Details

sample265.0ms

Algorithm

intervals

Results

122.0ms	211×	body	10240	exit
23.0ms	409×	body	80	nan
17.0ms	240×	body	80	valid
3.0ms	18×	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	185	12
6	764	12
done	5000	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize24.0ms

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))
3.9b	(- (exp (* 2.0 x)) 1.0)
4.0b	(- (exp x) 1.0)

rewrite172.0ms

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:

49.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
84.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
16.0ms	(- (exp (* 2.0 x)) 1.0)
15.0ms	(- (exp x) 1.0)

series275.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
77.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
33.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify1.2s

Counts

167 → 167

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	232	2954
1	503	2694
2	1532	2473
done	5000	2423

prune637.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(sqrt (+ (exp x) 1.0))
3.9b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`prod-diff`
10×	`add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `exp-sum` `difference-of-squares`
2×	`sub-neg` `flip3--` `flip3-+` `sqrt-div` `diff-log` `flip--` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `hypot-def` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

17.0ms	(+ (exp x) 1.0)
25.0ms	(sqrt (+ (exp x) 1.0))
29.0ms	(- (exp (* 2.0 x)) 1.0)
72.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series123.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (exp x) 1.0)
45.0ms	(sqrt (+ (exp x) 1.0))
38.0ms	(- (exp (* 2.0 x)) 1.0)
31.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.2s

Counts

100 → 100

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	166	1120
1	403	997
2	1525	861
done	5000	819

prune439.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (exp (* 2.0 x)) 1.0) 3)
0.3b	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
3.9b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
19×	`add-cube-cbrt`
16×	`cbrt-prod`
13×	`prod-diff`
10×	`unpow-prod-down` `cube-prod`
8×	`add-log-exp`
7×	`fma-neg` `difference-of-squares`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
4×	`cube-div` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`pow-unpow` `exp-sum`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 112

Calls

4 calls:

20.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
34.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
27.0ms	(- (exp (* 2.0 x)) 1.0)
79.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series164.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
35.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
38.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.0s

Counts

124 → 124

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	179	1792
1	492	1496
2	2341	1297
done	5000	1257

prune594.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
29.4b	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

1.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
4.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

series163.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
123.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

simplify2.3s

Counts

31 → 31

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	63	451
1	144	414
2	554	377
3	3737	369
done	5000	340

prune78.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

77.1% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.9b

bsearch54.0ms

Steps

Iters	Range		Point
6	-1.1215045282520511e-10	-1.846828719233542e-11	-1.1094191668549575e-10

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	36
1	28	36
done	28	36

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.6s	6723×	body	10240	exit
1.8s	12665×	body	80	nan
526.0ms	7393×	body	80	valid
103.0ms	732×	body	160	valid