Details

sample1.0s

Algorithm

intervals

Results

191.0ms	262×	body	10240	exit
31.0ms	440×	body	80	nan
19.0ms	237×	body	80	valid
4.0ms	22×	body	160	valid

simplify3.4s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.8b	(- (exp x) 1.0)

rewrite185.0ms

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:

39.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
85.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
28.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

series269.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
74.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
40.0ms	(- (exp (* 2.0 x)) 1.0)
28.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

135 → 135

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	904	2169
3	2293	2156
done	5001	2154

prune497.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
0.3b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite419.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
230×	`*-un-lft-identity`
188×	`add-sqr-sqrt`
102×	`add-cube-cbrt`
88×	`difference-of-squares`
36×	`distribute-lft-out`
30×	`exp-sum` `associate-/r*`
28×	`distribute-lft-out--`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
8×	`div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 253

Calls

4 calls:

167.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
147.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
13.0ms	(- (exp (* 2.0 x)) 1.0)
77.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series309.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))))
83.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
43.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.9s

Counts

265 → 265

Iterations

Useful iterations: 2 (844.0ms)

Iter	Nodes	Cost
0	362	8009
1	1020	7743
2	3660	7375
done	5001	7375

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
0.3b	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
4.6b	(- (exp (+ x x)) (* 1.0 1.0))
4.6b	(- (exp (* 2.0 x)) 1.0)

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
20×	`times-frac`
18×	`add-cube-cbrt`
16×	`cbrt-prod`
15×	`difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `exp-sum` `add-cbrt-cube` `distribute-lft-out`
5×	`unpow-prod-down` `cube-prod` `associate-/l*`
4×	`pow1` `flip3--` `associate-/r*` `flip--`
3×	`distribute-lft-out--`
2×	`cube-div` `sub-neg` `cbrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `frac-2neg` `flip3-+` `pow1/3` `unpow3` `div-sub` `div-exp` `clear-num` `rem-cbrt-cube` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 101

Calls

4 calls:

165.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
26.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
79.0ms	(- (exp (+ x x)) (* 1.0 1.0))
27.0ms	(- (exp (* 2.0 x)) 1.0)

series190.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
42.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
21.0ms	(- (exp (+ x x)) (* 1.0 1.0))
48.0ms	(- (exp (* 2.0 x)) 1.0)

simplify3.1s

Counts

113 → 113

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	189	1911
1	451	1715
2	1292	1573
3	4743	1562
done	5001	1562

prune556.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (sqrt 2.0) (* 0.5 (/ x (sqrt 2.0))))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r` `add-log-exp`
4×	`prod-exp`
3×	`cbrt-undiv` `div-inv`
2×	`distribute-rgt-in` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `associate-*r/` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 217

Calls

4 calls:

17.0ms	(+ (sqrt 2.0) (* 0.5 (/ x (sqrt 2.0))))
93.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
16.0ms	(/ (pow x 2) (sqrt 2.0))
8.0ms	(/ x (sqrt 2.0))

series426.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(+ (sqrt 2.0) (* 0.5 (/ x (sqrt 2.0))))
103.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
77.0ms	(/ (pow x 2) (sqrt 2.0))
86.0ms	(/ x (sqrt 2.0))

simplify1.5s

Counts

229 → 229

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	270	3092
1	615	2863
2	1914	2584
done	5000	2578

prune687.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes31.0ms

Accuracy

99.3% (0.0b remaining)

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

bsearch118.0ms

Steps

Iters	Range		Point
6	1.1811762867881907e-17	7.736728092336823e-17	5.535044263275192e-17
5	-4.7391386504541836e-17	-1.2828996200046889e-17	-4.0137027497971385e-17

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	46	89
1	53	89
done	53	89

end0.0ms

sample7.7s

Algorithm

intervals

Results

5.0s	6712×	body	10240	exit
1.3s	12336×	body	80	nan
504.0ms	7363×	body	80	valid
109.0ms	764×	body	160	valid