Details

Time bar (total: 2.1m)

sample92.0ms

Algorithm
intervals
Results
44.0ms75×body1280valid
19.0ms50×body640valid
9.0ms20×body2560valid
6.0ms25×body320valid
5.0ms75×body80valid
2.0ms11×body160valid

simplify24.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
24.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize9.0ms

Local error

Found 3 expressions with local error:

2.6b
(log (+ x (hypot 1 x)))
0.6b
(+ 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)

series331.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
159.0ms
(log (+ x (hypot 1 x)))
105.0ms
(+ x (hypot 1 x))
67.0ms
(hypot 1 x)

simplify3.9s

Counts
59 → 56
Calls
59 calls:
Slowest
380.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
378.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
329.0ms
(- (+ (* 1/2 (pow x 2)) 1) (* 1/8 (pow x 4)))
301.0ms
(* (* (+ x (hypot 1 x)) (+ x (hypot 1 x))) (+ x (hypot 1 x)))
279.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))

prune589.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 3 expressions with local error:

13.4b
(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)

rewrite12.0ms

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
10.0ms
(* x -1/6)
1.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.0ms
(fma 3/40 (pow x 5) x)

series344.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
210.0ms
(fma 3/40 (pow x 5) x)
108.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
24.0ms
(* x -1/6)

simplify3.8s

Counts
52 → 52
Calls
52 calls:
Slowest
492.0ms
(* (* (fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x)) (fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))) (fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x)))
392.0ms
(* (cbrt (fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))) (cbrt (fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))))
221.0ms
(* (* (fma 3/40 (pow x 5) x) (fma 3/40 (pow x 5) x)) (fma 3/40 (pow x 5) x))
201.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
198.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune481.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

2.6b
(log (sqrt (+ x (hypot 1 x))))
2.6b
(log (sqrt (+ x (hypot 1 x))))
0.6b
(+ x (hypot 1 x))
0.6b
(+ x (hypot 1 x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×log-prod
10×add-sqr-sqrt add-cube-cbrt
8×pow1 sqrt-prod add-log-exp
6×fma-def add-exp-log log-pow
4×expm1-log1p-u log-div flip3-+ add-cbrt-cube sqrt-div flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
2×+-commutative sum-log sqrt-pow1 pow1/2 rem-log-exp
Counts
4 → 82
Calls
4 calls:
Slowest
4.0ms
(+ x (hypot 1 x))
4.0ms
(+ x (hypot 1 x))
4.0ms
(log (sqrt (+ x (hypot 1 x))))
4.0ms
(log (sqrt (+ x (hypot 1 x))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
177.0ms
(log (sqrt (+ x (hypot 1 x))))
167.0ms
(log (sqrt (+ x (hypot 1 x))))
73.0ms
(+ x (hypot 1 x))
69.0ms
(+ x (hypot 1 x))

simplify5.4s

Counts
106 → 94
Calls
106 calls:
Slowest
577.0ms
(- (+ (* 1/2 x) (* 3/80 (pow x 5))) (* 1/12 (pow x 3)))
354.0ms
(log (sqrt (+ (pow x 3) (pow (hypot 1 x) 3))))
321.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
315.0ms
(log (sqrt (+ (pow x 3) (pow (hypot 1 x) 3))))
310.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))

prune809.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

20.1b
(- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))
10.5b
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))))
0.3b
(/ 1/16 (pow x 5))
0.1b
(* x (* x x))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
268×times-frac
200×add-sqr-sqrt
191×*-un-lft-identity
184×add-cube-cbrt
175×prod-diff
85×unpow-prod-down
34×div-inv
29×sqr-pow
25×fma-neg
19×pow1
15×add-exp-log
11×add-cbrt-cube
7×log-prod associate-/r*
6×add-log-exp difference-of-squares
5×log-div pow-prod-up frac-sub
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out--
3×flip3-- div-exp associate-*l* pow-prod-down prod-exp cbrt-unprod flip-- associate-/l*
1×pow2 pow-to-exp cbrt-undiv clear-num sub-neg frac-2neg pow-plus diff-log cube-unmult rem-log-exp associate-*r* pow-exp pow-sqr log-pow *-commutative unswap-sqr
Counts
4 → 320
Calls
4 calls:
Slowest
117.0ms
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))))
66.0ms
(- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))
14.0ms
(* x (* x x))
10.0ms
(/ 1/16 (pow x 5))

series477.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))
132.0ms
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))))
79.0ms
(/ 1/16 (pow x 5))
49.0ms
(* x (* x x))

simplify1.7m

Counts
546 → 332
Calls
546 calls:
Slowest
711.0ms
(fma (/ (* (cbrt 1/16) (cbrt 1/16)) (* (cbrt (pow x 5)) (cbrt (pow x 5)))) (/ (cbrt 1/16) (cbrt (pow x 5))) (- (* (/ 1/8 (* x (* x x))) 1)))
571.0ms
(fma (/ 1 (pow (sqrt x) 5)) (/ 1/16 (pow (sqrt x) 5)) (- (* (sqrt (/ 1/8 (* x (* x x)))) (sqrt (/ 1/8 (* x (* x x)))))))
524.0ms
(fma (/ 1 (sqrt (pow x 5))) (/ 1/16 (sqrt (pow x 5))) (- (* (sqrt (/ 1/8 (* x (* x x)))) (sqrt (/ 1/8 (* x (* x x)))))))
485.0ms
(fma (/ (sqrt 1/16) (sqrt (pow x 5))) (/ (sqrt 1/16) (sqrt (pow x 5))) (- (* (/ (cbrt 1/8) (* x x)) (/ (* (cbrt 1/8) (cbrt 1/8)) x))))
477.0ms
(+ (sqrt (/ 1/16 (pow x 5))) (sqrt (/ 1/8 (* x (* x x)))))

prune2.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.9b

bsearch87.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.9s2320×body1280valid
685.0ms1625×body640valid
377.0ms793×body2560valid
174.0ms753×body320valid
127.0ms2116×body80valid
56.0ms393×body160valid