Details

Time bar (total: 16.8s)

sample128.0ms

Algorithm
intervals
Results
54.0ms66×body1280valid
28.0ms29×body2560valid
18.0ms41×body640valid
10.0ms30×body320valid
6.0ms79×body80valid
2.0ms11×body160valid

simplify11.0ms

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.9b

localize9.0ms

Local error

Found 3 expressions with local error:

2.6b
(log (+ x (hypot 1 x)))
1.0b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite10.0ms

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

series324.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
172.0ms
(log (+ x (hypot 1 x)))
91.0ms
(+ x (hypot 1 x))
60.0ms
(hypot 1 x)

simplify2.3s

Counts
20 → 56
Calls
20 calls:
Slowest
320.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
300.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
264.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
234.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
231.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune495.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

15.5b
(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)

series295.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
165.0ms
(fma 3/40 (pow x 5) x)
104.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
27.0ms
(* x -1/6)

simplify964.0ms

Counts
18 → 52
Calls
18 calls:
Slowest
150.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
141.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
141.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
130.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
121.0ms
(+ x (* 3/40 (pow x 5)))

prune521.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

16.4b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))
2.6b
(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-prod
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×log-prod
2×pow1/3
1×rem-log-exp log-pow fma-udef
Counts
4 → 54
Calls
4 calls:
Slowest
2.0ms
(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))

series892.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
283.0ms
(cbrt x)
274.0ms
(cbrt x)
177.0ms
(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
158.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))

simplify1.5s

Counts
22 → 66
Calls
22 calls:
Slowest
325.0ms
(- (+ (* 1/2 (/ (pow x 2) (+ x 1))) (log (+ x 1))) (+ (* 1/8 (/ (pow x 4) (+ x 1))) (* 1/8 (/ (pow x 4) (pow (+ x 1) 2)))))
322.0ms
(- (+ x (+ (* 1/2 (pow x 2)) 1)) (* 1/8 (pow x 4)))
270.0ms
(- (* 1/2 (/ 1 (pow x 2))) (+ (log (/ -1 x)) 3/2))
142.0ms
(- (+ (* 1/2 (/ 1 (pow x 2))) 1/2) (log (/ 1 x)))
119.0ms
(* (pow (* x -1) 1/3) (cbrt -1))

prune672.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

16.4b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))
16.4b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))
16.4b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))
2.6b
(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt pow1 *-un-lft-identity add-exp-log add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×log-prod fma-udef
1×rem-log-exp log-pow
Counts
4 → 48
Calls
4 calls:
Slowest
2.0ms
(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
1.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))

series759.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
209.0ms
(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
203.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))
183.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))
163.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))

simplify2.0s

Counts
16 → 60
Calls
16 calls:
Slowest
355.0ms
(- (+ x (+ (* 1/2 (pow x 2)) 1)) (* 1/8 (pow x 4)))
327.0ms
(- (+ (* 1/2 (/ (pow x 2) (+ x 1))) (log (+ x 1))) (+ (* 1/8 (/ (pow x 4) (+ x 1))) (* 1/8 (/ (pow x 4) (pow (+ x 1) 2)))))
298.0ms
(- (+ x (+ (* 1/2 (pow x 2)) 1)) (* 1/8 (pow x 4)))
292.0ms
(- (+ x (+ (* 1/2 (pow x 2)) 1)) (* 1/8 (pow x 4)))
238.0ms
(- (* 1/2 (/ 1 (pow x 2))) (+ (log (/ -1 x)) 3/2))

prune627.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.1b

bsearch139.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.7s2366×body1280valid
896.0ms1556×body640valid
653.0ms837×body2560valid
288.0ms740×body320valid
228.0ms2111×body80valid
79.0ms390×body160valid