Details

Time bar (total: 1.2m)

sample369.0ms

Algorithm
intervals
Results
106.0ms341×body80nan
35.0ms164×body80valid
27.0ms26×body1280valid
24.0ms31×body640valid
20.0ms20×body1280nan
15.0ms23×body640nan
13.0ms23×body320valid
4.0ms12×body160valid
4.0ms9×body320nan
2.0ms6×body160nan

simplify292.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
267.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.0b

localize43.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
12.8b
(- (* (/ (+ 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))))

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
84.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
60.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
38.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
17.0ms
(* (sqrt 2) t)

series2.3s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
509.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
247.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
53.0ms
(* (sqrt 2) t)

simplify19.7s

Counts
120 → 106
Calls
120 calls:
Slowest
823.0ms
(* (* (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
557.0ms
(expm1 (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
445.0ms
(/ (* (* (* (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)))))
414.0ms
(- (* (* 2 (* t t)) (/ (+ x 1) (- x 1))) (* l l))
399.0ms
(- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3))

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.4b

localize30.0ms

Local error

Found 4 expressions with local error:

25.4b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.1b
(/ (* (* t t) 4) x)
3.4b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.5b
(* (sqrt 2) t)

rewrite46.0ms

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
25.0ms
(/ (* (* t t) 4) x)
19.0ms
(* (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))

series657.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
424.0ms
(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))
74.0ms
(* (sqrt 2) t)
44.0ms
(/ (* (* t t) 4) x)

simplify9.3s

Counts
96 → 90
Calls
96 calls:
Slowest
629.0ms
(* (* (/ (* (* t t) 4) x) (/ (* (* t t) 4) x)) (/ (* (* t t) 4) x))
398.0ms
(exp (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
305.0ms
(* (* (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)) (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
284.0ms
(* (* (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
250.0ms
(sqrt (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize53.0ms

Local error

Found 4 expressions with local error:

25.4b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.1b
(/ (* (* t t) 4) x)
3.4b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

rewrite71.0ms

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
51.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
17.0ms
(/ (* (* 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))

series711.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
513.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
77.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
76.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
44.0ms
(/ (* (* t t) 4) x)

simplify12.6s

Counts
94 → 90
Calls
94 calls:
Slowest
677.0ms
(* (* (/ (* (* t t) 4) x) (/ (* (* t t) 4) x)) (/ (* (* t t) 4) x))
624.0ms
(* (* (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
594.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)))
491.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
447.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize43.0ms

Local error

Found 4 expressions with local error:

25.4b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.1b
(/ (* (* t t) 4) x)
3.4b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

rewrite58.0ms

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
29.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
18.0ms
(/ (* (* t t) 4) x)
10.0ms
(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))

series699.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
503.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
83.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
75.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
38.0ms
(/ (* (* t t) 4) x)

simplify10.4s

Counts
96 → 92
Calls
96 calls:
Slowest
515.0ms
(* (* (/ (* (* t t) 4) x) (/ (* (* t t) 4) x)) (/ (* (* t t) 4) x))
401.0ms
(* (* (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))) (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t)))
390.0ms
(* (* (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)) (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
330.0ms
(exp (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
320.0ms
(* (* (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.3b

regimes692.0ms

Accuracy

78% (5.2b remaining)

Error of 8.9b against oracle of 3.7b and baseline of 27.5b

bsearch949.0ms

end0.0ms

sample9.0s

Algorithm
intervals
Results
2.5s10227×body80nan
1.2s5156×body80valid
1.0s612×body1280nan
1.0s1067×body640valid
964.0ms808×body1280valid
548.0ms591×body640nan
463.0ms148×body160nan
347.0ms645×body320valid
276.0ms323×body320nan
152.0ms324×body160valid