Details

sample385.0ms

Algorithm

intervals

Results

138.0ms	86×	body	2560	valid
122.0ms	108×	body	1280	valid
66.0ms	49×	body	10240	exit
24.0ms	47×	body	640	valid
11.0ms	305×	pre	80	true
3.0ms	7×	body	320	valid
1.0ms	7×	body	80	valid
0.0ms	1×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4181
4	694
3	215
2	98
1	43
0	17

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 60.6b

localize56.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
2.2b	(- (exp (* a eps)) 1)
3.8b	(- (exp (* b eps)) 1)
5.6b	(- (exp (* (+ a b) eps)) 1)

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
10×	`add-log-exp` `difference-of-squares`
9×	`flip3--` `flip--`
7×	`associate-r` `associate-l`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`sub-neg` `difference-of-sqr-1` `distribute-lft-out--`
4×	`frac-times` `insert-posit16`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `associate-r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

119.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
17.0ms	(- (exp (* a eps)) 1)
13.0ms	(- (exp (* b eps)) 1)
14.0ms	(- (exp (* (+ a b) eps)) 1)

series192.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
36.0ms	(- (exp (* a eps)) 1)
36.0ms	(- (exp (* b eps)) 1)
58.0ms	(- (exp (* (+ a b) eps)) 1)

simplify2.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	4593
2	1367
1	395
0	154

prune683.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 49.7b

localize68.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (exp (* a eps)) 1)
2.3b	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
2.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))))
5.6b	(- (exp (* (+ a b) eps)) 1)

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`add-cbrt-cube` `add-exp-log`
15×	`*-un-lft-identity`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-/r/` `add-log-exp`
7×	`associate-l`
6×	`pow1` `flip3-+` `associate-*r/` `add-cube-cbrt` `flip-+` `difference-of-squares`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `insert-posit16`
3×	`difference-of-sqr-1` `associate-r` `distribute-lft-out--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `times-frac` `pow-prod-down` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

18.0ms	(- (exp (* a eps)) 1)
1.5s	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
595.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))))
26.0ms	(- (exp (* (+ a b) eps)) 1)

series2.5s

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (exp (* a eps)) 1)
335.0ms	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
2.0s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))))
52.0ms	(- (exp (* (+ a b) eps)) 1)

simplify3.7s

Counts

111 → 111

Iterations

Iter	Nodes
done	5005
2	4302
1	793
0	236

prune917.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 a) (/ 1 b))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16`

Counts

1 → 20

Calls

1 calls:

25.0ms

(+ (/ 1 a) (/ 1 b))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(+ (/ 1 a) (/ 1 b))

simplify2.8s

Counts

23 → 23

Iterations

Iter	Nodes
done	5000
5	3361
4	1333
3	593
2	278
1	105
0	41

prune123.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize107.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (exp (* a eps)) 1)
2.3b	(* (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)) (- (exp (* a eps)) 1))
2.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)) (- (exp (* a eps)) 1)))
5.6b	(- (exp (* (+ a b) eps)) 1)

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`add-cbrt-cube` `add-exp-log`
15×	`*-un-lft-identity`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-/r/` `add-log-exp`
7×	`associate-r`
6×	`pow1` `flip3-+` `associate-*r/` `add-cube-cbrt` `flip-+` `difference-of-squares`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `sub-neg` `div-exp` `associate-*l/` `insert-posit16`
3×	`difference-of-sqr-1` `associate-l` `distribute-lft-out--`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `pow-prod-down` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

19.0ms	(- (exp (* a eps)) 1)
1.6s	(* (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)) (- (exp (* a eps)) 1))
515.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)) (- (exp (* a eps)) 1)))
38.0ms	(- (exp (* (+ a b) eps)) 1)

series2.2s

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (exp (* a eps)) 1)
161.0ms	(* (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)) (- (exp (* a eps)) 1))
1.9s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)) (- (exp (* a eps)) 1)))
71.0ms	(- (exp (* (+ a b) eps)) 1)

simplify3.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5018
2	4224
1	754
0	231

prune777.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes181.0ms

Accuracy

0% (2.9b remaining)

Error of 3.1b against oracle of 0.2b and baseline of 3.1b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample16.3s

Algorithm

intervals

Results

5.7s	2646×	body	2560	valid
4.1s	3431×	body	1280	valid
4.1s	1880×	body	10240	exit
1.2s	1052×	body	640	valid
551.0ms	9882×	pre	80	true
130.0ms	337×	body	320	valid
76.0ms	121×	body	160	valid
52.0ms	415×	body	80	valid