Details

sample314.0ms

Algorithm

intervals

Results

121.0ms	208×	body	10240	exit
27.0ms	451×	body	80	nan
13.0ms	232×	body	80	valid
4.0ms	26×	body	160	valid

simplify2.8s

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	181	12
6	489	12
7	1695	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.4b	(- (exp (* 2.0 x)) 1.0)
5.6b	(- (exp x) 1.0)

rewrite199.0ms

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:

50.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
94.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
32.0ms	(- (exp (* 2.0 x)) 1.0)
15.0ms	(- (exp x) 1.0)

series278.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
102.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
44.0ms	(- (exp (* 2.0 x)) 1.0)
27.0ms	(- (exp x) 1.0)

simplify2.4s

Counts

167 → 167

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	232	2954
1	482	2688
2	1071	2471
3	3554	2362
done	5000	2356

prune608.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
5.4b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite494.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
239×	`*-un-lft-identity`
197×	`add-sqr-sqrt`
111×	`add-cube-cbrt`
88×	`difference-of-squares`
36×	`distribute-lft-out`
32×	`exp-sum`
30×	`associate-/r*`
28×	`distribute-lft-out--`
15×	`associate-/r/`
13×	`prod-diff`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
8×	`div-inv` `add-log-exp`
7×	`flip3-+` `fma-neg` `flip-+`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 281

Calls

4 calls:

179.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
136.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
30.0ms	(- (exp (* 2.0 x)) 1.0)
125.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series279.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
136.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
44.0ms	(- (exp (* 2.0 x)) 1.0)
34.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.1s

Counts

293 → 293

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	399	8480
1	1100	8124
2	3908	7678
done	5001	7638

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.1b	(/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
5.4b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite433.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
145×	`*-un-lft-identity`
115×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
45×	`difference-of-squares`
30×	`associate-/r*`
26×	`distribute-lft-out`
24×	`exp-sum`
13×	`prod-diff`
11×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
8×	`associate-/l*` `add-log-exp`
7×	`fma-neg`
6×	`div-inv`
5×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/l/`
1×	`distribute-lft-out--` `expm1-udef`

Counts

4 → 225

Calls

4 calls:

184.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
128.0ms	(/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
24.0ms	(- (exp (* 2.0 x)) 1.0)
86.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series447.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
336.0ms	(/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
34.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.2s

Counts

237 → 237

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	363	6742
1	837	6043
2	3068	5652
done	5002	5612

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
5.4b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp (+ x x)) (* 1.0 1.0))
5.6b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`prod-diff`
10×	`add-log-exp`
8×	`fma-neg`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`sub-neg` `unpow-prod-down` `pow-unpow` `exp-prod` `flip3--` `diff-log` `cube-prod` `exp-sum` `flip--` `difference-of-squares`
1×	`cube-mult` `pow-to-exp` `distribute-rgt-out--` `unpow3` `pow-exp` `distribute-lft-out--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 97

Calls

4 calls:

5.0ms	(pow (exp x) 3)
15.0ms	(- (exp (* 2.0 x)) 1.0)
110.0ms	(- (exp (+ x x)) (* 1.0 1.0))
17.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series133.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (exp x) 3)
30.0ms	(- (exp (* 2.0 x)) 1.0)
31.0ms	(- (exp (+ x x)) (* 1.0 1.0))
39.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify1.5s

Counts

109 → 109

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	189	1248
1	430	1051
2	1325	898
done	5001	864

prune751.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes55.0ms

Accuracy

72.3% (0.8b remaining)

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

bsearch72.0ms

Steps

Iters	Range		Point
8	-0.0004704452395047321	-1.5977204101010247e-06	-1.2886839166735242e-05

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	26	35
done	26	35

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.8s	6651×	body	10240	exit
1.0s	12526×	body	80	nan
659.0ms	7404×	body	80	valid
113.0ms	747×	body	160	valid