Details

sample318.0ms

Algorithm

intervals

Results

35.0ms	173×	body	10240	exit
11.0ms	337×	body	80	nan
8.0ms	243×	body	80	valid
2.0ms	20×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	41	12
4	76	12
5	175	12
6	495	12
7	1569	12
done	5001	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize12.0ms

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))
3.9b	(- (exp (* 2.0 x)) 1.0)
4.1b	(- (exp x) 1.0)

rewrite50.0ms

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:

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

series206.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp x) 1.0)

simplify1.9s

Counts

167 → 167

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	232	2954
1	482	2688
2	1088	2471
3	3791	2398
done	5001	2396

prune394.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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:

6.0ms	(sqrt (+ (exp x) 1.0))
7.0ms	(+ (exp x) 1.0)
5.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series88.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (exp x) 1.0))
8.0ms	(+ (exp x) 1.0)
26.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.5s

Counts

100 → 100

Iterations

Useful iterations: 3 (553.0ms)

Iter	Nodes	Cost
0	166	1120
1	365	992
2	932	858
3	3385	795
done	5001	795

prune326.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp x))
0.1b	(* (cbrt (exp x)) (cbrt (exp x)))
3.9b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`cbrt-prod`
13×	`prod-diff`
11×	`pow1`
8×	`add-log-exp`
7×	`fma-neg` `pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`exp-sum` `difference-of-squares`
2×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 107

Calls

4 calls:

1.0ms	(cbrt (exp x))
9.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series218.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(cbrt (exp x))
95.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.8s

Counts

119 → 119

Iterations

Useful iterations: 3 (750.0ms)

Iter	Nodes	Cost
0	173	1335
1	356	1172
2	919	1012
3	3158	924
done	5000	924

prune427.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
27.5b	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

rewrite2.0ms

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:

0.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
1.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

series104.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
83.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

simplify759.0ms

Counts

31 → 31

Iterations

Useful iterations: done (757.0ms)

Iter	Nodes	Cost
0	63	451
1	139	414
2	419	377
3	1539	369
done	5000	365

prune74.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes31.0ms

Accuracy

99.1% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.8b

bsearch86.0ms

Steps

Iters	Range		Point
8	1.114667387229191e-09	5.139006765554396e-07	8.406069483656737e-09
7	-1.4191042175333267e-05	-5.670122129476186e-07	-1.2938199112682712e-05

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	70
1	37	70
done	37	70

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	6619×	body	10240	exit
383.0ms	12562×	body	80	nan
257.0ms	7441×	body	80	valid
58.0ms	695×	body	160	valid