Details

sample446.0ms

Algorithm

intervals

Results

179.0ms	203×	body	10240	exit
28.0ms	384×	body	80	nan
17.0ms	245×	body	80	valid
2.0ms	16×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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: 2.4b

localize13.0ms

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))
3.0b	(- (exp (* 2.0 x)) 1.0)
3.1b	(- (exp x) 1.0)

rewrite154.0ms

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)))
62.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
15.0ms	(- (exp (* 2.0 x)) 1.0)
16.0ms	(- (exp x) 1.0)

series291.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
95.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
40.0ms	(- (exp (* 2.0 x)) 1.0)
41.0ms	(- (exp x) 1.0)

simplify2.5s

Counts

167 → 167

Iterations

Useful iterations: done (2.5s)

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

prune692.0ms

Pruning

4 alts after pruning (4 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))
3.0b	(- (exp (* 2.0 x)) 1.0)
3.0b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite150.0ms

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:

11.0ms	(+ (exp x) 1.0)
15.0ms	(sqrt (+ (exp x) 1.0))
18.0ms	(- (exp (* 2.0 x)) 1.0)
101.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series139.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (exp x) 1.0)
43.0ms	(sqrt (+ (exp x) 1.0))
44.0ms	(- (exp (* 2.0 x)) 1.0)
36.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.8s

Counts

100 → 100

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	166	1120
1	362	992
2	908	860
3	3266	761
done	5000	757

prune525.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp x))
0.2b	(sqrt (exp x))
3.0b	(- (exp (* 2.0 x)) 1.0)
3.0b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`prod-diff`
8×	`sqrt-pow1` `add-log-exp`
7×	`fma-neg`
6×	`pow1` `exp-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-sum` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `pow1/2` `diff-log` `flip--`
1×	`distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

3.0ms	(sqrt (exp x))
3.0ms	(sqrt (exp x))
17.0ms	(- (exp (* 2.0 x)) 1.0)
78.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series99.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (exp x))
13.0ms	(sqrt (exp x))
30.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.5s

Counts

100 → 100

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	141	1009
1	288	881
2	647	762
3	2356	669
done	5000	651

prune565.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (+ (exp x) 1.0))
0.0b	(expm1 (log1p (+ (exp x) 1.0)))
3.0b	(- (exp (* 2.0 x)) 1.0)
3.0b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `prod-diff`
8×	`add-log-exp`
7×	`fma-neg`
5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-sum` `difference-of-squares`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `distribute-lft-out--` `expm1-udef`

Counts

4 → 74

Calls

4 calls:

0.0ms	(log1p (+ (exp x) 1.0))
0.0ms	(expm1 (log1p (+ (exp x) 1.0)))
15.0ms	(- (exp (* 2.0 x)) 1.0)
86.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series336.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(log1p (+ (exp x) 1.0))
170.0ms	(expm1 (log1p (+ (exp x) 1.0)))
45.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify3.1s

Counts

86 → 86

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	157	1030
1	333	900
2	808	765
3	2727	671
done	5000	653

prune530.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes42.0ms

Accuracy

73.9% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.7b

bsearch86.0ms

Steps

Iters	Range		Point
8	-4.403108084983288e-07	-5.598498926449877e-10	-3.6396238490178844e-07

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.8s	6421×	body	10240	exit
1.3s	12501×	body	80	nan
964.0ms	7417×	body	80	valid
145.0ms	708×	body	160	valid