Details

Time bar (total: 11.2s)

sample147.0ms

Algorithm
intervals
Results
40.0ms9×body160valid
23.0ms344×body80nan
15.0ms52×body640valid
11.0ms152×body80valid
8.0ms23×body1280valid
5.0ms21×body640nan
5.0ms16×body1280nan
4.0ms20×body320valid
3.0ms14×body320nan
1.0ms6×body160nan

simplify103.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.9b

localize23.0ms

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)
14.4b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.4b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite158.0ms

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:
58.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms
(* (sqrt 2.0) t)
30.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
56.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.0s

Counts
4 → 12
Calls
4 calls:
476.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
49.0ms
(* (sqrt 2.0) t)
242.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.3s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify55.0ms

Counts
92 → 92

prune317.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.5b

localize22.0ms

Local error

Found 4 expressions with local error:

3.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.3b
(/ (pow l 2) x)
9.0b
(/ (pow t 2) x)
25.5b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite64.0ms

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:
18.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
9.0ms
(/ (pow l 2) x)
9.0ms
(/ (pow t 2) x)
23.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
25.0ms
(/ (pow l 2) x)
23.0ms
(/ (pow t 2) x)
181.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify58.0ms

Counts
142 → 142

prune498.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
3.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
9.0b
(/ (pow t 2) x)
25.5b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite63.0ms

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
8×associate-*r/ add-cbrt-cube associate-/l*
7×pow1 sqrt-prod
6×associate-*l* add-log-exp
4×flip3-+ sqrt-div frac-add flip-+ unpow2 sqr-pow
3×div-exp associate-*r* associate-/r*
2×associate-+r+ unswap-sqr
1×cbrt-undiv +-commutative distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down pow-exp prod-exp clear-num sum-log *-commutative cbrt-unprod div-inv
Counts
4 → 103
Calls
4 calls:
10.0ms
(* (sqrt 2.0) t)
19.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
14.0ms
(/ (pow t 2) x)
17.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sqrt 2.0) t)
81.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
21.0ms
(/ (pow t 2) x)
185.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify66.0ms

Counts
115 → 115

prune457.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
3.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
9.0b
(/ (pow t 2) x)
25.5b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite98.0ms

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
8×associate-*r/ pow-prod-down prod-exp cbrt-unprod associate-/l*
6×add-log-exp
4×flip3-+ sqrt-div frac-add flip-+ unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×associate-+r+
1×cbrt-undiv +-commutative distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 associate-*r* associate-*l* pow-exp clear-num sum-log *-commutative div-inv
Counts
4 → 103
Calls
4 calls:
50.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
19.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
9.0ms
(/ (pow t 2) x)
18.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series336.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
76.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
21.0ms
(/ (pow t 2) x)
187.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify71.0ms

Counts
115 → 115

prune444.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.1b

regimes419.0ms

Accuracy

79.1% (4.9b remaining)

Error of 8.8b against oracle of 3.9b and baseline of 27.5b

bsearch571.0ms

Steps
ItersRangePoint
10
3.2765607520744054e+111
2.9128648643875498e+128
2.5553097889102982e+120
9
-1.2813900032142045e+106
-3.166552929383693e+99
-4.318745676503489e+101

simplify2.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s9904×body80nan
584.0ms626×body1280nan
532.0ms5136×body80valid
391.0ms844×body1280valid
387.0ms1034×body640valid
197.0ms614×body640nan
154.0ms617×body320valid
131.0ms313×body320nan
85.0ms369×body160valid
24.0ms184×body160nan