Details

Time bar (total: 12.9s)

sample71.0ms

Algorithm
intervals
Results
14.0ms306×body80nan
9.0ms159×body80valid
6.0ms24×body1280valid
5.0ms26×body640valid
4.0ms27×body320valid
4.0ms16×body1280nan
3.0ms17×body640nan
2.0ms20×body160valid
1.0ms8×body320nan
1.0ms11×body160nan

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01827
13927
28627
317727
434427
555027
689927
7159227
8322927
done500027

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize18.0ms

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)
12.4b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.7b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* 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 sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
30.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms
(* (sqrt 2.0) t)
13.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
429.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
44.0ms
(* (sqrt 2.0) t)
214.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify567.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (137.0ms)

IterNodesCost
01682472
14162283
215932085
done50002085

prune306.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.0b

localize17.0ms

Local error

Found 4 expressions with local error:

3.6b
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
5.9b
(/ (pow l 2) x)
9.7b
(/ (pow t 2) x)
27.0b
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
9×add-log-exp
8×add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r*
5×pow1
3×sum-log sqrt-prod
2×cbrt-undiv pow-to-exp frac-2neg flip3-+ sqrt-div pow-exp clear-num flip-+ div-inv
1×+-commutative rem-sqrt-square associate-+r+ sqrt-pow1 pow1/2
Counts
4 → 126
Calls
4 calls:
19.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow l 2) x)
5.0ms
(/ (pow t 2) x)
30.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

series375.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
268.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

simplify494.0ms

Counts
138 → 138
Iterations

Useful iterations: 2 (181.0ms)

IterNodesCost
02292129
14531871
215031692
done50001692

prune495.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 2.0) t)
3.6b
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x))))
9.7b
(/ (pow t 2) x)
27.0b
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
12×unpow-prod-down
11×add-exp-log
9×add-log-exp
8×add-cbrt-cube associate-/l*
7×pow1 sqrt-prod
6×associate-*l*
4×unpow2 sqr-pow
3×div-exp associate-*r* associate-/r* sum-log
2×flip3-+ sqrt-div flip-+ unswap-sqr
1×cbrt-undiv +-commutative pow-to-exp rem-sqrt-square associate-+r+ frac-2neg sqrt-pow1 pow1/2 pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 99
Calls
4 calls:
5.0ms
(* (sqrt 2.0) t)
51.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
102.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

series399.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (sqrt 2.0) t)
70.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow t 2) x)
268.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

simplify535.0ms

Counts
111 → 111
Iterations

Useful iterations: 2 (187.0ms)

IterNodesCost
01932013
14101539
213971403
done50011403

prune430.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(* t (sqrt 2.0))
3.6b
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x))))
9.7b
(/ (pow t 2) x)
27.0b
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
12×unpow-prod-down
11×add-exp-log
9×add-log-exp
8×add-cbrt-cube associate-/l*
7×pow1 sqrt-prod
6×associate-*r*
4×unpow2 sqr-pow
3×div-exp associate-*l* associate-/r* sum-log
2×flip3-+ sqrt-div flip-+ unswap-sqr
1×cbrt-undiv +-commutative pow-to-exp rem-sqrt-square associate-+r+ frac-2neg sqrt-pow1 pow1/2 pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 99
Calls
4 calls:
5.0ms
(* t (sqrt 2.0))
52.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
99.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* t (sqrt 2.0))
68.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
267.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

simplify515.0ms

Counts
111 → 111
Iterations

Useful iterations: 2 (171.0ms)

IterNodesCost
01952016
14151537
213391401
done50001401

prune416.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.9b

regimes489.0ms

Accuracy

75.9% (5.6b remaining)

Error of 9.4b against oracle of 3.8b and baseline of 27.0b

bsearch486.0ms

Steps
ItersRangePoint
8
2.856659494861968e+113
8.814288912248196e+117
2.4147196408338222e+115
6
-1.183890802660123e-282
-2.1055594324771466e-283
-4.937566382482769e-283
10
-2.4994760714008124e-200
-2.1048616109453496e-212
-3.4742680211531412e-205
9
-6.177616083621757e+80
-1.7667126674059824e+73
-6.061580330246335e+80

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
059208
177204
done77204

end0.0ms

sample2.0s

Algorithm
intervals
Results
485.0ms10109×body80nan
264.0ms5145×body80valid
197.0ms801×body1280valid
192.0ms1012×body640valid
140.0ms591×body1280nan
106.0ms587×body640nan
92.0ms654×body320valid
47.0ms337×body320nan
38.0ms388×body160valid
20.0ms215×body160nan