Details

Time bar (total: 1.4m)

sample175.0ms

Algorithm
intervals
Results
69.0ms69×body1280valid
55.0ms59×body640valid
18.0ms21×body2560valid
8.0ms21×body320valid
7.0ms66×body80valid
5.0ms20×body160valid

simplify22.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
22.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.2b

localize8.0ms

Local error

Found 2 expressions with local error:

4.1b
(log (+ x (hypot 1 x)))
1.8b
(+ x (hypot 1 x))

rewrite8.0ms

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
4.0ms
(+ x (hypot 1 x))
3.0ms
(log (+ x (hypot 1 x)))

series265.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
170.0ms
(log (+ x (hypot 1 x)))
95.0ms
(+ x (hypot 1 x))

simplify1.6s

Counts
17 → 42
Calls
17 calls:
Slowest
348.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
303.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
257.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
180.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
135.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune389.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 3 expressions with local error:

15.3b
(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)

rewrite13.0ms

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
12.0ms
(* 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)

series255.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
159.0ms
(fma 3/40 (pow x 5) x)
75.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
20.0ms
(* x -1/6)

simplify1.1s

Counts
18 → 52
Calls
18 calls:
Slowest
172.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
166.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
156.0ms
(+ x (* 3/40 (pow x 5)))
154.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
152.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))

prune434.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

17.7b
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
12.2b
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
0.1b
(/ 1/16 (pow x 5))
0.1b
(/ (/ 1/8 x) (* x x))

rewrite271.0ms

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
147.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
85.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
19.0ms
(/ (/ 1/8 x) (* x x))
10.0ms
(/ 1/16 (pow x 5))

series338.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
66.0ms
(/ 1/16 (pow x 5))
65.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
44.0ms
(/ (/ 1/8 x) (* x x))

simplify1.1m

Counts
329 → 261
Calls
329 calls:
Slowest
709.0ms
(fma (/ 1 x) (/ (/ 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)))))))
682.0ms
(fma (sqrt (/ (/ 1/8 x) (* x x))) (sqrt (/ (/ 1/8 x) (* x x))) (- (* (+ (/ 1/16 (pow x 5)) (/ 1/2 x)) (/ 1 1))))
435.0ms
(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)))))
425.0ms
(- (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (log -1/2))) (* 1/4 (/ 1 (pow x 2))))
423.0ms
(fma (sqrt (/ (/ 1/8 x) (* x x))) (sqrt (/ (/ 1/8 x) (* x x))) (- (* (sqrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) (sqrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))))

prune2.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

20.9b
(log (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))))
17.5b
(fma (* x x) x (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))
12.6b
(log (fma (* x x) x (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))))
10.2b
(- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt pow1 log-prod *-un-lft-identity add-exp-log add-cube-cbrt add-log-exp
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
2×log-div rem-log-exp log-pow
1×sub-neg flip3-+ flip3-- distribute-rgt-out-- fma-neg diff-log prod-diff flip-+ fma-udef flip--
Counts
4 → 61
Calls
4 calls:
Slowest
24.0ms
(log (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))))
14.0ms
(- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))
2.0ms
(log (fma (* x x) x (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))))
0.0ms
(fma (* x x) x (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))

series903.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
309.0ms
(log (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))))
261.0ms
(log (fma (* x x) x (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))))
186.0ms
(- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))
147.0ms
(fma (* x x) x (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))

simplify5.1s

Counts
28 → 73
Calls
28 calls:
Slowest
668.0ms
(- (+ (log 2) (* 3/4 (/ 1 (pow x 2)))) (+ (* 3 (log (/ 1 x))) (* 3/32 (/ 1 (pow x 4)))))
646.0ms
(log (+ (pow (* x x) 3) (pow (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))) 3)))
421.0ms
(+ (* 3/2 x) (+ (* 2 (pow x 3)) (* 3/8 (/ 1 x))))
343.0ms
(log (- (* (* x x) (* x x)) (* (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))))
340.0ms
(- (+ (log 3) (* 1/2 (/ 1 (pow x 2)))) (+ (* 2 (log (/ -1 x))) (* 1/6 (/ 1 (pow x 4)))))

prune671.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes34.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.3b

bsearch123.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.8s2324×body1280valid
769.0ms1561×body640valid
532.0ms817×body2560valid
233.0ms741×body320valid
148.0ms2122×body80valid
72.0ms435×body160valid