Details

Time bar (total: 40.9s)

sample286.0ms

Algorithm
intervals
Results
69.0ms320×body80nan
21.0ms166×body80valid
19.0ms37×body640valid
13.0ms20×body1280nan
13.0ms22×body1280valid
11.0ms24×body640nan
7.0ms19×body320valid
5.0ms12×body160valid
4.0ms12×body320nan
1.0ms6×body160nan

simplify525.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
524.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune50.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.3b

localize47.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
9.9b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.5b
(* (sqrt 2) t)
0.0b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite332.0ms

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
130.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
103.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
78.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
16.0ms
(* (sqrt 2) t)

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
490.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
243.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
53.0ms
(* (sqrt 2) t)

simplify8.7s

Counts
64 → 106
Calls
64 calls:
Slowest
389.0ms
(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)))))
344.0ms
(* (* l l) (/ (+ x 1) (- x 1)))
339.0ms
(/ (* (* (* (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)))))
331.0ms
(/ (* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* t t) 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)))))
326.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.9b

localize59.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
7.1b
(/ (* (* t t) 4) x)
5.6b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.5b
(* (sqrt 2) t)

rewrite37.0ms

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
21.0ms
(/ (* (* t t) 4) x)
12.0ms
(* (sqrt 2) t)
2.0ms
(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))

series668.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
466.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
102.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
68.0ms
(* (sqrt 2) t)
33.0ms
(/ (* (* t t) 4) x)

simplify2.7s

Counts
46 → 90
Calls
46 calls:
Slowest
238.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
238.0ms
(sqrt (* (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
221.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
213.0ms
(sqrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
209.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.8b

localize32.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
7.1b
(/ (* (* t t) 4) x)
5.6b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
12×sqrt-prod
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cube-cbrt
9×associate-*l*
6×prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* times-frac div-exp pow-prod-down
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r* *-commutative fma-udef div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
Slowest
47.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
42.0ms
(/ (* (* t t) 4) x)
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))

series656.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
458.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
101.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
60.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
36.0ms
(/ (* (* t t) 4) x)

simplify3.4s

Counts
46 → 92
Calls
46 calls:
Slowest
613.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
281.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))
222.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* t t) t)))
217.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
212.0ms
(sqrt (* (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.8b

localize71.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
7.1b
(/ (* (* t t) 4) x)
5.6b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
1.0b
(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
69×sqrt-prod
50×add-sqr-sqrt
33×sqrt-pow1
28×pow1
19×*-un-lft-identity add-cube-cbrt
17×pow1/2
15×add-cbrt-cube swap-sqr add-exp-log
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
5×pow-prod-down pow-sqr
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
1×pow2 rem-sqrt-square clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod *-commutative fma-udef div-inv associate-/l*
Counts
4 → 131
Calls
4 calls:
Slowest
34.0ms
(/ (* (* t t) 4) x)
16.0ms
(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))
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))

series573.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
447.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
81.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
45.0ms
(/ (* (* t t) 4) x)
0.0ms
(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))

simplify3.8s

Counts
128 → 141
Calls
128 calls:
Slowest
300.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
240.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
228.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
228.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
219.0ms
(sqrt (* (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))

prune1.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.8b

regimes513.0ms

Accuracy

77% (5.3b remaining)

Error of 9.3b against oracle of 4.0b and baseline of 27.2b

bsearch1.2s

end0.0ms

sample8.9s

Algorithm
intervals
Results
2.3s9953×body80nan
1.6s5179×body80valid
1.1s589×body1280nan
1.1s816×body1280valid
981.0ms1004×body640valid
585.0ms627×body640nan
428.0ms630×body320valid
165.0ms329×body320nan
159.0ms371×body160valid
73.0ms201×body160nan