Details

Time bar (total: 41.0s)

sample523.0ms

Algorithm
intervals
Results
110.0ms320×body80nan
85.0ms29×body1280valid
79.0ms166×body80valid
30.0ms30×body640valid
21.0ms19×body1280nan
12.0ms18×body320valid
10.0ms12×body640nan
6.0ms13×body160valid
5.0ms7×body320nan
2.0ms4×body160nan

simplify351.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
350.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.7b

localize76.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.1b
(- (* (/ (+ 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))))

rewrite153.0ms

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
67.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
45.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
24.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
14.0ms
(* (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)))
556.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
209.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
58.0ms
(* (sqrt 2) t)

simplify9.1s

Counts
64 → 106
Calls
64 calls:
Slowest
559.0ms
(/ (sqrt 2) (sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
409.0ms
(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)))))
388.0ms
(/ (* (* (* (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)))))
329.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
297.0ms
(* (* l l) (/ (+ x 1) (- x 1)))

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.2b

localize29.0ms

Local error

Found 4 expressions with local error:

27.3b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
9.9b
(/ (* (* t t) 4) x)
4.3b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b
(* (sqrt 2) t)

rewrite30.0ms

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)
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))

series716.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
504.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
116.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
58.0ms
(* (sqrt 2) t)
38.0ms
(/ (* (* t t) 4) x)

simplify2.7s

Counts
46 → 90
Calls
46 calls:
Slowest
226.0ms
(sqrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
207.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
204.0ms
(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)))))
200.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
194.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.2b

localize56.0ms

Local error

Found 4 expressions with local error:

27.3b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
9.9b
(/ (* (* t t) 4) x)
4.3b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

rewrite87.0ms

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
57.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
25.0ms
(/ (* (* 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))

series684.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
485.0ms
(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))
60.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
44.0ms
(/ (* (* t t) 4) x)

simplify4.2s

Counts
45 → 90
Calls
45 calls:
Slowest
493.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
401.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
256.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
255.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
224.0ms
(* (* (sqrt 2) (sqrt 2)) (* (sqrt 2) (* (* t t) t)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.2b

localize32.0ms

Local error

Found 4 expressions with local error:

27.3b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
9.9b
(/ (* (* t t) 4) x)
4.3b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b
(* t (sqrt 2))

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-*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
42.0ms
(/ (* (* t t) 4) x)
14.0ms
(* t (sqrt 2))
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))

series624.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
418.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
92.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
80.0ms
(* t (sqrt 2))
33.0ms
(/ (* (* t t) 4) x)

simplify2.9s

Counts
47 → 90
Calls
47 calls:
Slowest
291.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
243.0ms
(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)))))
228.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
215.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
192.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.2b

regimes550.0ms

Accuracy

76.4% (5.5b remaining)

Error of 9.3b against oracle of 3.7b and baseline of 27.1b

bsearch2.0s

end0.0ms

sample8.7s

Algorithm
intervals
Results
2.2s10171×body80nan
1.4s876×body1280valid
1.2s5104×body80valid
830.0ms1002×body640valid
797.0ms655×body320valid
672.0ms628×body1280nan
583.0ms645×body640nan
250.0ms345×body320nan
164.0ms363×body160valid
58.0ms166×body160nan