Details

sample334.0ms

Algorithm

intervals

Results

72.0ms	224×	body	10240	exit
58.0ms	230×	body	80	valid
21.0ms	353×	body	80	nan
4.0ms	32×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
6.9b	(- (exp (* 2.0 x)) 1.0)
7.1b	(- (exp x) 1.0)

rewrite161.0ms

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:

31.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
64.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
32.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp x) 1.0)

series280.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
78.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
27.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (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

prune573.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
6.9b	(- (exp (* 2.0 x)) 1.0)
6.9b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite477.0ms

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))
155.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
27.0ms	(- (exp (* 2.0 x)) 1.0)
96.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series256.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
121.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
27.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.2s

Counts

293 → 293

Iterations

Useful iterations: done (2.2s)

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

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
7.1b	(- (exp x) 1.0)
7.1b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
22×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sqrt-pow1` `fma-neg` `sqrt-prod` `associate-/l*`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `exp-prod` `exp-to-pow` `frac-2neg` `pow1/2` `diff-log` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 94

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
16.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
12.0ms	(- (exp x) 1.0)
0.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

series350.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (exp (* 2.0 x)))
170.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
20.0ms	(- (exp x) 1.0)
136.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify2.0s

Counts

106 → 106

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	157	1895
1	305	1270
2	673	1154
3	2172	1108
done	5000	1092

prune368.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize7.0ms

Local error

Found 1 expressions with local error:

22.4b

(sqrt (fma x (fma 0.5 x 1.0) 2.0))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
1×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

2.0ms

(sqrt (fma x (fma 0.5 x 1.0) 2.0))

series122.0ms

Counts

1 → 3

Calls

1 calls:

122.0ms

(sqrt (fma x (fma 0.5 x 1.0) 2.0))

simplify2.6s

Counts

18 → 18

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	53	257
1	124	230
2	337	213
3	993	205
4	3021	200
done	5000	199

prune40.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes114.0ms

Accuracy

99.1% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 3.1b

bsearch3.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	43
1	26	43
done	26	43

end0.0ms

sample7.0s

Algorithm

intervals

Results

4.5s	6510×	body	10240	exit
995.0ms	12470×	body	80	nan
664.0ms	7358×	body	80	valid
166.0ms	772×	body	160	valid