Details

sample203.0ms

Algorithm

intervals

Results

33.0ms	354×	body	80	nan
18.0ms	181×	body	80	valid
13.0ms	34×	body	640	valid
9.0ms	18×	body	1280	nan
9.0ms	19×	body	1280	valid
7.0ms	17×	body	640	nan
5.0ms	18×	body	320	valid
3.0ms	12×	body	320	nan
2.0ms	9×	body	160	nan
1.0ms	4×	body	160	valid

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4473
5	1119
4	393
3	181
2	93
1	42
0	18

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
9.8b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
24.2b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite188.0ms

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` `insert-posit16`
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 → 84

Calls

4 calls:

76.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
18.0ms	(* (sqrt 2) t)
40.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
49.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.4s

Counts

4 → 12

Calls

4 calls:

516.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
75.0ms	(* (sqrt 2) t)
299.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1525
1	458
0	170

prune660.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.4b

localize67.0ms

Local error

Found 4 expressions with local error:

4.6b	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
5.0b	(/ (* l l) x)
11.2b	(/ (* t t) x)
29.4b	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `associate-l/` `frac-add` `associate-r/` `flip-+` `insert-posit16`
3×	`sqrt-prod`
2×	`associate-+l+` `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 → 78

Calls

4 calls:

48.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
20.0ms	(/ (* l l) x)
10.0ms	(/ (* t t) x)
48.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
27.0ms	(/ (* l l) x)
36.0ms	(/ (* t t) x)
317.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify1.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5004
2	2246
1	536
0	172

prune572.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
4.6b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
11.2b	(/ (* t t) x)
29.4b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l` `add-log-exp`
4×	`flip3-+` `sqrt-div` `associate-l/` `frac-add` `associate-r/` `flip-+` `insert-posit16`
3×	`associate-/r` `times-frac` `associate-r*`
2×	`cbrt-undiv` `associate-+l+` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 79

Calls

4 calls:

18.0ms	(* (sqrt 2) t)
64.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
13.0ms	(/ (* t t) x)
105.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sqrt 2) t)
92.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
22.0ms	(/ (* t t) x)
290.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify1.8s

Counts

91 → 91

Iterations

Iter	Nodes
done	5002
2	2063
1	498
0	171

prune593.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b	(* t (sqrt 2))
4.6b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
11.2b	(/ (* t t) x)
29.4b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-r` `add-log-exp`
4×	`flip3-+` `sqrt-div` `associate-l/` `frac-add` `associate-r/` `flip-+` `insert-posit16`
3×	`associate-/r` `times-frac` `associate-l*`
2×	`cbrt-undiv` `associate-+l+` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 79

Calls

4 calls:

11.0ms	(* t (sqrt 2))
52.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
10.0ms	(/ (* t t) x)
131.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series509.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* t (sqrt 2))
97.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
28.0ms	(/ (* t t) x)
329.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify1.7s

Counts

91 → 91

Iterations

Iter	Nodes
done	5002
2	2058
1	497
0	172

prune551.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

regimes708.0ms

Accuracy

77.5% (5.3b remaining)

Error of 9.0b against oracle of 3.8b and baseline of 27.2b

bsearch1.8s

Steps

Iters	Range		Point
7	1.1309338413304086e+123	2.556259866195709e+124	1.9084252591087465e+124
11	2.7160922814063716e-171	2.320974549002931e-151	2.245304088873431e-167
9	2.7888354386856526e-229	2.5177007063076634e-220	9.75018164282627e-224
9	-2.757932199019658e-244	-4.4129812563248435e-253	-8.653026810570713e-249
5	-1.5326714186934164e-151	-6.409403706686988e-152	-6.488460202761919e-152
8	-3.7025101036668716e+145	-1.3245719886640114e+141	-1.9121810864395621e+142

simplify44.0ms

Iterations

Iter	Nodes
done	100
3	100
2	96
1	79
0	59

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.1s	10084×	body	80	nan
938.0ms	5177×	body	80	valid
601.0ms	961×	body	640	valid
466.0ms	866×	body	1280	valid
349.0ms	553×	body	1280	nan
325.0ms	662×	body	320	valid
274.0ms	576×	body	640	nan
113.0ms	334×	body	160	valid
113.0ms	357×	body	320	nan
38.0ms	190×	body	160	nan