Details

sample552.0ms

Algorithm

intervals

Results

214.0ms	85×	body	2560	valid
147.0ms	114×	body	1280	valid
121.0ms	57×	body	10240	exit
27.0ms	33×	body	640	valid
13.0ms	313×	pre	80	true
3.0ms	5×	body	320	valid
3.0ms	15×	body	80	valid
2.0ms	4×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.5b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
2.3b	(- (exp (* a eps)) 1)
3.9b	(- (exp (* b eps)) 1)
4.7b	(- (exp (* (+ a b) eps)) 1)

rewrite133.0ms

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:

71.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
20.0ms	(- (exp (* a eps)) 1)
19.0ms	(- (exp (* b eps)) 1)
22.0ms	(- (exp (* (+ a b) eps)) 1)

series164.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
35.0ms	(- (exp (* a eps)) 1)
31.0ms	(- (exp (* b eps)) 1)
50.0ms	(- (exp (* (+ a b) eps)) 1)

simplify2.9s

Counts

102 → 102

Iterations

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

prune693.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 45.9b

localize49.0ms

Local error

Found 4 expressions with local error:

2.5b	(+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))
3.3b	(/ (* 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))))
3.9b	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
4.7b	(- (exp (* (+ a b) eps)) 1)

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

242.0ms	(+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))
494.0ms	(/ (* 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))))
1.1s	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
14.0ms	(- (exp (* (+ a b) eps)) 1)

series2.3s

Counts

4 → 12

Calls

4 calls:

165.0ms	(+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))
1.8s	(/ (* 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))))
261.0ms	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
49.0ms	(- (exp (* (+ a b) eps)) 1)

simplify3.9s

Counts

108 → 108

Iterations

Iter	Nodes
done	5003
2	4187
1	785
0	232

prune930.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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:

11.0ms

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

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

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

simplify3.1s

Counts

23 → 23

Iterations

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

prune119.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 1 expressions with local error:

16.0b

(/ (+ a b) (* a b))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-cbrt-cube` `add-exp-log`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `distribute-lft-out` `associate-/l/`
1×	`pow1` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 26

Calls

1 calls:

34.0ms

(/ (+ a b) (* a b))

series61.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

(/ (+ a b) (* a b))

simplify4.4s

Counts

29 → 29

Iterations

Iter	Nodes
done	5004
4	4978
3	1536
2	468
1	146
0	56

prune132.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes138.0ms

Accuracy

0% (2.7b remaining)

Error of 2.9b against oracle of 0.2b and baseline of 2.9b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end1.0ms

sample19.6s

Algorithm

intervals

Results

6.2s	2592×	body	2560	valid
5.1s	3421×	body	1280	valid
4.8s	1994×	body	10240	exit
1.4s	1100×	body	640	valid
701.0ms	383×	body	320	valid
575.0ms	9995×	pre	80	true
458.0ms	389×	body	80	valid
71.0ms	116×	body	160	valid