))
48.0ms	(sqrt (exp (* x (- eps 1.0))))
224.0ms	(fma (* (sqrt (exp (* x (- eps 1.0)))) (sqrt (exp (* x (- eps 1.0))))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))))

simplify6.3s

Counts

138 → 138

Iterations

Iter	Nodes
done	5002
3	2690
2	932
1	419
0	210

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

regimes489.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.3b against oracle of 0.7b and baseline of 16.6b

bsearch361.0ms

Steps

Iters	Range		Point
10	4.3052657707541446e-11	1.5150962181605006	0.000489189965940405

simplify37.0ms

Iterations

Iter	Nodes
done	41
1	41
0	34

end0.0ms

sample9.9s

Algorithm

intervals

Results

2.9s	1905×	body	10240	exit
2.3s	10231×	body	80	valid
1.8s	1648×	body	1280	valid
1.8s	1245×	body	640	valid
326.0ms	650×	body	320	valid
94.0ms	314×	body	160	valid