Details

sample376.0ms

Algorithm

intervals

Results

148.0ms	84×	body	2560	valid
94.0ms	116×	body	1280	valid
77.0ms	45×	body	10240	exit
15.0ms	27×	body	640	valid
8.0ms	301×	pre	80	true
4.0ms	13×	body	320	valid
2.0ms	14×	body	80	valid
1.0ms	2×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	258	24
4	760	24
5	3738	24
done	5000	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.5b

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0b	(- (exp (* a eps)) 1.0)
3.3b	(- (exp (* b eps)) 1.0)
5.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

85.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
30.0ms	(- (exp (* a eps)) 1.0)
15.0ms	(- (exp (* b eps)) 1.0)
17.0ms	(- (exp (* (+ a b) eps)) 1.0)

series273.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
61.0ms	(- (exp (* a eps)) 1.0)
63.0ms	(- (exp (* b eps)) 1.0)
71.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.2s

Counts

150 → 150

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	221	3064
1	488	2615
2	1494	2203
done	5001	2038

prune910.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 52.9b

localize71.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (exp (* b eps)) 1.0)
5.5b	(- (exp (* (+ a b) eps)) 1.0)
7.0b	(* (* 1/2 (pow a 2)) eps)
15.0b	(* (pow a 3) (pow eps 3))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
26×	`add-exp-log`
25×	`add-cube-cbrt`
18×	`prod-diff`
16×	`prod-exp` `unswap-sqr`
15×	`associate-r`
14×	`unpow-prod-down` `cube-prod`
13×	`associate-l`
11×	`add-cbrt-cube`
10×	`sqr-pow`
8×	`add-log-exp`
7×	`pow-to-exp` `pow-exp`
6×	`pow1` `fma-neg`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 138

Calls

4 calls:

19.0ms	(- (exp (* b eps)) 1.0)
17.0ms	(- (exp (* (+ a b) eps)) 1.0)
35.0ms	(* (* 1/2 (pow a 2)) eps)
54.0ms	(* (pow a 3) (pow eps 3))

series275.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (exp (* b eps)) 1.0)
66.0ms	(- (exp (* (+ a b) eps)) 1.0)
35.0ms	(* (* 1/2 (pow a 2)) eps)
112.0ms	(* (pow a 3) (pow eps 3))

simplify1.7s

Counts

150 → 150

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	225	1981
1	520	1676
2	1674	1481
done	5000	1406

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 52.4b

localize55.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* a eps) 3) (* eps (+ (* (* 1/2 (pow a 2)) eps) a))) (- (exp (* b eps)) 1.0)))
3.3b	(- (exp (* b eps)) 1.0)
5.5b	(- (exp (* (+ a b) eps)) 1.0)
7.0b	(* (* 1/2 (pow a 2)) eps)

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
23×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`add-cbrt-cube`
19×	`add-cube-cbrt`
18×	`prod-diff`
11×	`prod-exp`
8×	`add-log-exp`
7×	`cbrt-unprod`
6×	`pow1` `fma-neg`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3--` `associate-*r/` `div-exp` `flip--` `log1p-expm1-u`
3×	`associate-r`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `frac-2neg` `times-frac` `associate-l` `pow-prod-down` `pow-exp` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 104

Calls

4 calls:

77.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* a eps) 3) (* eps (+ (* (* 1/2 (pow a 2)) eps) a))) (- (exp (* b eps)) 1.0)))
36.0ms	(- (exp (* b eps)) 1.0)
33.0ms	(- (exp (* (+ a b) eps)) 1.0)
47.0ms	(* (* 1/2 (pow a 2)) eps)

series1.3s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* a eps) 3) (* eps (+ (* (* 1/2 (pow a 2)) eps) a))) (- (exp (* b eps)) 1.0)))
44.0ms	(- (exp (* b eps)) 1.0)
89.0ms	(- (exp (* (+ a b) eps)) 1.0)
28.0ms	(* (* 1/2 (pow a 2)) eps)

simplify1.7s

Counts

116 → 116

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	246	2986
1	681	2711
2	2704	2187
done	5000	2101

prune731.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

29.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

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

simplify4.1s

Counts

37 → 37

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	42	245
1	108	231
2	251	211
3	523	210
4	1465	210
5	3712	210
done	5000	210

prune129.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes180.0ms

Accuracy

0% (3.1b remaining)

Error of 3.2b against oracle of 0.1b and baseline of 3.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
done	9	7

end0.0ms

sample15.8s

Algorithm

intervals

Results

5.0s	1982×	body	10240	exit
4.7s	2536×	body	2560	valid
3.5s	3476×	body	1280	valid
820.0ms	9989×	pre	80	true
624.0ms	1087×	body	640	valid
433.0ms	431×	body	80	valid
123.0ms	349×	body	320	valid
29.0ms	128×	body	160	valid