Details

sample40.0ms

Algorithm

intervals

Results

13.0ms	82×	body	1280	valid
6.0ms	165×	body	80	valid
5.0ms	45×	body	640	valid
2.0ms	24×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.2s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.6b	(- (exp (* a x)) 1.0)

rewrite26.0ms

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`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

2 → 24

Calls

2 calls:

6.0ms	(exp (* a x))
19.0ms	(- (exp (* a x)) 1.0)

series76.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
63.0ms	(- (exp (* a x)) 1.0)

simplify3.0s

Counts

30 → 30

Iterations

Iter	Nodes
done	5002
4	4038
3	1117
2	310
1	116
0	53

prune148.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x a) (* x a))
0.2b	(* (* x a) (* (* x a) 1/2))
5.0b	(+ (* x a) (* (* x a) (* (* x a) 1/2)))
12.6b	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* x a) (* (* x a) (* (* x a) 1/2))))

rewrite462.0ms

Algorithm

rewrite-expression-head

Rules

64×	`pow1`
37×	`add-cbrt-cube` `add-exp-log`
32×	`pow-prod-down`
23×	`prod-exp` `cbrt-unprod`
11×	`add-log-exp`
4×	`add-sqr-sqrt` `sum-log` `*-un-lft-identity` `pow-sqr` `pow-prod-up` `add-cube-cbrt`
2×	`+-commutative` `flip3-+` `pow-plus` `associate-r` `associate-l` `*-commutative` `flip-+`
1×	`pow2` `associate-+r+` `swap-sqr`

Counts

4 → 86

Calls

4 calls:

45.0ms	(* (* x a) (* x a))
75.0ms	(* (* x a) (* (* x a) 1/2))
8.0ms	(+ (* x a) (* (* x a) (* (* x a) 1/2)))
327.0ms	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* x a) (* (* x a) (* (* x a) 1/2))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* x a) (* x a))
61.0ms	(* (* x a) (* (* x a) 1/2))
83.0ms	(+ (* x a) (* (* x a) (* (* x a) 1/2)))
147.0ms	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* x a) (* (* x a) (* (* x a) 1/2))))

simplify2.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	1633
1	368
0	123

prune298.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.2b	(* x (* 3 a))
0.2b	(/ (- (exp (* x (* 3 a))) (* 1.0 (* 1.0 1.0))) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1.0 1.0) (* (exp (* a x)) 1.0))))
2.6b	(- (exp (* x (* 3 a))) (* 1.0 (* 1.0 1.0)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1` `times-frac`
8×	`add-log-exp`
3×	`associate-/r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `exp-prod` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `exp-to-pow` `diff-log` `div-sub` `div-exp` `associate-r` `*-commutative` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 72

Calls

4 calls:

6.0ms	(exp (* a x))
26.0ms	(* x (* 3 a))
75.0ms	(/ (- (exp (* x (* 3 a))) (* 1.0 (* 1.0 1.0))) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1.0 1.0) (* (exp (* a x)) 1.0))))
33.0ms	(- (exp (* x (* 3 a))) (* 1.0 (* 1.0 1.0)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(exp (* a x))
28.0ms	(* x (* 3 a))
163.0ms	(/ (- (exp (* x (* 3 a))) (* 1.0 (* 1.0 1.0))) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1.0 1.0) (* (exp (* a x)) 1.0))))
61.0ms	(- (exp (* x (* 3 a))) (* 1.0 (* 1.0 1.0)))

simplify1.7s

Counts

84 → 84

Iterations

Iter	Nodes
done	5013
2	1502
1	427
0	157

prune513.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 3) a)
0.2b	(/ (log (exp (- (exp (* (* x 3) a)) (* 1.0 (* 1.0 1.0))))) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1.0 1.0) (* (exp (* a x)) 1.0))))
2.6b	(log (exp (- (exp (* (* x 3) a)) (* 1.0 (* 1.0 1.0)))))
2.6b	(- (exp (* (* x 3) a)) (* 1.0 (* 1.0 1.0)))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
21×	`times-frac`
20×	`log-pow`
15×	`exp-prod`
14×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`log-prod`
3×	`associate-/r` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`log-div` `sub-neg` `exp-diff` `exp-sum` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `diff-log` `div-sub` `div-exp` `rem-log-exp` `associate-l` `*-commutative` `flip-+` `div-inv` `flip--`

Counts

4 → 94

Calls

4 calls:

26.0ms	(* (* x 3) a)
167.0ms	(/ (log (exp (- (exp (* (* x 3) a)) (* 1.0 (* 1.0 1.0))))) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1.0 1.0) (* (exp (* a x)) 1.0))))
22.0ms	(log (exp (- (exp (* (* x 3) a)) (* 1.0 (* 1.0 1.0)))))
11.0ms	(- (exp (* (* x 3) a)) (* 1.0 (* 1.0 1.0)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* x 3) a)
145.0ms	(/ (log (exp (- (exp (* (* x 3) a)) (* 1.0 (* 1.0 1.0))))) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1.0 1.0) (* (exp (* a x)) 1.0))))
55.0ms	(log (exp (- (exp (* (* x 3) a)) (* 1.0 (* 1.0 1.0)))))
70.0ms	(- (exp (* (* x 3) a)) (* 1.0 (* 1.0 1.0)))

simplify1.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1509
1	457
0	192

prune688.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes312.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch1.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	45
1	45
0	32

end0.0ms

sample2.0s

Algorithm

intervals

Results

948.0ms	2696×	body	1280	valid
263.0ms	1292×	body	640	valid
232.0ms	5427×	body	80	valid
94.0ms	757×	body	320	valid
34.0ms	410×	body	160	valid