Details

sample335.0ms

Algorithm

intervals

Results

112.0ms	84×	body	2560	valid
87.0ms	45×	body	10240	exit
86.0ms	116×	body	1280	valid
12.0ms	27×	body	640	valid
7.0ms	301×	pre	80	true
4.0ms	13×	body	320	valid
1.0ms	14×	body	80	valid
0.0ms	2×	body	160	valid

simplify2.0s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.5b

localize22.0ms

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)

rewrite132.0ms

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:

79.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
15.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* b eps)) 1.0)
21.0ms	(- (exp (* (+ a b) eps)) 1.0)

series184.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
40.0ms	(- (exp (* a eps)) 1.0)
34.0ms	(- (exp (* b eps)) 1.0)
55.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify879.0ms

Counts

88 → 88

Iterations

Useful iterations: done (876.0ms)

Iter	Nodes	Cost
0	143	1364
1	345	1326
2	1231	1196
done	5000	1190

prune419.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 52.9b

localize41.0ms

Local error

Found 4 expressions with local error:

5.5b	(- (exp (* (+ a b) eps)) 1.0)
6.1b	(* (* 1/6 (pow a 3)) eps)
7.4b	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2)))
11.6b	(* (pow eps 2) (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2))))

rewrite595.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
11×	`add-cbrt-cube`
10×	`*-un-lft-identity` `prod-exp`
9×	`associate-l`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `associate-r`
4×	`unpow-prod-down` `cbrt-unprod` `unswap-sqr`
2×	`pow-to-exp` `flip3-+` `associate-r/` `pow-exp` `-commutative` `flip-+` `unpow2` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `pow-prod-down` `sum-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 75

Calls

4 calls:

21.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (* 1/6 (pow a 3)) eps)
46.0ms	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2)))
491.0ms	(* (pow eps 2) (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2))))

series371.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (* 1/6 (pow a 3)) eps)
98.0ms	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2)))
165.0ms	(* (pow eps 2) (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2))))

simplify1.7s

Counts

87 → 87

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	151	1527
1	420	1424
2	1685	1265
done	5000	1261

prune657.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 52.8b

localize83.0ms

Local error

Found 4 expressions with local error:

5.5b	(- (exp (* (+ a b) eps)) 1.0)
6.1b	(* (* 1/6 (pow a 3)) eps)
7.0b	(* (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2))) eps)
7.4b	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
11×	`add-sqr-sqrt` `add-cbrt-cube`
9×	`*-un-lft-identity`
8×	`pow1` `prod-exp` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `cbrt-unprod`
2×	`flip3-+` `pow-prod-down` `associate-l/` `-commutative` `flip-+`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `sum-log` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

21.0ms	(- (exp (* (+ a b) eps)) 1.0)
27.0ms	(* (* 1/6 (pow a 3)) eps)
135.0ms	(* (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2))) eps)
46.0ms	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (exp (* (+ a b) eps)) 1.0)
53.0ms	(* (* 1/6 (pow a 3)) eps)
108.0ms	(* (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2))) eps)
120.0ms	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2)))

simplify1.5s

Counts

76 → 76

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	130	1213
1	338	1139
2	1259	993
done	5000	989

prune508.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 52.8b

localize50.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* b (+ eps (* (* 1/2 (pow eps 2)) b))) (* 1/6 (* (pow eps 3) (pow b 3))))))
5.5b	(- (exp (* (+ a b) eps)) 1.0)
7.7b	(* (* 1/2 (pow eps 2)) b)
16.5b	(* (pow eps 3) (pow b 3))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
37×	`add-sqr-sqrt`
23×	`add-cbrt-cube`
20×	`prod-exp`
16×	`unswap-sqr`
15×	`associate-r`
14×	`unpow-prod-down` `cube-prod`
13×	`-un-lft-identity` `associate-l*`
11×	`add-cube-cbrt`
10×	`sqr-pow`
8×	`associate-/r/` `cbrt-unprod`
7×	`pow-to-exp` `pow-exp`
6×	`pow1` `add-log-exp`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`cube-mult` `unpow3` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 123

Calls

4 calls:

119.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* b (+ eps (* (* 1/2 (pow eps 2)) b))) (* 1/6 (* (pow eps 3) (pow b 3))))))
29.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (* 1/2 (pow eps 2)) b)
42.0ms	(* (pow eps 3) (pow b 3))

series2.6s

Counts

4 → 12

Calls

4 calls:

2.4s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* b (+ eps (* (* 1/2 (pow eps 2)) b))) (* 1/6 (* (pow eps 3) (pow b 3))))))
63.0ms	(- (exp (* (+ a b) eps)) 1.0)
28.0ms	(* (* 1/2 (pow eps 2)) b)
100.0ms	(* (pow eps 3) (pow b 3))

simplify2.8s

Counts

135 → 135

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	259	3228
1	790	3046
2	4048	2568
done	5001	2567

prune988.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

0% (3.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample15.3s

Algorithm

intervals

Results

4.5s	2536×	body	2560	valid
4.1s	1982×	body	10240	exit
3.9s	3476×	body	1280	valid
1.2s	1087×	body	640	valid
822.0ms	9989×	pre	80	true
125.0ms	349×	body	320	valid
43.0ms	431×	body	80	valid
28.0ms	128×	body	160	valid