Details

Time bar (total: 1.4m)

sample112.0ms

Algorithm
intervals
Results
94.0ms478×body80valid

simplify975.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
975.0ms
(fabs (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.1b
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
119×add-exp-log
76×prod-exp
75×add-cbrt-cube
48×associate-*l*
46×add-sqr-sqrt
44×cbrt-unprod
40×times-frac
36×pow1
35×*-un-lft-identity
33×add-cube-cbrt
22×pow-prod-down
15×div-exp associate-*l/
14×sqrt-prod
12×frac-add
9×cbrt-undiv
6×frac-times rec-exp flip3-+ 1-exp associate-*r/ flip-+
5×associate-*r* unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 181
Calls
4 calls:
Slowest
1.7s
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
614.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
61.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series486.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
337.0ms
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
89.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
60.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify34.9s

Counts
151 → 191
Calls
151 calls:
Slowest
1.1s
(* 1 (- (* (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))))) (* (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
993.0ms
(* (sqrt PI) (* (+ (* (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x))))) (- (* (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))) 21))
986.0ms
(* (+ (* (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x))))) (- (* (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))) 21)
974.0ms
(* 1 (+ (* (- (* (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x))))) (* (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))))) 21) (* (- (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* 1 (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
963.0ms
(* 1 (+ (pow (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) 3) (pow (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))) 3)))

prune3.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (fabs x) (fabs x)) 2/3)
0.1b
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))))
0.1b
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
0.0b
(fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
20×associate-*l*
17×*-un-lft-identity
16×add-cube-cbrt sqrt-prod
13×pow1 add-cbrt-cube add-exp-log
11×times-frac
9×associate-*r*
6×unswap-sqr
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative fma-udef
2×distribute-rgt-in distribute-lft-in associate-*r/
1×flip3-+ sqrt-div associate-*l/ flip-+ div-inv
Counts
4 → 98
Calls
4 calls:
Slowest
60.0ms
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
24.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))))
14.0ms
(* (* (fabs x) (fabs x)) 2/3)
0.0ms
(fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
327.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))))
182.0ms
(fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))
58.0ms
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
55.0ms
(* (* (fabs x) (fabs x)) 2/3)

simplify8.5s

Counts
69 → 110
Calls
69 calls:
Slowest
458.0ms
(* (sqrt (/ 1 PI)) (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))))
432.0ms
(* (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))) (sqrt (/ 1 PI)))
423.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))
414.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))
389.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (fabs x) (fabs x)) 2/3)
0.1b
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (+ (* (fabs x) (* (* (fabs x) (fabs x)) 2/3)) (* (fabs x) 2)))))
0.1b
(* (fabs x) (* (* (fabs x) (fabs x)) 2/3))
0.0b
(fma (pow (fabs x) 7) 1/21 (+ (* (fabs x) (* (* (fabs x) (fabs x)) 2/3)) (* (fabs x) 2)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×pow1 add-cbrt-cube associate-*l* add-exp-log
16×*-un-lft-identity sqrt-prod
15×add-cube-cbrt
11×times-frac
10×pow-prod-down prod-exp cbrt-unprod
7×associate-*r*
5×unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div associate-*l/ div-inv
Counts
4 → 97
Calls
4 calls:
Slowest
72.0ms
(* (fabs x) (* (* (fabs x) (fabs x)) 2/3))
21.0ms
(* (* (fabs x) (fabs x)) 2/3)
13.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (+ (* (fabs x) (* (* (fabs x) (fabs x)) 2/3)) (* (fabs x) 2)))))
0.0ms
(fma (pow (fabs x) 7) 1/21 (+ (* (fabs x) (* (* (fabs x) (fabs x)) 2/3)) (* (fabs x) 2)))

series680.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
392.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (+ (* (fabs x) (* (* (fabs x) (fabs x)) 2/3)) (* (fabs x) 2)))))
207.0ms
(fma (pow (fabs x) 7) 1/21 (+ (* (fabs x) (* (* (fabs x) (fabs x)) 2/3)) (* (fabs x) 2)))
43.0ms
(* (fabs x) (* (* (fabs x) (fabs x)) 2/3))
38.0ms
(* (* (fabs x) (fabs x)) 2/3)

