Details

Time bar (total: 29.6s)

sample567.0ms

Algorithm
intervals
Results
196.0ms303×body80nan
56.0ms20×body1280nan
54.0ms14×body640nan
47.0ms169×body80valid
39.0ms38×body640valid
30.0ms21×body1280valid
16.0ms19×body320valid
9.0ms11×body320nan
4.0ms9×body160valid
4.0ms8×body160nan

simplify1.9s

Counts
1 → 1

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.3b

localize52.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
12.2b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b
(* (sqrt 2) t)
0.0b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r* times-frac associate-*l* add-log-exp
4×expm1-log1p-u sqrt-div insert-posit16 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 rem-sqrt-square clear-num sub-neg frac-2neg distribute-lft-in sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down *-commutative div-inv associate-/l*
Counts
4 → 94
Calls
4 calls:
Slowest
82.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
76.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
36.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
7.0ms
(* (sqrt 2) t)

series2.3s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
549.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
252.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
60.0ms
(* (sqrt 2) t)

simplify638.0ms

Counts
106 → 106

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.7b

localize67.0ms

Local error

Found 4 expressions with local error:

26.0b
(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l))))))
9.2b
(/ (* t t) x)
5.5b
(/ x (* l l))
3.2b
(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×times-frac
5×pow1
4×expm1-log1p-u cbrt-undiv associate-/r* div-exp insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×sqrt-prod
2×clear-num frac-2neg prod-exp cbrt-unprod div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 75
Calls
4 calls:
Slowest
18.0ms
(/ (* t t) x)
9.0ms
(/ x (* l l))
3.0ms
(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l))))))
0.0ms
(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l)))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
224.0ms
(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l))))))
91.0ms
(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l)))))
44.0ms
(/ x (* l l))
25.0ms
(/ (* t t) x)

simplify1.1s

Counts
87 → 87

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize73.0ms

Local error

Found 4 expressions with local error:

26.0b
(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l)))))
9.2b
(/ (* t t) x)
3.2b
(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l))))
0.5b
(/ 2 (/ (/ x l) l))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
396×times-frac
192×add-sqr-sqrt
191×*-un-lft-identity add-cube-cbrt
46×associate-/r*
18×add-cbrt-cube add-exp-log div-inv
8×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×sqrt-prod
2×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 prod-exp associate-/r/ cbrt-unprod fma-udef
Counts
4 → 246
Calls
4 calls:
Slowest
9.0ms
(/ (* t t) x)
7.0ms
(/ 2 (/ (/ x l) l))
2.0ms
(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l)))))
0.0ms
(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l))))

series319.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l)))))
70.0ms
(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l))))
35.0ms
(/ (* t t) x)
32.0ms
(/ 2 (/ (/ x l) l))

simplify791.0ms

Counts
258 → 258

prune4.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.3b

localize69.0ms

Local error

Found 4 expressions with local error:

26.0b
(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (/ 2 (/ x l)) (/ 1 l)))))
9.2b
(/ (* t t) x)
3.2b
(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (/ 2 (/ x l)) (/ 1 l))))
1.1b
(/ 2 (/ x l))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
50×add-sqr-sqrt
49×*-un-lft-identity add-cube-cbrt
16×associate-/r*
14×add-cbrt-cube add-exp-log
6×div-inv
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×sqrt-prod
2×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 prod-exp associate-/r/ cbrt-unprod fma-udef
Counts
4 → 124
Calls
4 calls:
Slowest
17.0ms
(/ (* t t) x)
6.0ms
(/ 2 (/ x l))
2.0ms
(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (/ 2 (/ x l)) (/ 1 l)))))
0.0ms
(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (/ 2 (/ x l)) (/ 1 l))))

series424.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
240.0ms
(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (/ 2 (/ x l)) (/ 1 l)))))
113.0ms
(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (/ 2 (/ x l)) (/ 1 l))))
42.0ms
(/ (* t t) x)
30.0ms
(/ 2 (/ x l))

simplify890.0ms

Counts
136 → 136

prune1.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.2b

regimes614.0ms

Accuracy

75.5% (5.7b remaining)

Error of 9.3b against oracle of 3.7b and baseline of 26.7b

bsearch1.6s

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.3s10129×body80nan
1.3s859×body1280valid
1.1s5126×body80valid
923.0ms1027×body640valid
727.0ms380×body320nan
598.0ms584×body1280nan
516.0ms573×body640nan
426.0ms636×body320valid
133.0ms352×body160valid
65.0ms189×body160nan