Details

sample363.0ms

Algorithm

intervals

Results

117.0ms	117×	body	1280	valid
111.0ms	67×	body	2560	valid
68.0ms	50×	body	10240	exit
22.0ms	37×	body	640	valid
8.0ms	306×	pre	80	true
4.0ms	13×	body	320	valid
2.0ms	18×	body	80	valid
1.0ms	4×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	245	24
4	692	24
5	3301	24
done	5001	24

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.3b

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* a eps)) 1.0)
4.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite144.0ms

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:

94.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
12.0ms	(- (exp (* b eps)) 1.0)
18.0ms	(- (exp (* a eps)) 1.0)
17.0ms	(- (exp (* (+ a b) eps)) 1.0)

series246.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
40.0ms	(- (exp (* b eps)) 1.0)
57.0ms	(- (exp (* a eps)) 1.0)
73.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.0s

Counts

88 → 88

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	143	1364
1	345	1326
2	1232	1196
done	5001	1190

prune475.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 48.9b

localize93.0ms

Local error

Found 4 expressions with local error:

3.1b	(* eps (+ (* (* 1/2 (pow a 2)) eps) a))
4.0b	(* (* 1/2 (pow a 2)) eps)
4.1b	(- (exp (* (+ a b) eps)) 1.0)
12.8b	(* (pow a 3) (pow eps 3))

rewrite223.0ms

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:

96.0ms	(* eps (+ (* (* 1/2 (pow a 2)) eps) a))
52.0ms	(* (* 1/2 (pow a 2)) eps)
28.0ms	(- (exp (* (+ a b) eps)) 1.0)
39.0ms	(* (pow a 3) (pow eps 3))

series271.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* eps (+ (* (* 1/2 (pow a 2)) eps) a))
32.0ms	(* (* 1/2 (pow a 2)) eps)
60.0ms	(- (exp (* (+ a b) eps)) 1.0)
106.0ms	(* (pow a 3) (pow eps 3))

simplify1.6s

Counts

126 → 126

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	180	1520
1	448	1363
2	1713	1263
done	5000	1262

prune863.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 48.7b

localize64.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (+ (* 1/6 (pow (* eps a) 3)) (* eps (+ (* (* 1/2 (pow a 2)) eps) a))) (- (exp (* b eps)) 1.0))
3.1b	(* eps (+ (* (* 1/2 (pow a 2)) eps) a))
4.0b	(* (* 1/2 (pow a 2)) eps)
4.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite243.0ms

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:

102.0ms	(* (+ (* 1/6 (pow (* eps a) 3)) (* eps (+ (* (* 1/2 (pow a 2)) eps) a))) (- (exp (* b eps)) 1.0))
89.0ms	(* eps (+ (* (* 1/2 (pow a 2)) eps) a))
35.0ms	(* (* 1/2 (pow a 2)) eps)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

series381.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (+ (* 1/6 (pow (* eps a) 3)) (* eps (+ (* (* 1/2 (pow a 2)) eps) a))) (- (exp (* b eps)) 1.0))
88.0ms	(* eps (+ (* (* 1/2 (pow a 2)) eps) a))
42.0ms	(* (* 1/2 (pow a 2)) eps)
67.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.8s

Counts

99 → 99

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	205	2299
1	582	2158
2	2486	1958
done	5000	1957

prune687.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 48.7b

localize68.0ms

Local error

Found 4 expressions with local error:

4.1b	(- (exp (* (+ a b) eps)) 1.0)
6.2b	(cbrt (+ (* (* 1/2 (pow a 2)) eps) a))
6.2b	(cbrt (+ (* (* 1/2 (pow a 2)) eps) a))
6.2b	(cbrt (+ (* (* 1/2 (pow a 2)) eps) a))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 53

Calls

4 calls:

28.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(cbrt (+ (* (* 1/2 (pow a 2)) eps) a))
44.0ms	(cbrt (+ (* (* 1/2 (pow a 2)) eps) a))
35.0ms	(cbrt (+ (* (* 1/2 (pow a 2)) eps) a))

series997.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (exp (* (+ a b) eps)) 1.0)
316.0ms	(cbrt (+ (* (* 1/2 (pow a 2)) eps) a))
296.0ms	(cbrt (+ (* (* 1/2 (pow a 2)) eps) a))
302.0ms	(cbrt (+ (* (* 1/2 (pow a 2)) eps) a))

simplify2.2s

Counts

65 → 65

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	126	1497
1	312	1456
2	855	1325
3	3077	1275
done	5001	1203

prune689.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 48.7b

regimes262.0ms

Accuracy

41.9% (4.7b remaining)

Error of 54.1b against oracle of 49.4b and baseline of 57.5b

bsearch878.0ms

Steps

Iters	Range	Point
7	1.8423430180599544e+124	5.7007244535432046e+125	1.862763256825557e+124
9	-3.336337897951449e+44	-6.895195114921403e+36	-4.265437250272592e+40
9	-6.654324194085478e+207	-6.594252900507075e+199	-2.1494946063080645e+206

Iters

Range

Point

1.8423430180599544e+124

5.7007244535432046e+125

1.862763256825557e+124

-3.336337897951449e+44

-6.895195114921403e+36

-4.265437250272592e+40

-6.654324194085478e+207

-6.594252900507075e+199

-2.1494946063080645e+206

simplify18.0ms

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	58	154
1	80	116
done	80	116

end0.0ms

sample15.5s

Algorithm

intervals

Results

5.0s	2528×	body	2560	valid
4.4s	1971×	body	10240	exit
3.9s	3530×	body	1280	valid
629.0ms	365×	body	320	valid
598.0ms	1025×	body	640	valid
348.0ms	9977×	pre	80	true
50.0ms	449×	body	80	valid
25.0ms	109×	body	160	valid