Details

Time bar (total: 1.7m)

sample154.0ms

Algorithm
intervals
Results
82.0ms73×body1280valid
27.0ms51×body640valid
20.0ms31×body2560valid
7.0ms22×body320valid
6.0ms64×body80valid
3.0ms15×body160valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.4b

localize17.0ms

Local error

Found 3 expressions with local error:

2.8b
(log (+ x (hypot 1 x)))
0.9b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube insert-posit16 log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef sum-log rem-log-exp log-pow
Counts
3 → 47
Calls
3 calls:
Slowest
4.0ms
(+ x (hypot 1 x))
3.0ms
(log (+ x (hypot 1 x)))
0.0ms
(hypot 1 x)

series297.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
149.0ms
(log (+ x (hypot 1 x)))
89.0ms
(+ x (hypot 1 x))
59.0ms
(hypot 1 x)

simplify2.0s

Counts
20 → 56
Calls
20 calls:
Slowest
295.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
285.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
207.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
167.0ms
(log (+ (pow x 3) (pow (hypot 1 x) 3)))
167.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune418.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

15.1b
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.3b
(* x -1/6)
0.0b
(fma 3/40 (pow x 5) x)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 43
Calls
3 calls:
Slowest
6.0ms
(* x -1/6)
0.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.0ms
(fma 3/40 (pow x 5) x)

series682.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
575.0ms
(fma 3/40 (pow x 5) x)
81.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
26.0ms
(* x -1/6)

simplify1.2s

Counts
18 → 52
Calls
18 calls:
Slowest
190.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
181.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
164.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
161.0ms
(+ x (* 3/40 (pow x 5)))
155.0ms
(+ x (* 3/40 (pow x 5)))

prune523.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

18.0b
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
11.2b
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
0.2b
(/ 1/16 (pow x 5))
0.1b
(/ (/ 1/8 x) (* x x))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
224×times-frac
212×*-un-lft-identity
114×add-sqr-sqrt
100×add-cube-cbrt
85×prod-diff
36×distribute-lft-out
22×add-exp-log
18×add-cbrt-cube
17×fma-neg
16×div-inv associate-/l*
12×unpow-prod-down
9×div-exp add-log-exp
8×log-prod associate-/r*
7×cbrt-undiv
6×frac-sub difference-of-squares
5×pow1 log-div
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out-- sqr-pow
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add prod-exp cbrt-unprod flip-+ flip--
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp log-pow associate--r+ associate-/l/
Counts
4 → 249
Calls
4 calls:
Slowest
115.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
77.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
13.0ms
(/ (/ 1/8 x) (* x x))
9.0ms
(/ 1/16 (pow x 5))

series380.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
89.0ms
(/ 1/16 (pow x 5))
75.0ms
(/ (/ 1/8 x) (* x x))
61.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))

simplify1.0m

Counts
329 → 261
Calls
329 calls:
Slowest
680.0ms
(fma (- (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) 1 (* (+ (/ 1/16 (pow x 5)) (/ 1/2 x)) 1))
457.0ms
(fma (/ (/ (* (cbrt 1/8) (cbrt 1/8)) 1) x) (/ (/ (cbrt 1/8) x) x) (- (* (+ (/ 1/16 (pow x 5)) (/ 1/2 x)) (/ 1 1))))
457.0ms
(fma (/ (* (cbrt (/ 1/8 x)) (cbrt (/ 1/8 x))) x) (/ (cbrt (/ 1/8 x)) x) (- (* (sqrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) (sqrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))))
423.0ms
(fma (/ (/ (* (cbrt 1/8) (cbrt 1/8)) 1) x) (/ (/ (cbrt 1/8) x) x) (- (* (cbrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) (* (cbrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) (cbrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))))))
418.0ms
(log (- (* (/ 1/8 x) (+ (* (/ 1/16 (pow x 5)) (/ 1/16 (pow x 5))) (- (* (/ 1/2 x) (/ 1/2 x)) (* (/ 1/16 (pow x 5)) (/ 1/2 x))))) (* (* x x) (+ (pow (/ 1/16 (pow x 5)) 3) (pow (/ 1/2 x) 3)))))

prune2.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

11.6b
(- (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))) (/ 1/4 (* x x)))
0.5b
(/ 1/4 (* x x))
0.1b
(/ 3/32 (* (* x x) (* x x)))
0.1b
(* (* x x) (* x x))

rewrite498.0ms

Algorithm
rewrite-expression-head
Rules
124×pow1
57×*-un-lft-identity
39×add-cbrt-cube add-exp-log
36×pow-prod-up
35×prod-diff
30×add-sqr-sqrt
26×add-cube-cbrt
23×pow-prod-down
22×times-frac pow-sqr
18×pow-plus distribute-lft-out
17×prod-exp cbrt-unprod
13×pow2
9×log-pow
8×add-log-exp
7×cbrt-undiv div-exp div-inv
6×associate-/l*
5×fma-neg
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-out--
2×clear-num associate-/r* frac-2neg diff-log frac-sub difference-of-squares
1×sum-log sub-neg flip3-+ flip3-- swap-sqr associate-*r* associate-*l* associate--l+ *-commutative flip-+ flip-- unswap-sqr
Counts
4 → 184
Calls
4 calls:
Slowest
416.0ms
(- (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))) (/ 1/4 (* x x)))
43.0ms
(* (* x x) (* x x))
27.0ms
(/ 3/32 (* (* x x) (* x x)))
6.0ms
(/ 1/4 (* x x))

series289.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(- (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))) (/ 1/4 (* x x)))
66.0ms
(/ 3/32 (* (* x x) (* x x)))
59.0ms
(* (* x x) (* x x))
48.0ms
(/ 1/4 (* x x))

simplify21.9s

Counts
196 → 196
Calls
196 calls:
Slowest
756.0ms
(fma 1 (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))) (- (* (/ (sqrt 1/4) x) (/ (sqrt 1/4) x))))
479.0ms
(fma 1 (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))) (- (* (/ 1/4 (* x x)) 1)))
475.0ms
(fma 1 (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))) (- (* (/ (sqrt 1/4) x) (/ (sqrt 1/4) x))))
456.0ms
(fma 1 (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))) (- (* (/ 1/4 (* x x)) 1)))
442.0ms
(fma 1 (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))) (- (* (/ 1 (* x x)) 1/4)))

prune1.6s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch114.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.1s2251×body1280valid
829.0ms1629×body640valid
513.0ms811×body2560valid
265.0ms725×body320valid
186.0ms2148×body80valid
97.0ms436×body160valid