Details

sample346.0ms

Algorithm

intervals

Results

182.0ms	1573×	body	80	nan
68.0ms	490×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
5	1717
4	477
3	179
2	71
1	33
0	17

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.8b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.4b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite453.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`log-prod` `exp-sum` `add-exp-log`
10×	`pow1` `add-log-exp`
9×	`prod-diff`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `associate--l+` `associate-r/` `div-inv` `flip--` `associate-/l` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

44.0ms	(* (- t 1.0) (log a))
17.0ms	(* y (log z))
150.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
237.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series478.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (- t 1.0) (log a))
53.0ms	(* y (log z))
131.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
221.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify2.1s

Counts

128 → 128

Iterations

Iter	Nodes
done	5002
2	1896
1	626
0	281

prune842.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.8b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y (log z))
0.8b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
0.8b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.4b	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`exp-sum` `add-cube-cbrt`
18×	`prod-diff`
16×	`add-log-exp`
15×	`add-cbrt-cube` `add-exp-log`
10×	`exp-prod`
7×	`pow1`
6×	`log-prod` `exp-diff` `rem-exp-log`
4×	`expm1-log1p-u` `sqrt-div` `diff-log` `associate-r` `prod-exp` `associate-*r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `cbrt-undiv` `associate-/r` `distribute-lft-in` `times-frac` `div-exp` `associate-l*` `associate-/l/`
2×	`sum-log` `sub-neg` `associate--l+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

9.0ms	(* y (log z))
79.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
79.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.5s	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

series647.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* y (log z))
163.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
169.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
267.0ms	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

simplify1.8s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1678
1	539
0	233

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.8b

localize98.0ms

Local error

Found 4 expressions with local error:

0.8b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.4b	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
1.4b	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
1.4b	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

rewrite4.5s

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`exp-diff`
12×	`sqrt-div` `exp-sum` `associate-*r/`
10×	`add-log-exp`
9×	`cbrt-undiv` `associate-/r*` `times-frac` `div-exp` `prod-diff` `prod-exp` `cbrt-unprod` `associate-/l/`
5×	`exp-prod`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `div-inv` `associate-/l` `rem-exp-log`
2×	`diff-log`
1×	`sum-log` `sub-neg` `associate--l+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

126.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.6s	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
1.3s	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
1.5s	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

series836.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
246.0ms	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
219.0ms	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
227.0ms	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

simplify1.7s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1445
1	464
0	191

prune1.6s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.7b

localize141.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
1.4b	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
1.4b	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
1.4b	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

rewrite6.3s

Algorithm

rewrite-expression-head

Rules

40×	`add-cbrt-cube` `add-exp-log`
16×	`exp-diff` `sqrt-div` `associate-*r/`
12×	`add-sqr-sqrt` `cbrt-undiv` `associate-/r` `-un-lft-identity` `times-frac` `div-exp` `prod-exp` `add-cube-cbrt` `cbrt-unprod` `associate-/l/`
4×	`expm1-log1p-u` `frac-times` `pow1` `clear-num` `frac-2neg` `associate-l/` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`

Counts

4 → 116

Calls

4 calls:

1.6s	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
1.5s	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
1.5s	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
1.6s	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

series803.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
185.0ms	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
193.0ms	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
223.0ms	(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

simplify1.6s

Counts

128 → 128

Iterations

Iter	Nodes
done	5009
2	1151
1	328
0	125

prune1.4s

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 0.7b

regimes2.6s

Accuracy

38% (0.8b remaining)

Error of 1.5b against oracle of 0.7b and baseline of 2.0b

bsearch485.0ms

Steps

Iters	Range		Point
6	4.501248878042361e+138	2.886908496868437e+139	4.564051854504764e+138
8	-1.5824693290191063e-201	-2.093601214607291e-205	-1.874142655497601e-203

simplify21.0ms

Iterations

Iter	Nodes
done	51
2	51
1	49
0	41

end0.0ms

sample11.2s

Algorithm

intervals

Results

6.7s	46213×	body	80	nan
2.1s	15277×	body	80	valid