Details

Time bar (total: 1.3m)

sample302.0ms

Algorithm
intervals
Results
79.0ms306×body80nan
28.0ms156×body80valid
25.0ms32×body1280valid
25.0ms37×body640valid
13.0ms22×body640nan
11.0ms24×body320valid
8.0ms11×body1280nan
7.0ms15×body320nan
3.0ms9×body160nan
2.0ms7×body160valid

simplify188.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
187.0ms
(/ (* (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: 42.9b

localize41.0ms

Local error

Found 4 expressions with local error:

19.1b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.8b
(- (* (/ (+ 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))))

rewrite243.0ms

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
89.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
83.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
51.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
16.0ms
(* (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)))
485.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
261.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
61.0ms
(* (sqrt 2) t)

simplify19.4s

Counts
120 → 106
Calls
120 calls:
Slowest
832.0ms
(* (* (- (* (/ (+ 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)))
535.0ms
(expm1 (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
404.0ms
(- (* (* 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))
393.0ms
(/ (* (sqrt 2) t) (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: 3.5b

localize67.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
7.6b
(/ (* (* t t) 4) x)
3.8b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b
(* (sqrt 2) t)

rewrite54.0ms

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)
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))

series687.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
478.0ms
(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))
76.0ms
(* (sqrt 2) t)
45.0ms
(/ (* (* t t) 4) x)

simplify8.9s

Counts
96 → 90
Calls
96 calls:
Slowest
552.0ms
(* (* (/ (* (* t t) 4) x) (/ (* (* t t) 4) x)) (/ (* (* t t) 4) x))
392.0ms
(exp (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
383.0ms
(* (* (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)))
274.0ms
(* (* (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))))
223.0ms
(cbrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize83.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
7.6b
(/ (* (* t t) 4) x)
3.8b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.2b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

rewrite93.0ms

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
58.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
31.0ms
(/ (* (* t t) 4) x)
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))

series605.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
410.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
86.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
77.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
33.0ms
(/ (* (* t t) 4) x)

simplify12.7s

Counts
94 → 90
Calls
94 calls:
Slowest
629.0ms
(* (* (* (* (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)))
528.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
517.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
503.0ms
(- (+ (log (* t t)) (log 4)) (log x))
494.0ms
(* (* (/ (* (* t t) 4) x) (/ (* (* t t) 4) x)) (/ (* (* t t) 4) x))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.4b

localize49.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
7.6b
(/ (* (* t t) 4) x)
3.8b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) t)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
16×add-cbrt-cube
14×pow1
11×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×associate-*l* prod-exp cbrt-unprod
6×cbrt-prod pow-prod-down sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* times-frac div-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r* *-commutative fma-udef div-inv associate-/l*
Counts
4 → 83
Calls
4 calls:
Slowest
85.0ms
(* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) t)))
34.0ms
(/ (* (* t t) 4) x)
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))

series704.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
485.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
89.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
84.0ms
(* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) t)))
45.0ms
(/ (* (* t t) 4) x)

simplify11.3s

Counts
99 → 95
Calls
99 calls:
Slowest
572.0ms
(* (* (/ (* (* t t) 4) x) (/ (* (* t t) 4) x)) (/ (* (* t t) 4) x))
458.0ms
(* (* (* (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))))
428.0ms
(* (sqrt 2) (* (* (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) t))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) t))))
371.0ms
(exp (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
334.0ms
(* (sqrt 2) (* (sqrt 2) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t))))

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.4b

regimes791.0ms

Accuracy

74.8% (5.9b remaining)

Error of 9.7b against oracle of 3.8b and baseline of 27.3b

bsearch2.5s

end0.0ms

sample9.2s

Algorithm
intervals
Results
2.8s10387×body80nan
1.6s5077×body80valid
1.0s857×body1280valid
882.0ms1051×body640valid
665.0ms554×body1280nan
583.0ms594×body640nan
474.0ms663×body320valid
256.0ms370×body320nan
194.0ms352×body160valid
75.0ms189×body160nan