Details

sample234.0ms

Algorithm

intervals

Results

66.0ms	358×	body	80	nan
18.0ms	157×	body	80	valid
15.0ms	32×	body	1280	valid
14.0ms	34×	body	640	valid
9.0ms	21×	body	640	nan
8.0ms	18×	body	1280	nan
5.0ms	20×	body	320	valid
3.0ms	11×	body	320	nan
2.0ms	13×	body	160	valid
1.0ms	6×	body	160	nan

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3799
6	1449
5	797
4	423
3	199
2	93
1	39
0	18

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
13.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

59.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
16.0ms	(* (sqrt 2.0) t)
46.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
72.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.7s

Counts

4 → 12

Calls

4 calls:

587.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
67.0ms	(* (sqrt 2.0) t)
332.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.3s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	2619
1	455
0	167

prune686.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.2b

localize53.0ms

Local error

Found 4 expressions with local error:

4.4b	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
6.4b	(/ (* l l) x)
8.6b	(/ x (* t t))
25.2b	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

rewrite475.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r` `flip3-+` `sqrt-div` `div-exp` `frac-add` `associate-r/` `flip-+` `associate-/l*`
3×	`sqrt-prod`
2×	`associate-+l+` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 74

Calls

4 calls:

37.0ms	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
386.0ms	(/ (* l l) x)
6.0ms	(/ x (* t t))
44.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

series559.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
20.0ms	(/ (* l l) x)
37.0ms	(/ x (* t t))
405.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

simplify1.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	3089
1	509
0	168

prune584.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.3b

localize79.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
4.8b	(+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t))))
6.4b	(/ (* 2.0 (* l l)) x)
25.2b	(sqrt (+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t)))))

rewrite381.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`add-log-exp`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`prod-exp` `cbrt-unprod`
3×	`cbrt-undiv` `associate-/r` `sum-log` `times-frac` `div-exp` `associate-r*`
2×	`flip3-+` `sqrt-div` `flip-+` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `associate-+r+` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 73

Calls

4 calls:

13.0ms	(* (sqrt 2.0) t)
121.0ms	(+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t))))
16.0ms	(/ (* 2.0 (* l l)) x)
229.0ms	(sqrt (+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t)))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sqrt 2.0) t)
116.0ms	(+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t))))
34.0ms	(/ (* 2.0 (* l l)) x)
344.0ms	(sqrt (+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t)))))

simplify1.1s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	2667
1	455
0	160

prune682.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
4.8b	(+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t))))
6.4b	(/ (* 2.0 (* l l)) x)
25.2b	(sqrt (+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t)))))

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
12×	`sqrt-prod`
11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l` `add-log-exp`
6×	`prod-exp` `cbrt-unprod`
3×	`cbrt-undiv` `associate-/r*` `sum-log` `times-frac` `div-exp` `pow-prod-down`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `associate-+r+` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `-commutative` `div-inv` `associate-/l`

Counts

4 → 75

Calls

4 calls:

25.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
116.0ms	(+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t))))
22.0ms	(/ (* 2.0 (* l l)) x)
205.0ms	(sqrt (+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t)))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
108.0ms	(+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t))))
40.0ms	(/ (* 2.0 (* l l)) x)
349.0ms	(sqrt (+ (* 2.0 (* t t)) (+ (/ (* 2.0 (* l l)) x) (/ (* t 4.0) (/ x t)))))

simplify1.2s

Counts

87 → 87

Iterations

Iter	Nodes
done	5002
2	2679
1	482
0	168

prune555.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.2b

regimes965.0ms

Accuracy

77.4% (5.5b remaining)

Error of 9.4b against oracle of 3.9b and baseline of 28.0b

bsearch909.0ms

Steps

Iters	Range		Point
9	8.029604051112713e+47	4.771574953324125e+55	4.214549585149478e+55
10	3.1913228427846884e-157	3.080469255526081e-145	3.2479806443803153e-157
10	7.396249846299801e-250	6.414192999540213e-240	1.8396588411989053e-241
9	-2.2008797770019196e+94	-2.884593901536308e+87	-1.940005881918409e+94

simplify13.0ms

Iterations

Iter	Nodes
done	79
3	79
2	76
1	73
0	55

end0.0ms

sample6.3s

Algorithm

intervals

Results

1.7s	9922×	body	80	nan
1.2s	5112×	body	80	valid
1.0s	819×	body	1280	valid
691.0ms	1060×	body	640	valid
292.0ms	625×	body	640	nan
279.0ms	599×	body	1280	nan
216.0ms	644×	body	320	valid
118.0ms	365×	body	160	valid
97.0ms	335×	body	320	nan
37.0ms	191×	body	160	nan