Details

Time bar (total: 33.5s)

sample328.0ms

Algorithm
intervals
Results
94.0ms296×body80nan
23.0ms166×body80valid
22.0ms33×body640valid
19.0ms26×body1280valid
11.0ms22×body640nan
10.0ms15×body1280nan
9.0ms20×body320valid
3.0ms8×body320nan
3.0ms11×body160valid
2.0ms7×body160nan

simplify6.4s

Counts
1 → 1
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
01827
14126
210026
323426
453126
5105126
6192926
7459326
done500026

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize69.0ms

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)
13.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.7b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite297.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u
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 fma-neg diff-log prod-diff pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
106.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
18.0ms
(* (sqrt 2.0) t)
59.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
108.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series3.3s

Counts
4 → 12
Calls
4 calls:
757.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
78.0ms
(* (sqrt 2.0) t)
393.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.1s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.9s

Counts
102 → 102
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01792660
14842380
227402183
done50012176

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.1b

localize62.0ms

Local error

Found 4 expressions with local error:

3.6b
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
5.9b
(/ (pow l 2) x)
10.0b
(/ (pow t 2) x)
27.5b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

rewrite49.0ms

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×add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 127
Calls
4 calls:
1.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
18.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
3.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

series592.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
39.0ms
(/ (pow l 2) x)
45.0ms
(/ (pow t 2) x)
349.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

simplify1.3s

Counts
139 → 139
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02161767
13981621
215761429
done50001426

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize78.0ms

Local error

Found 4 expressions with local error:

1.5b
(fma t t (/ (pow l (/ 2 2)) (/ x l)))
3.6b
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
10.0b
(/ (pow t 2) x)
27.5b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
9×add-exp-log
8×associate-/l*
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×div-exp associate-/r* sqrt-prod
2×fma-udef
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
1.0ms
(fma t t (/ (pow l (/ 2 2)) (/ x l)))
1.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
18.0ms
(/ (pow t 2) x)
3.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

series655.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(fma t t (/ (pow l (/ 2 2)) (/ x l)))
156.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
43.0ms
(/ (pow t 2) x)
358.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

simplify1.0s

Counts
98 → 98
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01591532
12981346
211571124
done50011119

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize75.0ms

Local error

Found 4 expressions with local error:

10.0b
(/ (pow t 2) x)
27.5b
(sqrt (fma t t (/ l (/ x l))))
27.5b
(sqrt (fma t t (/ l (/ x l))))
27.5b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity times-frac
12×unpow-prod-down
9×add-exp-log sqrt-prod
8×associate-/l*
7×pow1
6×add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r*
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 96
Calls
4 calls:
18.0ms
(/ (pow t 2) x)
3.0ms
(sqrt (fma t t (/ l (/ x l))))
3.0ms
(sqrt (fma t t (/ l (/ x l))))
4.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))))))

series713.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (pow t 2) x)
164.0ms
(sqrt (fma t t (/ l (/ x l))))
152.0ms
(sqrt (fma t t (/ l (/ x l))))
357.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))))))

simplify895.0ms

Counts
108 → 108
Iterations

Useful iterations: done (890.0ms)

IterNodesCost
01551536
12901194
210021090
done50001088

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

regimes1.1s

Accuracy

75.9% (5.9b remaining)

Error of 9.7b against oracle of 3.8b and baseline of 28.2b

bsearch452.0ms

Steps
ItersRangePoint
8
6.753203435084242e+100
2.2870795443321386e+105
1.5497059210109297e+104
7
-1.1980052479942145e+71
-3.057474683283312e+69
-5.89661864480626e+70

simplify19.0ms

Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
045113
153111
255109
done55109

end0.0ms

sample8.1s

Algorithm
intervals
Results
2.3s9955×body80nan
1.2s1046×body640valid
981.0ms5080×body80valid
617.0ms826×body1280valid
509.0ms591×body640nan
494.0ms592×body1280nan
444.0ms693×body320valid
139.0ms370×body320nan
92.0ms355×body160valid
45.0ms178×body160nan