Details

sample3.1s

Algorithm

intervals

Results

1.1s	326×	body	80	nan
964.0ms	211×	body	10240	exit
58.0ms	244×	body	80	valid
3.0ms	15×	body	160	valid

simplify22.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5006
8	3863
7	1042
6	332
5	133
4	65
3	37
2	27
1	19
0	10

prune87.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.8b

localize141.0ms

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))
3.4b	(- (exp (* 2.0 x)) 1.0)
3.4b	(- (exp x) 1.0)

rewrite674.0ms

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:

43.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
296.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
36.0ms	(- (exp (* 2.0 x)) 1.0)
203.0ms	(- (exp x) 1.0)

series1.6s

Counts

4 → 12

Calls

4 calls:

355.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
469.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
128.0ms	(- (exp (* 2.0 x)) 1.0)
615.0ms	(- (exp x) 1.0)

simplify11.9s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
3	3152
2	993
1	396
0	189

prune2.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
0.0b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
3.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.4b	(- (exp x) 1.0)

rewrite703.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
14×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`flip3--` `associate-r` `flip--`
8×	`frac-times` `add-cube-cbrt` `associate-/l/` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow1` `flip3-+` `flip-+`
5×	`times-frac` `associate-l` `associate-/r*`
4×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

204.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
374.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
80.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
23.0ms	(- (exp x) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

741.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
348.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
209.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
84.0ms	(- (exp x) 1.0)

simplify7.8s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	1983
1	499
0	180

prune2.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize729.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.4b	(- (exp x) 1.0)
3.4b	(- (exp x) 1.0)
3.4b	(- (exp x) 1.0)

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-log-exp`
7×	`difference-of-squares`
6×	`sqrt-prod`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--`

Counts

4 → 60

Calls

4 calls:

69.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
51.0ms	(- (exp x) 1.0)
40.0ms	(- (exp x) 1.0)
36.0ms	(- (exp x) 1.0)

series426.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
31.0ms	(- (exp x) 1.0)
52.0ms	(- (exp x) 1.0)
61.0ms	(- (exp x) 1.0)

simplify7.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
4	2291
3	945
2	390
1	162
0	76

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ (* 0.5 x) 1.0))
25.5b	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 37

Calls

2 calls:

51.0ms	(* x (+ (* 0.5 x) 1.0))
114.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

series769.0ms

Counts

2 → 6

Calls

2 calls:

368.0ms	(* x (+ (* 0.5 x) 1.0))
397.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

simplify4.7s

Counts

43 → 43

Iterations

Iter	Nodes
done	5003
2	1128
1	298
0	106

prune584.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes146.0ms

Accuracy

80% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.6b

bsearch324.0ms

Steps

Iters	Range		Point
6	-0.00015200343398984049	-1.963203309137196e-05	-1.9984726555003664e-05

simplify62.0ms

Iterations

Iter	Nodes
done	37
1	37
0	30

end0.0ms

sample51.8s

Algorithm

intervals

Results

37.0s	6584×	body	10240	exit
6.8s	7320×	body	80	valid
5.5s	12492×	body	80	nan
1.3s	798×	body	160	valid