Details

Time bar (total: 39.6s)

sample404.0ms

Algorithm
intervals
Results
99.0ms295×body80nan
67.0ms21×body640nan
33.0ms155×body80valid
28.0ms36×body640valid
27.0ms27×body1280valid
23.0ms21×body1280nan
18.0ms26×body320valid
6.0ms10×body320nan
4.0ms12×body160valid
1.0ms3×body160nan

simplify239.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
238.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.4b

localize51.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.9b
(- (* (/ (+ 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))))

rewrite203.0ms

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
87.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
67.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
31.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
14.0ms
(* (sqrt 2) t)

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
465.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
220.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
76.0ms
(* (sqrt 2) t)

simplify8.5s

Counts
64 → 106
Calls
64 calls:
Slowest
441.0ms
(sqrt (+ (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (+ (* (* l l) (* l l)) (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
353.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
314.0ms
(/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) t)) (* (* (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
292.0ms
(- (+ (* 2 (pow t 2)) (+ (* 2 (* x (pow l 2))) (* 2 (pow l 2)))))
281.0ms
(fma (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))) (- (* l l)))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.4b

localize65.0ms

Local error

Found 4 expressions with local error:

28.0b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
10.1b
(/ (* (* t t) 4) x)
3.4b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b
(* (sqrt 2) t)

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
7×pow1 sqrt-prod
6×associate-*l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* times-frac div-exp associate-*r*
2×unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down *-commutative fma-udef div-inv associate-/l*
Counts
4 → 78
Calls
4 calls:
Slowest
34.0ms
(/ (* (* t t) 4) x)
10.0ms
(* (sqrt 2) t)
3.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series673.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
477.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
95.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
58.0ms
(* (sqrt 2) t)
43.0ms
(/ (* (* t t) 4) x)

simplify2.8s

Counts
46 → 90
Calls
46 calls:
Slowest
244.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
234.0ms
(sqrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
228.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
226.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
225.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

localize29.0ms

Local error

Found 4 expressions with local error:

28.0b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
10.1b
(/ (* (* t t) 4) x)
3.4b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b
(* t (sqrt 2))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
7×pow1 sqrt-prod
6×associate-*r*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* times-frac div-exp associate-*l*
2×unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down *-commutative fma-udef div-inv associate-/l*
Counts
4 → 78
Calls
4 calls:
Slowest
29.0ms
(/ (* (* t t) 4) x)
11.0ms
(* t (sqrt 2))
1.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series707.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
500.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
112.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
52.0ms
(* t (sqrt 2))
43.0ms
(/ (* (* t t) 4) x)

simplify2.6s

Counts
47 → 90
Calls
47 calls:
Slowest
314.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
209.0ms
(sqrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
200.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
185.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
177.0ms
(/ (* (* (* (* t t) t) (* (* t t) t)) (* (* 4 4) 4)) (* (* x x) x))

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.3b

localize82.0ms

Local error

Found 4 expressions with local error:

28.0b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
10.1b
(/ (* (* t t) 4) x)
3.4b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (* t (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
17×add-cbrt-cube
14×pow1
11×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×associate-*r* prod-exp cbrt-unprod
6×cbrt-prod pow-prod-down sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* times-frac div-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*l* *-commutative fma-udef div-inv associate-/l*
Counts
4 → 83
Calls
4 calls:
Slowest
110.0ms
(* (* t (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
34.0ms
(/ (* (* t t) 4) x)
3.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series705.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
502.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
114.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
64.0ms
(* (* t (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
26.0ms
(/ (* (* t t) 4) x)

simplify4.6s

Counts
50 → 95
Calls
50 calls:
Slowest
653.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
553.0ms
(* (* (* (* t t) t) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt 2))
460.0ms
(* (* (* (* t (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* t (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* t (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt 2))
336.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
216.0ms
(* (* (* (* t t) t) (* (sqrt 2) (sqrt 2))) (sqrt 2))

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.3b

regimes1.1s

Accuracy

79.3% (4.9b remaining)

Error of 8.7b against oracle of 3.8b and baseline of 27.3b

bsearch484.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
2.2s10213×body80nan
1.4s5135×body80valid
1.4s878×body1280valid
749.0ms1003×body640valid
701.0ms628×body1280nan
616.0ms630×body640nan
397.0ms629×body320valid
217.0ms355×body160valid
216.0ms351×body320nan
68.0ms184×body160nan