Details

sample342.0ms

Algorithm

intervals

Results

43.0ms	214×	body	10240	exit
21.0ms	457×	body	80	nan
8.0ms	231×	body	80	valid
2.0ms	30×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	41	12
4	76	12
5	176	12
6	496	12
7	1977	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.3b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.9b	(- (exp x) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
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 → 155

Calls

4 calls:

16.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series202.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
25.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp x) 1.0)

simplify622.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (139.0ms)

Iter	Nodes	Cost
0	232	2954
1	492	2688
2	1505	2453
done	5001	2453

prune390.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
0.3b	(sqrt (+ (exp x) 1.0))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`times-frac`
21×	`difference-of-squares`
13×	`prod-diff`
9×	`exp-sum`
8×	`add-log-exp`
7×	`fma-neg` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `flip3--` `sqrt-prod` `flip--` `log1p-expm1-u`
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-+` `hypot-def` `div-inv` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

41.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
6.0ms	(sqrt (+ (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series238.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
33.0ms	(sqrt (+ (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify700.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (165.0ms)

Iter	Nodes	Cost
0	223	2351
1	521	2210
2	1838	1979
done	5001	1979

prune447.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
0.3b	(sqrt (exp x))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`times-frac`
21×	`difference-of-squares`
13×	`prod-diff`
9×	`exp-sum`
8×	`add-log-exp`
7×	`fma-neg` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `flip3--` `sqrt-pow1` `flip--` `log1p-expm1-u`
3×	`exp-prod` `sqrt-prod`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 124

Calls

4 calls:

39.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
1.0ms	(sqrt (exp x))
5.0ms	(- (exp (* 2.0 x)) 1.0)
32.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series225.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
12.0ms	(sqrt (exp x))
28.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify628.0ms

Counts

136 → 136

Iterations

Useful iterations: 2 (145.0ms)

Iter	Nodes	Cost
0	209	2258
1	476	2125
2	1517	1899
done	5000	1899

prune494.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (- (exp (+ x x)) (* 1.0 1.0)))
0.3b	(sqrt (exp x))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
96×	`cbrt-prod`
95×	`times-frac`
85×	`*-un-lft-identity`
59×	`add-cube-cbrt`
55×	`difference-of-squares`
30×	`unpow-prod-down` `cube-prod`
23×	`exp-sum`
19×	`associate-/l*`
13×	`prod-diff` `distribute-lft-out--`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-exp-log` `cube-mult` `unpow3` `sqr-pow`
5×	`pow1` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3--` `sqrt-pow1` `flip--` `log1p-expm1-u`
3×	`exp-prod` `sqrt-prod`
2×	`cube-div` `sub-neg` `cbrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 207

Calls

4 calls:

51.0ms	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (- (exp (+ x x)) (* 1.0 1.0)))
2.0ms	(sqrt (exp x))
5.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series228.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (- (exp (+ x x)) (* 1.0 1.0)))
17.0ms	(sqrt (exp x))
25.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify977.0ms

Counts

219 → 219

Iterations

Useful iterations: 2 (211.0ms)

Iter	Nodes	Cost
0	314	5353
1	600	4570
2	2107	4184
done	5000	4184

prune674.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes33.0ms

Accuracy

77.4% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.7b

bsearch37.0ms

Steps

Iters	Range		Point
5	-4.022447873684564e-15	-1.6668736937815573e-15	-2.5679454952614643e-15

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	57
1	40	57
done	40	57

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6643×	body	10240	exit
392.0ms	12688×	body	80	nan
258.0ms	7478×	body	80	valid
54.0ms	664×	body	160	valid