Details

sample300.0ms

Algorithm

intervals

Results

95.0ms	181×	body	10240	exit
73.0ms	232×	body	80	valid
31.0ms	348×	body	80	nan
5.0ms	25×	body	160	valid

simplify960.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	179	12
6	752	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize20.0ms

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))
5.4b	(- (exp (* 2.0 x)) 1.0)
5.6b	(- (exp x) 1.0)

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
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 → 123

Calls

4 calls:

55.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
14.0ms	(- (exp (* 2.0 x)) 1.0)
13.0ms	(- (exp x) 1.0)

series314.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
88.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
55.0ms	(- (exp (* 2.0 x)) 1.0)
43.0ms	(- (exp x) 1.0)

simplify864.0ms

Counts

135 → 135

Iterations

Useful iterations: done (855.0ms)

Iter	Nodes	Cost
0	189	2376
1	396	2279
2	1220	2169
done	5000	2156

prune488.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp x) 1.0))
0.0b	(+ (exp x) 1.0)
5.4b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
3×	`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` `exp-sum` `sum-log` `distribute-lft-out--`

Counts

4 → 56

Calls

4 calls:

25.0ms	(sqrt (+ (exp x) 1.0))
10.0ms	(+ (exp x) 1.0)
16.0ms	(- (exp (* 2.0 x)) 1.0)
85.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series148.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (+ (exp x) 1.0))
18.0ms	(+ (exp x) 1.0)
44.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.3s

Counts

68 → 68

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	127	697
1	292	657
2	936	598
3	4004	585
done	5002	585

prune347.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.1b	(* (sqrt (sqrt (+ (exp x) 1.0))) (sqrt (sqrt (+ (exp x) 1.0))))
5.4b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
49×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
32×	`sqrt-pow1`
27×	`pow1`
24×	`sqrt-div`
18×	`swap-sqr`
16×	`add-cube-cbrt` `pow1/2`
10×	`associate-r` `associate-l` `add-log-exp`
9×	`pow-prod-up` `unswap-sqr`
7×	`flip3-+` `flip-+` `distribute-lft-out`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
3×	`difference-of-squares`
2×	`sub-neg` `flip3--` `diff-log` `associate-r/` `associate-l/` `flip--`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `exp-sum` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 128

Calls

4 calls:

12.0ms	(+ (exp x) 1.0)
106.0ms	(* (sqrt (sqrt (+ (exp x) 1.0))) (sqrt (sqrt (+ (exp x) 1.0))))
24.0ms	(- (exp (* 2.0 x)) 1.0)
93.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series126.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (exp x) 1.0)
50.0ms	(* (sqrt (sqrt (+ (exp x) 1.0))) (sqrt (sqrt (+ (exp x) 1.0))))
30.0ms	(- (exp (* 2.0 x)) 1.0)
31.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.5s

Counts

140 → 140

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	196	2210
1	433	1393
2	1744	1279
done	5000	1267

prune568.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (sqrt 2.0) (* 0.5 (/ x (sqrt 2.0))))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.2b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r` `add-log-exp`
4×	`prod-exp`
3×	`cbrt-undiv` `div-inv`
2×	`distribute-rgt-in` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `associate-*r/` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 217

Calls

4 calls:

17.0ms	(+ (sqrt 2.0) (* 0.5 (/ x (sqrt 2.0))))
122.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
21.0ms	(/ (pow x 2) (sqrt 2.0))
12.0ms	(/ x (sqrt 2.0))

series459.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(+ (sqrt 2.0) (* 0.5 (/ x (sqrt 2.0))))
98.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
102.0ms	(/ (pow x 2) (sqrt 2.0))
65.0ms	(/ x (sqrt 2.0))

simplify2.0s

Counts

229 → 229

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	270	3092
1	653	2863
2	3325	2584
done	5001	2578

prune782.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

73.9% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 3.0b

bsearch81.0ms

Steps

Iters	Range		Point
6	-8.379592348074455e-16	-5.485042039459814e-17	-1.6356558846354128e-16

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.8s	6467×	body	10240	exit
959.0ms	12626×	body	80	nan
531.0ms	7380×	body	80	valid
198.0ms	733×	body	160	valid