Details

sample186.0ms

Algorithm

intervals

Results

54.0ms	58×	body	1280	valid
45.0ms	61×	body	10240	exit
31.0ms	294×	body	80	valid
21.0ms	47×	body	640	valid
9.0ms	27×	body	320	valid
1.0ms	7×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
4	1357
3	352
2	122
1	46
0	19

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- eps 1.0) x)
0.0b	(exp (* x (+ 1.0 eps)))
0.0b	(exp (* (- eps 1.0) x))
4.4b	(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`associate-l`
3×	`exp-to-pow` `associate-r`
2×	`distribute-rgt-in` `associate-+r+` `exp-prod` `distribute-lft-in` `flip3-+` `exp-sum` `associate-l/` `frac-add` `associate-r/` `flip-+` `rem-exp-log`
1×	`+-commutative` `sum-log` `flip3--` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

18.0ms	(* (- eps 1.0) x)
4.0ms	(exp (* x (+ 1.0 eps)))
9.0ms	(exp (* (- eps 1.0) x))
84.0ms	(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

series502.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (- eps 1.0) x)
21.0ms	(exp (* x (+ 1.0 eps)))
42.0ms	(exp (* (- eps 1.0) x))
382.0ms	(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

simplify1.8s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
2	1611
1	431
0	162

prune477.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 2.7755575615628914e-17 (/ eps (* (* x x) x)))
0.1b	(* (* x x) x)
3.4b	(/ eps (* (* x x) x))
5.0b	(+ (/ 2.7755575615628914e-17 (/ eps (* (* x x) x))) (* (* 1.0 x) x))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
32×	`add-cbrt-cube` `add-exp-log`
24×	`add-sqr-sqrt`
23×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-/r*`
6×	`pow-plus` `pow-prod-up` `div-inv` `associate-/l*` `add-log-exp`
3×	`associate-r` `pow-prod-down`
2×	`pow2` `clear-num` `frac-2neg` `pow-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `associate-l` `pow3` `associate-/r/` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

38.0ms	(/ 2.7755575615628914e-17 (/ eps (* (* x x) x)))
29.0ms	(* (* x x) x)
29.0ms	(/ eps (* (* x x) x))
69.0ms	(+ (/ 2.7755575615628914e-17 (/ eps (* (* x x) x))) (* (* 1.0 x) x))

series258.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ 2.7755575615628914e-17 (/ eps (* (* x x) x)))
62.0ms	(* (* x x) x)
43.0ms	(/ eps (* (* x x) x))
94.0ms	(+ (/ 2.7755575615628914e-17 (/ eps (* (* x x) x))) (* (* 1.0 x) x))

simplify1.7s

Counts

124 → 124

Iterations

Iter	Nodes
done	5004
2	1699
1	454
0	169

prune620.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x)))))
0.1b	(* (* x x) x)
1.5b	(log (exp (* (* x x) x)))
5.0b	(+ (/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x))))) (* (* 1.0 x) x))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
70×	`add-sqr-sqrt`
69×	`*-un-lft-identity` `add-cube-cbrt`
39×	`log-pow`
36×	`pow1`
22×	`associate-/r*`
19×	`add-log-exp`
14×	`add-cbrt-cube` `add-exp-log`
13×	`exp-prod` `exp-to-pow`
6×	`pow-plus` `pow-prod-up`
5×	`div-inv`
3×	`cbrt-undiv` `log-prod` `div-exp` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`pow2` `pow-sqr`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `rem-log-exp` `associate-l` `pow3` `associate-/r/` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

9.0ms	(/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x)))))
14.0ms	(* (* x x) x)
5.0ms	(log (exp (* (* x x) x)))
93.0ms	(+ (/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x))))) (* (* 1.0 x) x))

series268.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x)))))
41.0ms	(* (* x x) x)
46.0ms	(log (exp (* (* x x) x)))
102.0ms	(+ (/ 2.7755575615628914e-17 (/ eps (log (exp (* (* x x) x))))) (* (* 1.0 x) x))

simplify1.8s

Counts

171 → 171

Iterations

Iter	Nodes
done	5003
2	2566
1	652
0	245

prune885.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (+ 1.0 eps)))
0.0b	(/ (/ 1.0 eps) (exp (* x (+ 1.0 eps))))
0.0b	(/ 1.0 (exp (* x (+ 1.0 eps))))
4.4b	(- (/ (/ 1.0 eps) (exp (* x (+ 1.0 eps)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
70×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
38×	`exp-sum`
20×	`distribute-rgt-in` `distribute-lft-in`
16×	`associate-/l*`
11×	`add-cbrt-cube`
10×	`associate-/r*`
8×	`add-exp-log` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `div-exp`
2×	`clear-num` `frac-2neg` `associate-*r/` `frac-sub` `associate--r+`
1×	`exp-prod` `sub-neg` `flip3-+` `flip3--` `exp-to-pow` `diff-log` `flip-+` `flip--` `rem-exp-log` `associate-/l/`

Counts

4 → 161

Calls

4 calls:

8.0ms	(exp (* x (+ 1.0 eps)))
26.0ms	(/ (/ 1.0 eps) (exp (* x (+ 1.0 eps))))
14.0ms	(/ 1.0 (exp (* x (+ 1.0 eps))))
110.0ms	(- (/ (/ 1.0 eps) (exp (* x (+ 1.0 eps)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp (* x (+ 1.0 eps)))
41.0ms	(/ (/ 1.0 eps) (exp (* x (+ 1.0 eps))))
42.0ms	(/ 1.0 (exp (* x (+ 1.0 eps))))
234.0ms	(- (/ (/ 1.0 eps) (exp (* x (+ 1.0 eps)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

simplify2.0s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
2	2461
1	832
0	335

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

regimes112.0ms

Accuracy

97.1% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.8b

bsearch231.0ms

Steps

Iters	Range		Point
10	0.0009624679332913742	37605091470.942024	15.696054514468523

simplify35.0ms

Iterations

Iter	Nodes
done	54
3	54
2	47
1	43
0	31

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.6s	1994×	body	10240	exit
2.0s	1692×	body	1280	valid
1.9s	10203×	body	80	valid
1.1s	1263×	body	640	valid
208.0ms	661×	body	320	valid
68.0ms	319×	body	160	valid