Details

sample237.0ms

Algorithm

intervals

Results

107.0ms	105×	body	2560	valid
53.0ms	65×	body	10240	exit
44.0ms	97×	body	1280	valid
8.0ms	30×	body	640	valid
5.0ms	321×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	10×	body	80	valid
0.0ms	3×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	240	24
4	663	24
5	3002	24
done	5000	24

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.2b	(- (exp (* b eps)) 1.0)
3.2b	(- (exp (* a eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite39.0ms

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:

26.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series158.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
31.0ms	(- (exp (* b eps)) 1.0)
35.0ms	(- (exp (* a eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify435.0ms

Counts

88 → 88

Iterations

Useful iterations: done (432.0ms)

Iter	Nodes	Cost
0	143	1364
1	349	1326
2	1364	1196
done	5002	1190

prune295.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 52.9b

localize26.0ms

Local error

Found 4 expressions with local error:

3.3b	(* eps (+ a (* (* 1/2 (pow a 2)) eps)))
4.4b	(- (exp (* (+ a b) eps)) 1.0)
6.5b	(* (* 1/2 (pow a 2)) eps)
16.1b	(* (pow a 3) (pow eps 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
28×	`add-exp-log`
18×	`associate-r`
17×	`prod-exp` `unswap-sqr`
16×	`associate-l`
15×	`*-un-lft-identity`
14×	`unpow-prod-down` `cube-prod`
13×	`add-cube-cbrt` `add-cbrt-cube`
10×	`sqr-pow`
8×	`pow1`
7×	`pow-to-exp` `pow-exp`
6×	`add-log-exp`
5×	`cbrt-unprod`
3×	`pow-prod-down` `*-commutative`
2×	`cube-mult` `unpow3` `associate-*r/`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `diff-log` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

7.0ms	(* eps (+ a (* (* 1/2 (pow a 2)) eps)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (* 1/2 (pow a 2)) eps)
11.0ms	(* (pow a 3) (pow eps 3))

series186.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* eps (+ a (* (* 1/2 (pow a 2)) eps)))
47.0ms	(- (exp (* (+ a b) eps)) 1.0)
20.0ms	(* (* 1/2 (pow a 2)) eps)
62.0ms	(* (pow a 3) (pow eps 3))

simplify1.1s

Counts

126 → 126

Iterations

Useful iterations: 2 (169.0ms)

Iter	Nodes	Cost
0	180	1520
1	473	1361
2	2376	1263
done	5001	1263

prune476.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 51.8b

localize24.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (+ (* 1/6 (pow (* a eps) 3)) (* eps (+ a (* (* 1/2 (pow a 2)) eps)))) (- (exp (* b eps)) 1.0))
3.3b	(* eps (+ a (* (* 1/2 (pow a 2)) eps)))
4.4b	(- (exp (* (+ a b) eps)) 1.0)
6.5b	(* (* 1/2 (pow a 2)) eps)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

23.0ms	(* (+ (* 1/6 (pow (* a eps) 3)) (* eps (+ a (* (* 1/2 (pow a 2)) eps)))) (- (exp (* b eps)) 1.0))
7.0ms	(* eps (+ a (* (* 1/2 (pow a 2)) eps)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (* 1/2 (pow a 2)) eps)

series237.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (+ (* 1/6 (pow (* a eps) 3)) (* eps (+ a (* (* 1/2 (pow a 2)) eps)))) (- (exp (* b eps)) 1.0))
57.0ms	(* eps (+ a (* (* 1/2 (pow a 2)) eps)))
44.0ms	(- (exp (* (+ a b) eps)) 1.0)
21.0ms	(* (* 1/2 (pow a 2)) eps)

simplify996.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (189.0ms)

Iter	Nodes	Cost
0	205	2299
1	594	2158
2	2883	1958
done	5001	1958

prune423.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 51.5b

localize17.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (exp (* b eps)) 1.0)
2.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* a eps) 3)) (* a eps)) (- (exp (* b eps)) 1.0)))
3.2b	(* (+ (* 1/6 (pow (* a eps) 3)) (* a eps)) (- (exp (* b eps)) 1.0))
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

4.0ms	(- (exp (* b eps)) 1.0)
18.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* a eps) 3)) (* a eps)) (- (exp (* b eps)) 1.0)))
21.0ms	(* (+ (* 1/6 (pow (* a eps) 3)) (* a eps)) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series430.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (exp (* b eps)) 1.0)
267.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* a eps) 3)) (* a eps)) (- (exp (* b eps)) 1.0)))
86.0ms	(* (+ (* 1/6 (pow (* a eps) 3)) (* a eps)) (- (exp (* b eps)) 1.0))
45.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify846.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (199.0ms)

Iter	Nodes	Cost
0	190	2804
1	609	2738
2	3052	2266
done	5001	2266

prune390.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 3.0b

regimes63.0ms

Accuracy

0% (8.2b remaining)

Error of 11.0b against oracle of 2.9b and baseline of 11.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	15
1	18	15
done	18	15

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.5s	2610×	body	2560	valid
1.7s	1977×	body	10240	exit
1.7s	3486×	body	1280	valid
286.0ms	1067×	body	640	valid
170.0ms	9978×	pre	80	true
55.0ms	306×	body	320	valid
21.0ms	414×	body	80	valid
14.0ms	118×	body	160	valid