Details

sample237.0ms

Algorithm

intervals

Results

77.0ms	77×	body	2560	valid
65.0ms	67×	body	10240	exit
57.0ms	115×	body	1280	valid
10.0ms	34×	body	640	valid
5.0ms	323×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	16×	body	80	valid
0.0ms	3×	body	160	valid

simplify94.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	245	13
3	697	13
4	3463	13
5	5001	13
done	5001	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.9b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* a eps)) 1.0)
3.7b	(- (exp (* (+ a b) eps)) 1.0)

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

69.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
12.0ms	(- (exp (* b eps)) 1.0)
12.0ms	(- (exp (* a eps)) 1.0)
16.0ms	(- (exp (* (+ a b) eps)) 1.0)

series168.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
31.0ms	(- (exp (* b eps)) 1.0)
33.0ms	(- (exp (* a eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify41.0ms

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	346	733
1	1449	673
2	5001	673
done	5001	673

prune330.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 48.0b

localize29.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
3.7b	(- (exp (* (+ a b) eps)) 1.0)
13.3b	(* (pow a 2) (pow eps 2))
15.7b	(* (pow a 3) (pow eps 3))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
33×	`unswap-sqr`
30×	`add-exp-log`
28×	`unpow-prod-down`
25×	`associate-r`
23×	`associate-l`
20×	`*-un-lft-identity` `sqr-pow`
19×	`prod-exp`
16×	`add-cube-cbrt`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`add-cbrt-cube` `unpow2`
6×	`pow1` `add-log-exp`
4×	`frac-times` `flip3--` `flip--`
3×	`sub-neg` `flip3-+` `pow-prod-down` `*-commutative` `cbrt-unprod` `flip-+`
2×	`distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3` `associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log`

Counts

4 → 156

Calls

4 calls:

232.0ms	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* (pow a 2) (pow eps 2))
22.0ms	(* (pow a 3) (pow eps 3))

series267.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
51.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))
63.0ms	(* (pow a 3) (pow eps 3))

simplify127.0ms

Counts

168 → 168

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	674	1509
1	3525	1362
2	5001	1319
done	5001	1319

prune648.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 47.5b

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
3.2b	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
3.7b	(- (exp (* (+ a b) eps)) 1.0)
13.3b	(* (pow a 2) (pow eps 2))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
14×	`unpow-prod-down` `*-un-lft-identity` `prod-exp`
13×	`associate-r`
11×	`associate-l`
10×	`add-cube-cbrt` `unpow2` `sqr-pow`
8×	`frac-times` `flip3--` `associate-/r/` `flip--`
6×	`pow1` `pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `cbrt-unprod` `flip-+` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-*l/`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 128

Calls

4 calls:

83.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
191.0ms	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
20.0ms	(* (pow a 2) (pow eps 2))

series1.0s

Counts

4 → 12

Calls

4 calls:

829.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
128.0ms	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
48.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow a 2) (pow eps 2))

simplify126.0ms

Counts

140 → 140

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	839	2261
1	4666	1896
2	5001	1896
done	5001	1896

prune582.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite27.0ms

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` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

26.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify63.0ms

Counts

22 → 22

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2775	90
4	5001	90
done	5001	90

prune33.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

0% (3.1b remaining)

Error of 3.1b against oracle of 0.1b and baseline of 3.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3
done	9	3

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	2611×	body	2560	valid
1.7s	2019×	body	10240	exit
1.7s	3447×	body	1280	valid
296.0ms	1072×	body	640	valid
153.0ms	10020×	pre	80	true
60.0ms	324×	body	320	valid
28.0ms	422×	body	80	valid
15.0ms	125×	body	160	valid