Details

Time bar (total: 26.4s)

sample318.0ms

Algorithm
intervals
Results
76.0ms292×body80nan
26.0ms168×body80valid
21.0ms27×body1280valid
20.0ms25×body1280nan
16.0ms29×body640valid
12.0ms22×body640nan
10.0ms22×body320valid
6.0ms12×body320nan
3.0ms10×body160valid
2.0ms6×body160nan

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
62403
5990
4463
3210
299
142
018

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.3b

localize80.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
0.4b
(* (sqrt 2) t)
13.5b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
22.3b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt *-un-lft-identity
40×associate-*l*
29×times-frac
21×add-cube-cbrt
11×add-cbrt-cube add-exp-log
9×pow1
8×difference-of-squares
7×sqrt-prod distribute-lft-out
6×associate-*r* add-log-exp
4×expm1-log1p-u difference-of-sqr-1 insert-posit16 log1p-expm1-u distribute-lft-out-- unswap-sqr
3×flip3-- prod-exp cbrt-unprod flip--
2×distribute-rgt-in frac-times distribute-lft-in flip3-+ sqrt-div pow-prod-down associate--l+ associate-*r/ associate-/r/ *-commutative flip-+
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log div-exp prod-diff associate-*l/ div-inv
Counts
4 → 124
Calls
4 calls:
63.0ms
(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
15.0ms
(* (sqrt 2) t)
54.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
81.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.0s

Counts
4 → 12
Calls
4 calls:
165.0ms
(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
62.0ms
(* (sqrt 2) t)
258.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.5s

Counts
136 → 136
Iterations
IterNodes
23440
1796
0247

prune779.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.0b

localize66.0ms

Local error

Found 4 expressions with local error:

3.8b
(fma (* t t) 2 (fma (/ (* l l) x) 2 (/ 4 (/ x (* t t)))))
7.6b
(/ (* l l) x)
12.3b
(/ x (* t t))
27.8b
(sqrt (fma (* t t) 2 (fma (/ (* l l) x) 2 (/ 4 (/ x (* t t))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×times-frac
5×pow1
4×expm1-log1p-u cbrt-undiv associate-/r* div-exp insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×sqrt-prod
2×clear-num frac-2neg prod-exp cbrt-unprod div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 75
Calls
4 calls:
0.0ms
(fma (* t t) 2 (fma (/ (* l l) x) 2 (/ 4 (/ x (* t t)))))
12.0ms
(/ (* l l) x)
13.0ms
(/ x (* t t))
3.0ms
(sqrt (fma (* t t) 2 (fma (/ (* l l) x) 2 (/ 4 (/ x (* t t))))))

series506.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(fma (* t t) 2 (fma (/ (* l l) x) 2 (/ 4 (/ x (* t t)))))
34.0ms
(/ (* l l) x)
41.0ms
(/ x (* t t))
338.0ms
(sqrt (fma (* t t) 2 (fma (/ (* l l) x) 2 (/ 4 (/ x (* t t))))))

simplify1.3s

Counts
87 → 87
Iterations
IterNodes
33117
2903
1301
0135

prune564.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 4 (/ x (* t t)))
3.8b
(fma (* t t) 2 (fma (/ l (/ x l)) 2 (/ 4 (/ x (* t t)))))
12.3b
(/ x (* t t))
27.8b
(sqrt (fma (* t t) 2 (fma (/ l (/ x l)) 2 (/ 4 (/ x (* t t))))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
24×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
18×add-cbrt-cube add-exp-log
8×associate-/r*
7×cbrt-undiv div-exp
6×div-inv associate-/l*
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×clear-num frac-2neg prod-exp cbrt-unprod
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ fma-udef
Counts
4 → 102
Calls
4 calls:
18.0ms
(/ 4 (/ x (* t t)))
1.0ms
(fma (* t t) 2 (fma (/ l (/ x l)) 2 (/ 4 (/ x (* t t)))))
13.0ms
(/ x (* t t))
3.0ms
(sqrt (fma (* t t) 2 (fma (/ l (/ x l)) 2 (/ 4 (/ x (* t t))))))

series517.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ 4 (/ x (* t t)))
80.0ms
(fma (* t t) 2 (fma (/ l (/ x l)) 2 (/ 4 (/ x (* t t)))))
38.0ms
(/ x (* t t))
366.0ms
(sqrt (fma (* t t) 2 (fma (/ l (/ x l)) 2 (/ 4 (/ x (* t t))))))

simplify2.0s

Counts
114 → 114
Iterations
IterNodes
34244
21098
1383
0174

prune779.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.5b

localize98.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
3.8b
(fma (* t t) 2 (fma (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2 (/ 4 (/ x (* t t)))))
12.3b
(/ x (* t t))
27.8b
(sqrt (fma (* t t) 2 (fma (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2 (/ 4 (/ x (* t t))))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×cbrt-prod
15×*-un-lft-identity add-cube-cbrt
12×pow1
11×add-exp-log
9×add-cbrt-cube
6×pow1/3 swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×times-frac sqrt-prod associate-/l*
2×cbrt-undiv div-exp pow-prod-down prod-exp pow-sqr pow-prod-up cbrt-unprod
1×pow2 rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow-plus pow1/2 *-commutative fma-udef div-inv
Counts
4 → 94
Calls
4 calls:
15.0ms
(* (cbrt x) (cbrt x))
0.0ms
(fma (* t t) 2 (fma (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2 (/ 4 (/ x (* t t)))))
14.0ms
(/ x (* t t))
3.0ms
(sqrt (fma (* t t) 2 (fma (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2 (/ 4 (/ x (* t t))))))

series908.0ms

Counts
4 → 12
Calls
4 calls:
298.0ms
(* (cbrt x) (cbrt x))
134.0ms
(fma (* t t) 2 (fma (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2 (/ 4 (/ x (* t t)))))
41.0ms
(/ x (* t t))
435.0ms
(sqrt (fma (* t t) 2 (fma (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2 (/ 4 (/ x (* t t))))))

simplify1.3s

Counts
106 → 106
Iterations
IterNodes
33231
2918
1332
0152

prune601.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

regimes802.0ms

Accuracy

78% (5.1b remaining)

Error of 9.1b against oracle of 4.0b and baseline of 27.3b

bsearch418.0ms

Steps
ItersRangePoint
6
4.7332403373153464e+123
3.3768436627244136e+124
3.3304656260583313e+124
10
-1.5304224262738304e+84
-6.960410891925428e+71
-6.377624199137871e+80

simplify10.0ms

Iterations
IterNodes
239
139
036

end0.0ms

sample9.6s

Algorithm
intervals
Results
2.5s9884×body80nan
1.5s868×body1280valid
1.4s5062×body80valid
1.0s1015×body640valid
826.0ms686×body320valid
766.0ms613×body1280nan
547.0ms609×body640nan
218.0ms344×body320nan
140.0ms369×body160valid
70.0ms192×body160nan