Details

Time bar (total: 18.5s)

sample140.0ms

Algorithm
intervals
Results
72.0ms76×body1280valid
26.0ms45×body640valid
15.0ms23×body2560valid
7.0ms21×body320valid
6.0ms73×body80valid
4.0ms18×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize36.0ms

Local error

Found 3 expressions with local error:

4.4b
(log (+ x (hypot 1 x)))
0.7b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite9.0ms

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
5.0ms
(+ x (hypot 1 x))
4.0ms
(log (+ x (hypot 1 x)))
0.0ms
(hypot 1 x)

series355.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
194.0ms
(log (+ x (hypot 1 x)))
99.0ms
(+ x (hypot 1 x))
61.0ms
(hypot 1 x)

simplify2.4s

Counts
20 → 56
Calls
20 calls:
Slowest
371.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
313.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
262.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
256.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
237.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune538.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

13.8b
(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)

rewrite18.0ms

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
16.0ms
(* 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)

series313.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
180.0ms
(fma 3/40 (pow x 5) x)
107.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
26.0ms
(* x -1/6)

simplify1.1s

Counts
18 → 52
Calls
18 calls:
Slowest
209.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
181.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
173.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
173.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
169.0ms
(+ x (* 3/40 (pow x 5)))

prune523.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

10.3b
(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))
4.4b
(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
0.3b
(cbrt (hypot 1 x))
0.3b
(cbrt (hypot 1 x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×log-prod fma-def
2×log-div flip3-+ pow1/3 flip-+
1×+-commutative sum-log rem-log-exp log-pow
Counts
4 → 62
Calls
4 calls:
Slowest
12.0ms
(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))
6.0ms
(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
1.0ms
(cbrt (hypot 1 x))
1.0ms
(cbrt (hypot 1 x))

series616.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
189.0ms
(cbrt (hypot 1 x))
179.0ms
(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
165.0ms
(cbrt (hypot 1 x))
83.0ms
(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

simplify3.9s

Counts
27 → 74
Calls
27 calls:
Slowest
408.0ms
(log (+ (pow x 3) (pow (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))) 3)))
400.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
313.0ms
(- (+ (pow (/ -1 x) -1/3) (* 1/6 (pow (/ -1 (pow x 5)) 1/3))) (* 5/72 (pow (/ -1 (pow x 11)) 1/3)))
298.0ms
(- (+ (pow (/ 1 x) -1/3) (* 1/6 (pow (/ 1 (pow x 5)) 1/3))) (* 5/72 (pow (/ 1 (pow x 11)) 1/3)))
281.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))

prune642.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

4.4b
(log (+ (hypot 1 x) x))
0.7b
(+ (hypot 1 x) x)
0.0b
(hypot 1 x)

rewrite11.0ms

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
6.0ms
(+ (hypot 1 x) x)
3.0ms
(log (+ (hypot 1 x) x))
0.0ms
(hypot 1 x)

series374.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
209.0ms
(log (+ (hypot 1 x) x))
102.0ms
(+ (hypot 1 x) x)
63.0ms
(hypot 1 x)

simplify2.2s

Counts
20 → 56
Calls
20 calls:
Slowest
338.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
268.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
235.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
207.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
203.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune357.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes66.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.3b

bsearch104.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.3s2333×body1280valid
884.0ms1643×body640valid
595.0ms762×body2560valid
280.0ms762×body320valid
266.0ms2064×body80valid
121.0ms436×body160valid