Details

Time bar (total: 2.2m)

sample159.0ms

Algorithm
intervals
Results
73.0ms82×body1280valid
36.0ms46×body640valid
20.0ms26×body2560valid
10.0ms28×body320valid
5.0ms60×body80valid
3.0ms14×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.4b

localize17.0ms

Local error

Found 2 expressions with local error:

2.3b
(log (+ x (hypot 1 x)))
1.1b
(+ x (hypot 1 x))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
4×add-sqr-sqrt log-prod add-cube-cbrt add-log-exp
3×pow1 fma-def add-exp-log
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
1×+-commutative sum-log rem-log-exp log-pow
Counts
2 → 36
Calls
2 calls:
Slowest
8.0ms
(+ x (hypot 1 x))
7.0ms
(log (+ x (hypot 1 x)))

series273.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
188.0ms
(log (+ x (hypot 1 x)))
85.0ms
(+ x (hypot 1 x))

simplify2.9s

Counts
45 → 42
Calls
45 calls:
Slowest
354.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
321.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
266.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
257.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
243.0ms
(* (* (+ x (hypot 1 x)) (+ x (hypot 1 x))) (+ x (hypot 1 x)))

prune341.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 3 expressions with local error:

13.5b
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.3b
(* x -1/6)
0.1b
(fma 3/40 (pow x 5) x)

rewrite6.0ms

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
5.0ms
(* 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)

series270.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
186.0ms
(fma 3/40 (pow x 5) x)
68.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
16.0ms
(* x -1/6)

simplify3.8s

Counts
52 → 52
Calls
52 calls:
Slowest
494.0ms
(* (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))))
476.0ms
(* (* (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)))
194.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
184.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
184.0ms
(* (* (* x -1/6) (* x -1/6)) (* x -1/6))

prune437.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

18.4b
(- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))
10.7b
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))))
0.1b
(* x (* x x))
0.1b
(/ 1/8 (* x (* x x)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
250×times-frac
186×add-sqr-sqrt
177×*-un-lft-identity
175×prod-diff
170×add-cube-cbrt
73×unpow-prod-down
34×div-inv
25×fma-neg sqr-pow
19×pow1 add-exp-log
18×add-cbrt-cube
7×log-prod
6×prod-exp cbrt-unprod 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×cbrt-undiv flip3-- div-exp associate-*l* pow-prod-down flip-- associate-/l*
1×pow2 clear-num associate-/r* sub-neg frac-2neg pow-plus diff-log cube-unmult rem-log-exp associate-*r* pow-sqr log-pow *-commutative unswap-sqr
Counts
4 → 298
Calls
4 calls:
Slowest
116.0ms
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))))
77.0ms
(- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))
18.0ms
(/ 1/8 (* x (* x x)))
14.0ms
(* x (* x x))

series476.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
187.0ms
(- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))
150.0ms
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* x (* x x))))))
73.0ms
(/ 1/8 (* x (* x x)))
66.0ms
(* x (* x x))

simplify1.9m

Counts
506 → 310
Calls
506 calls:
Slowest
797.0ms
(fma (/ (* (cbrt 1/16) (cbrt 1/16)) (* (cbrt (pow x 5)) (cbrt (pow x 5)))) (/ (cbrt 1/16) (cbrt (pow x 5))) (- (* (/ (sqrt 1/8) (* x x)) (/ (sqrt 1/8) x))))
665.0ms
(fma 1/16 (/ 1 (pow x 5)) (- (* (/ (cbrt 1/8) (* x x)) (/ (* (cbrt 1/8) (cbrt 1/8)) x))))
640.0ms
(fma (- (/ (cbrt 1/8) (* x x))) (/ (* (cbrt 1/8) (cbrt 1/8)) x) (* (/ (cbrt 1/8) (* x x)) (/ (* (cbrt 1/8) (cbrt 1/8)) x)))
639.0ms
(fma (/ 1 (pow (sqrt x) 5)) (/ 1/16 (pow (sqrt x) 5)) (- (* (sqrt (/ 1/8 (* x (* x x)))) (sqrt (/ 1/8 (* x (* x x)))))))
476.0ms
(fma (/ (* (cbrt 1/16) (cbrt 1/16)) (pow 1 5)) (/ (cbrt 1/16) (pow x 5)) (- (* (/ (sqrt 1/8) (* x x)) (/ (sqrt 1/8) x))))

prune2.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.8b

bsearch113.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.5s2370×body1280valid
977.0ms1567×body640valid
430.0ms849×body2560valid
201.0ms780×body320valid
146.0ms2022×body80valid
56.0ms412×body160valid