Details

Time bar (total: 21.8s)

sample507.0ms

Algorithm
intervals
Results
115.0ms331×body80nan
49.0ms25×body1280valid
27.0ms164×body80valid
18.0ms33×body640valid
18.0ms22×body1280nan
10.0ms24×body320valid
7.0ms13×body640nan
5.0ms10×body320nan
3.0ms10×body160valid
1.0ms5×body160nan

simplify1.3s

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize22.0ms

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)
13.6b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.9b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite256.0ms

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:
103.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
21.0ms
(* (sqrt 2.0) t)
51.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
75.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.6s

Counts
4 → 12
Calls
4 calls:
625.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
73.0ms
(* (sqrt 2.0) t)
322.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.6s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.1s

Counts
92 → 92

prune561.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.4b

localize48.0ms

Local error

Found 4 expressions with local error:

4.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.9b
(/ (pow l 2) x)
8.7b
(/ (pow t 2) x)
26.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite103.0ms

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
8×associate-*r/ add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r* add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×sqrt-prod
2×cbrt-undiv pow-to-exp associate-+r+ frac-2neg pow-exp clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 130
Calls
4 calls:
44.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms
(/ (pow l 2) x)
12.0ms
(/ (pow t 2) x)
19.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
29.0ms
(/ (pow l 2) x)
26.0ms
(/ (pow t 2) x)
280.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify1.2s

Counts
142 → 142

prune710.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
4.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
8.7b
(/ (pow t 2) x)
26.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity times-frac
23×add-sqr-sqrt
22×add-cube-cbrt
12×unpow-prod-down
9×add-exp-log
8×associate-*r/ associate-/l* add-log-exp
6×add-cbrt-cube
5×pow1 flip3-+ flip-+
4×sqrt-div frac-add unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×+-commutative associate-+r+ sum-log
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp clear-num div-inv distribute-lft-out
Counts
4 → 93
Calls
4 calls:
73.0ms
(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
20.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
15.0ms
(/ (pow t 2) x)
18.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series444.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
100.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
43.0ms
(/ (pow t 2) x)
249.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify893.0ms

Counts
105 → 105

prune569.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize54.0ms

Local error

Found 4 expressions with local error:

8.7b
(/ (pow t 2) x)
26.4b
(sqrt (+ (pow t 2) (/ (pow l 1) (/ x l))))
26.4b
(sqrt (+ (pow t 2) (/ (pow l 1) (/ x l))))
26.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ (pow l 1) (/ x l)))) (sqrt (+ (pow t 2) (/ (pow l 1) (/ x l))))))))

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
27×add-sqr-sqrt
26×sqrt-div
24×add-cube-cbrt times-frac
18×associate-*r/
12×unpow-prod-down
11×sqrt-prod
9×add-exp-log flip3-+ flip-+
8×frac-add associate-/l*
7×pow1
6×add-cbrt-cube
4×frac-times unpow2 add-log-exp sqr-pow
3×rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r*
2×associate-*l/ distribute-lft-out
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 104
Calls
4 calls:
17.0ms
(/ (pow t 2) x)
169.0ms
(sqrt (+ (pow t 2) (/ (pow l 1) (/ x l))))
148.0ms
(sqrt (+ (pow t 2) (/ (pow l 1) (/ x l))))
31.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ (pow l 1) (/ x l)))) (sqrt (+ (pow t 2) (/ (pow l 1) (/ x l))))))))

series520.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (pow t 2) x)
137.0ms
(sqrt (+ (pow t 2) (/ (pow l 1) (/ x l))))
116.0ms
(sqrt (+ (pow t 2) (/ (pow l 1) (/ x l))))
237.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ (pow l 1) (/ x l)))) (sqrt (+ (pow t 2) (/ (pow l 1) (/ x l))))))))

simplify914.0ms

Counts
116 → 116

prune776.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

regimes519.0ms

Accuracy

77.7% (5.3b remaining)

Error of 9.2b against oracle of 3.9b and baseline of 27.7b

bsearch307.0ms

Steps
ItersRangePoint
7
8.356385605711534e+64
1.1858048988060262e+67
5.25971673049714e+65
6
-1.918162219372515e+136
-3.230996460513484e+135
-5.835726090767109e+135

simplify686.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
1.9s10092×body80nan
971.0ms851×body1280valid
954.0ms1004×body640valid
730.0ms5127×body80valid
329.0ms595×body1280nan
267.0ms586×body640nan
191.0ms654×body320valid
141.0ms322×body320nan
122.0ms364×body160valid
33.0ms178×body160nan