Details

Time bar (total: 13.8s)

sample83.0ms

Algorithm
intervals
Results
15.0ms315×body80nan
8.0ms168×body80valid
7.0ms36×body640valid
6.0ms23×body1280valid
5.0ms20×body1280nan
4.0ms22×body640nan
2.0ms14×body320valid
1.0ms15×body160valid
1.0ms9×body320nan
1.0ms6×body160nan

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01827
13927
28627
317727
434427
555027
689927
7159227
8322927
done500027

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize17.0ms

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)
15.0b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.7b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite72.0ms

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:
28.0ms
(/ (* (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))
22.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts
4 → 12
Calls
4 calls:
415.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
40.0ms
(* (sqrt 2.0) t)
216.0ms
(- (* (/ (+ 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)))

simplify698.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
01682472
14162283
215932085
done50002085

prune304.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
6.9b
(/ (pow t 2) x)
6.9b
(/ (pow l 2) x)
27.7b
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite58.0ms

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:
17.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
4.0ms
(/ (pow l 2) x)
29.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

series360.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
19.0ms
(/ (pow l 2) x)
258.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

simplify551.0ms

Counts
138 → 138
Iterations

Useful iterations: 2 (181.0ms)

IterNodesCost
02292129
14531871
215031692
done50001692

prune488.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 2.0) t)
5.6b
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x))))
6.9b
(/ (pow t 2) x)
27.7b
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

rewrite148.0ms

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)
47.0ms
(+ (* 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)
90.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

series396.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (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)
264.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

simplify688.0ms

Counts
111 → 111
Iterations

Useful iterations: 2 (193.0ms)

IterNodesCost
01932013
14101539
213971403
done50011403

prune426.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
5.6b
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x))))
6.9b
(/ (pow t 2) x)
27.7b
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
21×add-exp-log
17×pow1
12×unpow-prod-down add-cbrt-cube
9×add-log-exp
8×pow-prod-down prod-exp cbrt-unprod associate-/l*
4×unpow2 sqr-pow
3×div-exp associate-/r* sum-log sqrt-prod
2×flip3-+ sqrt-div flip-+
1×cbrt-undiv +-commutative pow-to-exp rem-sqrt-square associate-+r+ frac-2neg sqrt-pow1 pow1/2 associate-*r* associate-*l* pow-exp clear-num *-commutative div-inv
Counts
4 → 99
Calls
4 calls:
20.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
46.0ms
(+ (* 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)
90.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

series391.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
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)
260.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l (/ 2 2)) (/ x (pow l 1)))) (* 4.0 (/ (pow t 2) x)))))

simplify683.0ms

Counts
111 → 111
Iterations

Useful iterations: 2 (185.0ms)

IterNodesCost
02012256
14601773
215071462
done50011462

prune432.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.2b

regimes389.0ms

Accuracy

75.6% (5.9b remaining)

Error of 9.8b against oracle of 3.8b and baseline of 28.1b

bsearch531.0ms

Steps
ItersRangePoint
9
8249416806277068.0
6.908956904862703e+24
6.769189022626266e+24
9
-5.149414502062706e-287
-6.479421214823862e-296
-5.07338813022938e-287
9
-1.9154334448410318e-177
-2.122947083583308e-184
-2.1093237783967825e-178
10
-7.10480317732965e+72
-7.474441928331378e+61
-4.413416346136292e+69

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
057198
171194
done71194

end0.0ms

sample2.0s

Algorithm
intervals
Results
482.0ms10142×body80nan
262.0ms5082×body80valid
215.0ms879×body1280valid
188.0ms994×body640valid
137.0ms587×body1280nan
108.0ms590×body640nan
91.0ms649×body320valid
43.0ms316×body320nan
39.0ms396×body160valid
20.0ms217×body160nan