Details

Time bar (total: 43.0s)

sample428.0ms

Algorithm
intervals
Results
118.0ms307×body80nan
40.0ms172×body80valid
26.0ms27×body640valid
21.0ms19×body1280valid
18.0ms19×body640nan
16.0ms14×body1280nan
12.0ms17×body320valid
10.0ms14×body320nan
10.0ms21×body160valid
3.0ms6×body160nan

simplify221.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
221.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.9b

localize48.0ms

Local error

Found 4 expressions with local error:

22.0b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
12.4b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.5b
(* (sqrt 2) t)
0.1b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite151.0ms

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
61.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
46.0ms
(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)

series2.4s

Counts
4 → 12
Calls
4 calls:
Slowest
1.6s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
468.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
287.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
81.0ms
(* (sqrt 2) t)

simplify9.1s

Counts
64 → 106
Calls
64 calls:
Slowest
620.0ms
(sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
429.0ms
(/ (* (* (* (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)))))
364.0ms
(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)))))
356.0ms
(/ (* (* (* (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)))))
339.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.0b

localize38.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
10.7b
(/ (* (* t t) 4) x)
2.8b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.5b
(* (sqrt 2) t)

rewrite45.0ms

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
31.0ms
(/ (* (* t t) 4) x)
7.0ms
(* (sqrt 2) t)
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))

series719.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
508.0ms
(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))
78.0ms
(* (sqrt 2) t)
45.0ms
(/ (* (* t t) 4) x)

simplify2.9s

Counts
46 → 90
Calls
46 calls:
Slowest
274.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
229.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
214.0ms
(* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* t t) t))
203.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
199.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize55.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
10.7b
(/ (* (* t t) 4) x)
2.8b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
19×add-cbrt-cube
17×pow1
11×prod-exp cbrt-unprod
8×add-sqr-sqrt pow-prod-down
7×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* times-frac div-exp sqrt-prod
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r* associate-*l* *-commutative fma-udef div-inv associate-/l*
Counts
4 → 78
Calls
4 calls:
Slowest
37.0ms
(/ (* (* t t) 4) x)
30.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
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))

series618.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
435.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
86.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
62.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
36.0ms
(/ (* (* t t) 4) x)

simplify4.1s

Counts
45 → 90
Calls
45 calls:
Slowest
488.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
425.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
249.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
219.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
202.0ms
(/ (* (* (* (* t t) t) (* (* t t) t)) (* (* 4 4) 4)) (* (* x x) x))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize73.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
10.7b
(/ (* (* t t) 4) x)
2.8b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

rewrite80.0ms

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
42.0ms
(/ (* (* t t) 4) x)
35.0ms
(* (sqrt (sqrt 2)) (* (sqrt (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))

series674.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
473.0ms
(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))
58.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
41.0ms
(/ (* (* t t) 4) x)

simplify3.2s

Counts
46 → 92
Calls
46 calls:
Slowest
328.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))
213.0ms
(sqrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
208.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* t t) t)))
199.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
196.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.9b

regimes841.0ms

Accuracy

77.8% (5.3b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 27.9b

bsearch2.4s

end0.0ms

sample9.2s

Algorithm
intervals
Results
2.6s9880×body80nan
1.3s5202×body80valid
973.0ms985×body640valid
959.0ms827×body1280valid
881.0ms619×body320valid
793.0ms579×body1280nan
651.0ms576×body640nan
253.0ms328×body320nan
172.0ms367×body160valid
71.0ms180×body160nan