Details

sample100.0ms

Algorithm

intervals

Results

34.0ms	86×	body	1280	valid
12.0ms	37×	body	320	valid
11.0ms	176×	body	80	valid
11.0ms	40×	body	640	valid
1.0ms	11×	body	160	valid

simplify7.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5028
8	3392
7	883
6	221
5	93
4	44
3	23
2	16
1	11
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize34.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (* a x))
4.6b	(- (exp (* a x)) 1.0)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

2 → 26

Calls

2 calls:

15.0ms	(exp (* a x))
45.0ms	(- (exp (* a x)) 1.0)

series99.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(exp (* a x))
74.0ms	(- (exp (* a x)) 1.0)

simplify7.4s

Counts

32 → 32

Iterations

Iter	Nodes
done	5016
4	4063
3	1104
2	311
1	118
0	55

prune352.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize137.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a x) (* (* a x) (* a x)))
0.2b	(* (* x a) (* (* x a) 1/2))
0.2b	(* (* a x) (* a x))
9.1b	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* x a) (* (* x a) 1/2)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

192×	`pow1`
92×	`pow-prod-down`
78×	`add-cbrt-cube` `add-exp-log`
54×	`prod-exp` `cbrt-unprod`
34×	`pow-prod-up`
12×	`pow-sqr`
6×	`pow-plus` `add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16`
3×	`pow2` `associate-r` `associate-l` `*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `cube-unmult` `swap-sqr` `flip-+`

Counts

4 → 140

Calls

4 calls:

331.0ms	(* (* a x) (* (* a x) (* a x)))
132.0ms	(* (* x a) (* (* x a) 1/2))
85.0ms	(* (* a x) (* a x))
850.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* x a) (* (* x a) 1/2)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (* a x) (* (* a x) (* a x)))
63.0ms	(* (* x a) (* (* x a) 1/2))
86.0ms	(* (* a x) (* a x))
304.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* x a) (* (* x a) 1/2)))

simplify5.4s

Counts

152 → 152

Iterations

Iter	Nodes
done	5001
2	1864
1	424
0	142

prune761.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize90.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (exp (* x a)) 1.0))
0.1b	(exp (* x a))
4.5b	(log (exp (- (exp (* x a)) 1.0)))
4.6b	(- (exp (* x a)) 1.0)

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`exp-prod` `add-log-exp`
7×	`add-cube-cbrt`
6×	`log-pow`
5×	`pow1` `log-prod`
4×	`add-cbrt-cube` `exp-sum` `add-exp-log` `insert-posit16`
3×	`sub-neg` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`
2×	`exp-diff` `diff-log`
1×	`log-div` `flip3--` `exp-to-pow` `rem-log-exp` `flip--`

Counts

4 → 65

Calls

4 calls:

112.0ms	(exp (- (exp (* x a)) 1.0))
10.0ms	(exp (* x a))
96.0ms	(log (exp (- (exp (* x a)) 1.0)))
29.0ms	(- (exp (* x a)) 1.0)

series246.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(exp (- (exp (* x a)) 1.0))
20.0ms	(exp (* x a))
65.0ms	(log (exp (- (exp (* x a)) 1.0)))
63.0ms	(- (exp (* x a)) 1.0)

simplify9.4s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
4	4986
3	1440
2	459
1	190
0	93

prune766.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* x a) (* x a)) (* x a))
0.2b	(* (* x a) (* x a))
0.2b	(* (* x a) (* x a))
9.0b	(+ (+ (* x a) (* 1/6 (* (* (* x a) (* x a)) (* x a)))) (/ (* (* x a) (* x a)) 2))

rewrite554.0ms

Algorithm

rewrite-expression-head

Rules

237×	`pow1`
103×	`pow-prod-down`
69×	`add-cbrt-cube` `add-exp-log`
47×	`prod-exp` `cbrt-unprod`
42×	`pow-prod-up`
21×	`pow-plus`
20×	`pow-sqr`
9×	`add-log-exp`
6×	`*-un-lft-identity`
5×	`pow2`
4×	`add-sqr-sqrt` `add-cube-cbrt` `insert-posit16`
3×	`sum-log` `associate-r` `associate-l` `*-commutative`
2×	`flip3-+` `swap-sqr` `frac-add` `flip-+`
1×	`+-commutative` `associate-+l+` `pow3` `distribute-lft-out`

Counts

4 → 162

Calls

4 calls:

257.0ms	(* (* (* x a) (* x a)) (* x a))
105.0ms	(* (* x a) (* x a))
89.0ms	(* (* x a) (* x a))
86.0ms	(+ (+ (* x a) (* 1/6 (* (* (* x a) (* x a)) (* x a)))) (/ (* (* x a) (* x a)) 2))

series478.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (* (* x a) (* x a)) (* x a))
77.0ms	(* (* x a) (* x a))
55.0ms	(* (* x a) (* x a))
226.0ms	(+ (+ (* x a) (* 1/6 (* (* (* x a) (* x a)) (* x a)))) (/ (* (* x a) (* x a)) 2))

simplify5.1s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
2	1564
1	394
0	128

prune881.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes449.0ms

Accuracy

35% (14.0b remaining)

Error of 14.1b against oracle of 0.1b and baseline of 21.7b

bsearch396.0ms

Steps

Iters	Range		Point
10	3.331204183500167e+120	7.812499575074096e+137	3.983314979150684e+121
8	-5.1266664932071965e-87	-1.4042772886075332e-89	-5.060005299698439e-87
8	-5.171729517309714e-51	-1.3613776417074444e-55	-2.7809807833631145e-53
6	-5.038384936634917e+85	-8.927875500473959e+84	-4.978355442950795e+85

simplify34.0ms

Iterations

Iter	Nodes
done	60
1	60
0	49

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	2560×	body	1280	valid
458.0ms	1367×	body	640	valid
395.0ms	5475×	body	80	valid
161.0ms	810×	body	320	valid
52.0ms	399×	body	160	valid