Details

sample313.0ms

Algorithm

intervals

Results

166.0ms	204×	body	10240	exit
30.0ms	388×	body	80	nan
21.0ms	242×	body	80	valid
4.0ms	20×	body	160	valid

simplify2.9s

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: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp x) 1.0)

rewrite183.0ms

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:

72.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
42.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
22.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

series333.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
141.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
40.0ms	(- (exp (* 2.0 x)) 1.0)
40.0ms	(- (exp x) 1.0)

simplify2.7s

Counts

167 → 167

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	232	2954
1	482	2688
2	1074	2471
3	3564	2362
done	5000	2357

prune610.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite517.0ms

Algorithm

rewrite-expression-head

Rules

253×	`times-frac`
217×	`*-un-lft-identity`
187×	`add-sqr-sqrt`
135×	`sqrt-prod`
101×	`add-cube-cbrt`
79×	`difference-of-squares`
31×	`distribute-lft-out`
28×	`exp-sum`
27×	`distribute-lft-out--`
13×	`prod-diff` `associate-/r/`
8×	`add-log-exp`
7×	`fma-neg` `div-inv`
6×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`rem-sqrt-square` `flip3--` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 250

Calls

4 calls:

220.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
152.0ms	(sqrt (/ (- (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)
90.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series344.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
191.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
48.0ms	(- (exp (* 2.0 x)) 1.0)
42.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.8s

Counts

262 → 262

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	549	8003
1	1156	7635
2	3382	7237
done	5001	7083

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (* (- (exp (+ x x)) (* 1.0 1.0)) (/ 1 (+ (exp x) 1.0)))))
0.3b	(* (- (exp (+ x x)) (* 1.0 1.0)) (/ 1 (+ (exp x) 1.0)))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite585.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
24×	`add-cube-cbrt`
19×	`times-frac`
18×	`associate-r`
15×	`sqrt-prod`
13×	`add-exp-log` `prod-diff`
9×	`add-cbrt-cube`
8×	`associate-/r/` `add-log-exp`
7×	`pow1` `fma-neg`
6×	`flip3--` `flip--` `difference-of-squares`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `exp-sum` `associate-*l/` `prod-exp` `log1p-expm1-u`
3×	`distribute-lft-out` `unswap-sqr`
2×	`sub-neg` `diff-log` `associate-*r/` `div-exp` `un-div-inv` `cbrt-unprod` `div-inv` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `1-exp` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 129

Calls

4 calls:

199.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (* (- (exp (+ x x)) (* 1.0 1.0)) (/ 1 (+ (exp x) 1.0)))))
271.0ms	(* (- (exp (+ x x)) (* 1.0 1.0)) (/ 1 (+ (exp x) 1.0)))
21.0ms	(- (exp (* 2.0 x)) 1.0)
85.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series354.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (* (- (exp (+ x x)) (* 1.0 1.0)) (/ 1 (+ (exp x) 1.0)))))
72.0ms	(* (- (exp (+ x x)) (* 1.0 1.0)) (/ 1 (+ (exp x) 1.0)))
51.0ms	(- (exp (* 2.0 x)) 1.0)
36.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.9s

Counts

141 → 141

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	270	2759
1	628	2410
2	1823	2094
done	5001	1714

prune646.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp (+ x x)) (* 1.0 1.0))
4.5b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `prod-diff`
22×	`add-cube-cbrt`
14×	`fma-neg`
12×	`add-log-exp`
6×	`exp-sum` `difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`distribute-lft-out--`

Counts

4 → 104

Calls

4 calls:

27.0ms	(- (exp (* 2.0 x)) 1.0)
36.0ms	(- (exp (* 2.0 x)) 1.0)
117.0ms	(- (exp (+ x x)) (* 1.0 1.0))
87.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series128.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (exp (* 2.0 x)) 1.0)
37.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp (+ x x)) (* 1.0 1.0))
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.6s

Counts

116 → 116

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	114	1602
1	251	1402
2	593	1168
3	2154	982
done	5002	954

prune715.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes31.0ms

Accuracy

74.5% (0.7b remaining)

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

bsearch26.0ms

Steps

Iters	Range		Point
3	-5.2146422133700853e-08	-4.424072945734607e-08	-4.9675893172339993e-08

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	48
1	40	48
done	40	48

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.8s	6588×	body	10240	exit
1.6s	12585×	body	80	nan
739.0ms	7352×	body	80	valid
163.0ms	757×	body	160	valid