Details

sample227.0ms

Algorithm

intervals

Results

50.0ms	27×	body	640	valid
31.0ms	311×	body	80	nan
17.0ms	161×	body	80	valid
17.0ms	30×	body	1280	valid
10.0ms	20×	body	1280	nan
7.0ms	19×	body	640	nan
5.0ms	19×	body	320	valid
5.0ms	19×	body	160	valid
4.0ms	8×	body	320	nan
1.0ms	5×	body	160	nan

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	2276
6	1138
5	616
4	361
3	179
2	90
1	39
0	18

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize64.0ms

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))))
0.4b	(* (sqrt 2.0) t)
16.0b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite143.0ms

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:

57.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
8.0ms	(* (sqrt 2.0) t)
35.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
40.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.7s

Counts

4 → 12

Calls

4 calls:

554.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
78.0ms	(* (sqrt 2.0) t)
325.0ms	(- (* (/ (+ 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)))

simplify1.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1572
1	445
0	167

prune550.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 7.0b

localize34.0ms

Local error

Found 4 expressions with local error:

3.8b	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
6.7b	(/ (* l l) x)
8.1b	(/ (* t t) x)
29.1b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

33.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
8.0ms	(/ (* l l) x)
8.0ms	(/ (* t t) x)
33.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
31.0ms	(/ (* l l) x)
35.0ms	(/ (* t t) x)
272.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
done	5012
2	2531
1	547
0	167

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.7b

localize72.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
3.8b	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
8.1b	(/ (* t t) x)
29.1b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

46.0ms	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
27.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
10.0ms	(/ (* t t) x)
36.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
110.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
39.0ms	(/ (* t t) x)
253.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	2238
1	482
0	151

prune567.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.7b

localize259.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (* (* (cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))) (cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))) (cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))))
29.9b	(cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
29.9b	(cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
29.9b	(cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

336×	`associate-*r/`
312×	`cbrt-div`
176×	`frac-times`
156×	`flip3-+` `frac-add` `flip-+`
124×	`sqrt-div`
44×	`associate-*l/`
24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 193

Calls

4 calls:

280.0ms	(sqrt (* (* (cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))) (cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))) (cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))))
15.0ms	(cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
15.0ms	(cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
18.0ms	(cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

256.0ms	(sqrt (* (* (cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))) (cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))) (cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))))
350.0ms	(cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
373.0ms	(cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
358.0ms	(cbrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

simplify3.3s

Counts

205 → 205

Iterations

Iter	Nodes
done	5001
2	2089
1	1021
0	582

prune2.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.7b

regimes640.0ms

Accuracy

75% (5.9b remaining)

Error of 10.0b against oracle of 4.0b and baseline of 27.8b

bsearch1.5s

Steps

Iters	Range		Point
10	1.3717035908280058e+110	9.416773298407726e+123	4.3989158505625655e+111
9	7.880712048074117e-244	6.696361263611533e-237	3.5177750870459065e-239
9	-2.267750316242303e-307	5.4650818186550785e-304	8.79911984523004e-305
6	-1.644420621869611e-274	-1.9344149889410284e-275	-9.405973531316699e-275
8	-1.048914663983069e-155	-1.9657921853589755e-159	-1.9933494186781088e-159
10	-1.0150002838305954e+118	-7.086310576970351e+104	-3.715046482673699e+110

simplify32.0ms

Iterations

Iter	Nodes
done	81
1	81
0	63

end0.0ms

sample6.3s

Algorithm

intervals

Results

1.7s	9898×	body	80	nan
827.0ms	575×	body	1280	nan
726.0ms	5169×	body	80	valid
644.0ms	653×	body	320	valid
590.0ms	818×	body	1280	valid
540.0ms	993×	body	640	valid
300.0ms	606×	body	640	nan
107.0ms	367×	body	160	valid
104.0ms	335×	body	320	nan
32.0ms	170×	body	160	nan