Details

sample258.0ms

Algorithm

intervals

Results

138.0ms	204×	body	10240	exit
23.0ms	388×	body	80	nan
20.0ms	242×	body	80	valid
3.0ms	20×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	175	12
6	479	12
7	1665	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp x) 1.0)

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

68.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
56.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
25.0ms	(- (exp (* 2.0 x)) 1.0)
15.0ms	(- (exp x) 1.0)

series273.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
133.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
40.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

simplify1.8s

Counts

135 → 135

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	903	2169
3	2294	2156
done	5001	2154

prune497.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
0.2b	(sqrt (+ (exp x) 1.0))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
25×	`times-frac`
21×	`difference-of-squares`
17×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`exp-sum` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l`
4×	`flip3--` `sqrt-prod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

125.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
17.0ms	(sqrt (+ (exp x) 1.0))
13.0ms	(- (exp (* 2.0 x)) 1.0)
87.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series406.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
39.0ms	(sqrt (+ (exp x) 1.0))
28.0ms	(- (exp (* 2.0 x)) 1.0)
33.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.4s

Counts

108 → 108

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	184	1906
1	423	1852
2	1179	1709
3	4098	1694
done	5000	1694

prune534.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ (exp x) 1.0))
0.3b	(* (- (exp (* 2.0 x)) 1.0) (/ 1 (- (exp (+ x x)) (* 1.0 1.0))))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`associate-r`
17×	`times-frac`
15×	`add-cube-cbrt`
13×	`add-exp-log`
10×	`difference-of-squares`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`flip3--` `associate-l` `flip--`
4×	`exp-sum` `prod-exp` `sqrt-prod`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `flip3-+` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 94

Calls

4 calls:

14.0ms	(sqrt (+ (exp x) 1.0))
238.0ms	(* (- (exp (* 2.0 x)) 1.0) (/ 1 (- (exp (+ x x)) (* 1.0 1.0))))
27.0ms	(- (exp (* 2.0 x)) 1.0)
87.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series408.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (+ (exp x) 1.0))
273.0ms	(* (- (exp (* 2.0 x)) 1.0) (/ 1 (- (exp (+ x x)) (* 1.0 1.0))))
44.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.3s

Counts

106 → 106

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	199	1711
1	451	1545
2	1341	1362
done	5000	1347

prune594.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))
4.5b	(- (exp (+ x x)) (* 1.0 1.0))
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

29.0ms	(- (exp (* 2.0 x)) 1.0)
79.0ms	(- (exp (+ x x)) (* 1.0 1.0))
78.0ms	(- (exp (+ x x)) (* 1.0 1.0))
96.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series126.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (exp (* 2.0 x)) 1.0)
33.0ms	(- (exp (+ x x)) (* 1.0 1.0))
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.7s

Counts

68 → 68

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	78	840
1	171	808
2	433	696
3	1150	682
4	3602	674
done	5001	674

prune838.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes61.0ms

Accuracy

74.3% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch67.0ms

Steps

Iters	Range		Point
6	-4.509995249856902e-05	-5.9023817294571485e-06	-1.343314734760439e-05

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	38
1	37	38
done	37	38

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.0s	6588×	body	10240	exit
1.5s	12585×	body	80	nan
1.1s	7352×	body	80	valid
174.0ms	757×	body	160	valid