Details

Time bar (total: 1.5m)

sample156.0ms

Algorithm
intervals
Results
130.0ms442×body80valid

simplify493.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
493.0ms
(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

localize87.0ms

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)))))

rewrite2.6s

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
1.8s
(* (/ 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)))))
682.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
46.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series491.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
369.0ms
(* (/ 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)))))
62.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
60.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (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))))))
1.0s
(* (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))
967.0ms
(* (+ (* (+ (* 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)
948.0ms
(* 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)))
857.0ms
(* 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))))))

prune3.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize50.0ms

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)))))
0.0b
(* (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)))

rewrite110.0ms

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
74.0ms
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
19.0ms
(* (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)))))
15.0ms
(* (* (fabs x) (fabs x)) 2/3)
0.0ms
(fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))

series586.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
338.0ms
(* (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)))))
131.0ms
(fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))
65.0ms
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
53.0ms
(* (* (fabs x) (fabs x)) 2/3)

simplify8.2s

Counts
69 → 110
Calls
69 calls:
Slowest
424.0ms
(* (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))) (sqrt (/ 1 PI)))
387.0ms
(* (sqrt (/ 1 PI)) (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))))
374.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))
369.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))
356.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* 2/3 2/3) 2/3))

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize54.0ms

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
39×associate-*r*
38×add-sqr-sqrt
29×sqrt-prod
25×*-un-lft-identity
24×add-cube-cbrt
21×add-exp-log
20×times-frac
13×add-cbrt-cube
11×prod-exp
8×pow1
7×associate-*l* unswap-sqr
5×cbrt-unprod
4×expm1-log1p-u unpow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-to-exp sqrt-div pow-prod-down pow-exp associate-*r/ div-inv sqr-pow
1×fma-udef
Counts
4 → 113
Calls
4 calls:
Slowest
25.0ms
(* (* 1/5 (pow (fabs x) 5)) (sqrt (/ 1 PI)))
18.0ms
(* (fma 1/21 (pow (fabs x) 7) (* (fabs x) (fma 2/3 (* (fabs x) (fabs x)) 2))) (sqrt (/ 1 PI)))
15.0ms
(* 1/5 (pow (fabs x) 5))
0.0ms
(fma 2/3 (* (fabs x) (fabs x)) 2)

series598.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
273.0ms
(* (fma 1/21 (pow (fabs x) 7) (* (fabs x) (fma 2/3 (* (fabs x) (fabs x)) 2))) (sqrt (/ 1 PI)))
170.0ms
(* (* 1/5 (pow (fabs x) 5)) (sqrt (/ 1 PI)))
92.0ms
(* 1/5 (pow (fabs x) 5))
62.0ms
(fma 2/3 (* (fabs x) (fabs x)) 2)

simplify8.9s

Counts
85 → 125
Calls
85 calls:
Slowest
650.0ms
(* (+ (* 2 (fabs x)) (+ (* 2/3 (pow (fabs x) 3)) (* 1/21 (pow (fabs x) 7)))) (sqrt (/ 1 PI)))
479.0ms
(sqrt (fma 1/21 (pow (fabs x) 7) (* (fabs x) (fma 2/3 (* (fabs x) (fabs x)) 2))))
446.0ms
(* (cbrt (fma 1/21 (pow (fabs x) 7) (* (fabs x) (fma 2/3 (* (fabs x) (fabs x)) 2)))) (cbrt (fma 1/21 (pow (fabs x) 7) (* (fabs x) (fma 2/3 (* (fabs x) (fabs x)) 2)))))
377.0ms
(* (fma 1/21 (pow (fabs x) 7) (* (fabs x) (fma 2/3 (* (fabs x) (fabs x)) 2))) (sqrt (/ 1 PI)))
352.0ms
(+ (+ (log 1/5) (log (pow (fabs x) 5))) (log (sqrt (/ 1 PI))))

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (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))))))
0.2b
(* (sqrt (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)))))
0.2b
(* (* (fabs x) (fabs x)) 2/3)
0.0b
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
65×sqrt-prod
42×associate-*l*
40×add-sqr-sqrt
27×*-un-lft-identity
26×add-cube-cbrt
20×times-frac
18×pow1 add-cbrt-cube add-exp-log
10×sqrt-div associate-*r*
8×pow-prod-down prod-exp cbrt-unprod
7×unswap-sqr
6×distribute-rgt-in distribute-lft-in fma-udef
4×expm1-log1p-u associate-*l/ *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r/
2×div-inv
1×frac-times flip3-+ flip-+
Counts
4 → 135
Calls
4 calls:
Slowest
67.0ms
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (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))))))
48.0ms
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
17.0ms
(* (* (fabs x) (fabs x)) 2/3)
13.0ms
(* (sqrt (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)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
580.0ms
(* (sqrt (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)))))
355.0ms
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (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))))))
64.0ms
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
34.0ms
(* (* (fabs x) (fabs x)) 2/3)

simplify13.1s

Counts
107 → 147
Calls
107 calls:
Slowest
642.0ms
(* (* (* (sqrt (sqrt (/ 1 PI))) (sqrt (sqrt (/ 1 PI)))) (sqrt (sqrt (/ 1 PI)))) (* (* (* (sqrt (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))))) (* (sqrt (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)))))) (* (sqrt (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)))))))
428.0ms
(* (sqrt (sqrt (/ 1 PI))) (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))))
418.0ms
(* (sqrt (sqrt 1)) (* (sqrt (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))))))
401.0ms
(* (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))) (sqrt (sqrt (/ 1 PI))))
398.0ms
(* (* (* (sqrt (sqrt (/ 1 PI))) (sqrt (sqrt (/ 1 PI)))) (sqrt (sqrt (/ 1 PI)))) (* (* (* (sqrt (sqrt (/ 1 PI))) (sqrt (sqrt (/ 1 PI)))) (sqrt (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)))) (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))))) (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))))))

prune2.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes156.0ms

Accuracy

0% (0.1b remaining)

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

bsearch7.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
4.9s13897×body80valid