Details

Time bar (total: 4.5s)

sample63.0ms

Algorithm
intervals
Results
32.0ms92×body1280valid
9.0ms133×body80valid
5.0ms20×body640valid
2.0ms9×body320valid
0.0ms2×body160valid

simplify4.0ms

Counts
1 → 1

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize10.0ms

Local error

Found 1 expressions with local error:

1.5b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 14
Calls
1 calls:
6.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series96.0ms

Counts
1 → 3
Calls
1 calls:
96.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify55.0ms

Counts
17 → 17

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.0b
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
10×add-sqr-sqrt add-log-exp
8×add-exp-log add-cbrt-cube
5×add-cube-cbrt times-frac
4×flip3-- associate-*r/ associate-/r* frac-sub flip-- associate-/l/
3×pow1 diff-log distribute-lft-out distribute-lft-out--
2×cbrt-undiv sub-neg flip3-+ div-exp associate--l+ associate-/r/ flip-+ difference-of-squares
1×+-commutative associate--l- frac-2neg prod-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
3 → 63
Calls
3 calls:
60.0ms
(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
6.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
40.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series319.0ms

Counts
3 → 9
Calls
3 calls:
195.0ms
(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
87.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
37.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

simplify39.0ms

Counts
72 → 72

prune186.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b
(/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
0.1b
(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
1.0b
(- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
60×times-frac
55×add-sqr-sqrt
48×frac-sub
43×add-cube-cbrt
41×frac-times
39×flip3-- flip--
29×associate-*r/ associate-*l/
26×associate-/l/
18×add-exp-log add-cbrt-cube
13×swap-sqr associate-*r* associate-*l*
11×pow1 distribute-lft-out
8×add-log-exp
7×difference-of-squares
5×cbrt-undiv div-exp associate-/r* div-inv distribute-lft-out--
4×prod-exp associate--l+ associate-/r/ cbrt-unprod associate-/l* unswap-sqr
3×sub-neg
2×distribute-rgt-in distribute-lft-in flip3-+ frac-add flip-+
1×+-commutative pow2 frac-2neg pow-plus diff-log div-sub pow-prod-down clear-num sum-log pow-sqr *-commutative pow-prod-up
Counts
4 → 192
Calls
4 calls:
5.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
94.0ms
(/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
26.0ms
(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
25.0ms
(- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
104.0ms
(/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
27.0ms
(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
60.0ms
(- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

simplify48.0ms

Counts
204 → 204

prune669.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 13.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.1b
(pow (/ 0.5 (hypot 1.0 x)) 6)
1.0b
(- (* (- 1.0 0.5) (- 1.0 0.5)) (cbrt (pow (/ 0.5 (hypot 1.0 x)) 6)))
12.7b
(cbrt (pow (/ 0.5 (hypot 1.0 x)) 6))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
28×unpow-prod-down
25×add-sqr-sqrt
22×*-un-lft-identity
21×cbrt-prod
20×add-cube-cbrt
19×times-frac
8×add-log-exp
7×add-exp-log
5×pow1 difference-of-squares
4×associate--l+ add-cbrt-cube
3×sub-neg pow-unpow sqr-pow
2×distribute-rgt-in distribute-lft-in pow-exp div-inv
1×+-commutative pow-to-exp flip3-- pow-pow flip3-+ pow1/3 diff-log div-exp sum-log flip-- flip-+ distribute-lft-out
Counts
4 → 86
Calls
4 calls:
5.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms
(pow (/ 0.5 (hypot 1.0 x)) 6)
44.0ms
(- (* (- 1.0 0.5) (- 1.0 0.5)) (cbrt (pow (/ 0.5 (hypot 1.0 x)) 6)))
5.0ms
(cbrt (pow (/ 0.5 (hypot 1.0 x)) 6))

series237.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
54.0ms
(pow (/ 0.5 (hypot 1.0 x)) 6)
59.0ms
(- (* (- 1.0 0.5) (- 1.0 0.5)) (cbrt (pow (/ 0.5 (hypot 1.0 x)) 6)))
41.0ms
(cbrt (pow (/ 0.5 (hypot 1.0 x)) 6))

simplify45.0ms

Counts
98 → 98

prune329.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 13.3b

regimes32.0ms

Accuracy

0% (0.2b remaining)

Error of 14.7b against oracle of 14.4b and baseline of 14.7b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
816.0ms2838×body1280valid
436.0ms607×body640valid
193.0ms4087×body80valid
38.0ms327×body320valid
11.0ms141×body160valid