Details

Time bar (total: 38.1s)

sample790.0ms

Algorithm
intervals
Results
513.0ms350×body80nan
27.0ms38×body640valid
26.0ms151×body80valid
25.0ms28×body1280valid
14.0ms22×body640nan
13.0ms16×body1280nan
12.0ms22×body320valid
6.0ms17×body160valid
5.0ms9×body320nan
1.0ms4×body160nan

simplify320.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
319.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.4b

localize44.0ms

Local error

Found 4 expressions with local error:

19.4b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.0b
(- (* (/ (+ 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))))

rewrite170.0ms

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
71.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
57.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
32.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
7.0ms
(* (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)))
469.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
260.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
56.0ms
(* (sqrt 2) t)

simplify8.5s

Counts
64 → 106
Calls
64 calls:
Slowest
373.0ms
(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 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)))))
329.0ms
(/ (* (* (* (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)))))
303.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
274.0ms
(- (+ (* 2 (pow t 2)) (+ (* 2 (* x (pow l 2))) (* 2 (pow l 2)))))

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.3b

localize61.0ms

Local error

Found 4 expressions with local error:

27.7b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
6.9b
(/ (* (* t t) 4) x)
4.2b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b
(* (sqrt 2) t)

rewrite60.0ms

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)
15.0ms
(* (sqrt 2) t)
7.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
3.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))

series677.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
493.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
104.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
53.0ms
(* (sqrt 2) t)
26.0ms
(/ (* (* t t) 4) x)

simplify2.6s

Counts
46 → 90
Calls
46 calls:
Slowest
202.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
198.0ms
(/ (* (* (* (* t t) t) (* (* t t) t)) (* (* 4 4) 4)) (* (* x x) x))
177.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
176.0ms
(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)))))
175.0ms
(sqrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize29.0ms

Local error

Found 4 expressions with local error:

27.7b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
6.9b
(/ (* (* t t) 4) x)
4.2b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b
(* (sqrt 2) t)

rewrite33.0ms

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
18.0ms
(/ (* (* t t) 4) x)
7.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
7.0ms
(* (sqrt 2) t)
0.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series671.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
460.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
99.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
73.0ms
(* (sqrt 2) t)
39.0ms
(/ (* (* t t) 4) x)

simplify2.8s

Counts
46 → 90
Calls
46 calls:
Slowest
306.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
283.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
196.0ms
(sqrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
185.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
178.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.2b

localize40.0ms

Local error

Found 4 expressions with local error:

27.7b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
6.9b
(/ (* (* t t) 4) x)
4.2b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

rewrite52.0ms

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
31.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
19.0ms
(/ (* (* 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))

series624.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
436.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
88.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
67.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
34.0ms
(/ (* (* t t) 4) x)

simplify3.1s

Counts
46 → 92
Calls
46 calls:
Slowest
304.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))
269.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
221.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* t t) t)))
206.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
190.0ms
(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)))))

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.2b

regimes555.0ms

Accuracy

76.4% (5.5b remaining)

Error of 9.3b against oracle of 3.8b and baseline of 27.1b

bsearch402.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.0s10019×body80nan
1.7s5129×body80valid
877.0ms866×body1280valid
753.0ms979×body640valid
661.0ms604×body1280nan
568.0ms630×body640nan
455.0ms627×body320valid
179.0ms350×body320nan
144.0ms399×body160valid
92.0ms170×body160nan