simplify9.2s

Counts
66 → 109
Calls
66 calls:
Slowest
596.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (* (fabs x) (fabs x)) 2/3) (* (* (fabs x) (fabs x)) 2/3)) (* (* (fabs x) (fabs x)) 2/3)))
522.0ms
(* (sqrt (/ 1 (sqrt PI))) (sqrt (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (+ (* (fabs x) (* (* (fabs x) (fabs x)) 2/3)) (* (fabs x) 2))))))
472.0ms
(* (sqrt (/ 1 PI)) (fma (pow (fabs x) 7) 1/21 (+ (* (fabs x) (* (* (fabs x) (fabs x)) 2/3)) (* (fabs x) 2))))
464.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* 2/3 2/3) 2/3)))
377.0ms
(* (fma (pow (fabs x) 7) 1/21 (+ (* (fabs x) (* (* (fabs x) (fabs x)) 2/3)) (* (fabs x) 2))) (sqrt (/ 1 PI)))

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/5 (pow (fabs x) 5))
0.1b
(* (fma 1/21 (pow (fabs x) 7) (* (fma (* (fabs x) (fabs x)) 2/3 2) (fabs x))) (sqrt (/ 1 PI)))
0.1b
(* (* 1/5 (pow (fabs x) 5)) (sqrt (/ 1 PI)))
0.1b
(* (fma (* (fabs x) (fabs x)) 2/3 2) (fabs x))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt associate-*r*
29×sqrt-prod
27×*-un-lft-identity
26×add-cube-cbrt
23×add-exp-log
20×times-frac
15×add-cbrt-cube
12×prod-exp
10×pow1 associate-*l*
8×unswap-sqr
6×cbrt-unprod
4×expm1-log1p-u unpow-prod-down *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down
2×pow-to-exp sqrt-div pow-exp associate-*r/ div-inv sqr-pow
Counts
4 → 123
Calls
4 calls:
Slowest
23.0ms
(* (* 1/5 (pow (fabs x) 5)) (sqrt (/ 1 PI)))
9.0ms
(* (fma 1/21 (pow (fabs x) 7) (* (fma (* (fabs x) (fabs x)) 2/3 2) (fabs x))) (sqrt (/ 1 PI)))
8.0ms
(* 1/5 (pow (fabs x) 5))
5.0ms
(* (fma (* (fabs x) (fabs x)) 2/3 2) (fabs x))

series544.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
266.0ms
(* (fma 1/21 (pow (fabs x) 7) (* (fma (* (fabs x) (fabs x)) 2/3 2) (fabs x))) (sqrt (/ 1 PI)))
151.0ms
(* (* 1/5 (pow (fabs x) 5)) (sqrt (/ 1 PI)))
65.0ms
(* 1/5 (pow (fabs x) 5))
63.0ms
(* (fma (* (fabs x) (fabs x)) 2/3 2) (fabs x))

simplify10.1s

Counts
95 → 135
Calls
95 calls:
Slowest
519.0ms
(* (cbrt (fma 1/21 (pow (fabs x) 7) (* (fma (* (fabs x) (fabs x)) 2/3 2) (fabs x)))) (cbrt (fma 1/21 (pow (fabs x) 7) (* (fma (* (fabs x) (fabs x)) 2/3 2) (fabs x)))))
454.0ms
(* (* (* (fma (* (fabs x) (fabs x)) 2/3 2) (fma (* (fabs x) (fabs x)) 2/3 2)) (fma (* (fabs x) (fabs x)) 2/3 2)) (* (* (fabs x) (fabs x)) (fabs x)))
436.0ms
(sqrt (fma 1/21 (pow (fabs x) 7) (* (fma (* (fabs x) (fabs x)) 2/3 2) (fabs x))))
410.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))
406.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))

prune2.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes356.0ms

Accuracy

0% (0.1b remaining)

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

bsearch6.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
5.5s14036×body80valid