Details

Time bar (total: 2.5m)

sample1.3s

Algorithm
intervals
Results
1.2s3253×body80valid

simplify711.0ms

Calls
1 calls:
Slowest
710.0ms
(* (* (/ 1 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (* (/ 1 2) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 3 4) (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 15 8) (* (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))))

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize48.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
0.3b
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
0.3b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
182×add-exp-log
140×times-frac
110×add-cbrt-cube
103×pow1
90×div-exp
64×pow-div
57×add-sqr-sqrt
55×prod-exp
50×cbrt-undiv
48×*-un-lft-identity
45×add-cube-cbrt
31×cbrt-unprod
30×associate-/l*
21×associate-*l*
16×pow2 pow-plus pow-sqr pow-prod-up pow-flip inv-pow
11×div-inv
8×rec-exp 1-exp
5×unswap-sqr
4×associate-*r* insert-posit16 add-log-exp
3×sqrt-prod
2×frac-times clear-num associate-/r* frac-2neg flip3-+ associate-*r/ flip-+ associate-/l/
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative distribute-lft-out
Calls
4 calls:
Slowest
87.0ms
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
43.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
10.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series241.0ms

Calls
4 calls:
Slowest
109.0ms
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
77.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
55.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify36.7s

Calls
278 calls:
Slowest
1.5s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.3s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.2s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.1s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.1s
(* (/ (* (* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))

prune3.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.3b

localize90.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.3b
(* (/ 1 (pow (fabs x) 5)) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
0.3b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.3b
(/ 1 (pow (fabs x) 5))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
79×times-frac
66×add-sqr-sqrt
55×*-un-lft-identity
50×add-cube-cbrt
45×add-exp-log
25×associate-*l*
23×unpow-prod-down add-cbrt-cube
18×div-exp
16×associate-/l*
12×prod-exp
9×sqr-pow
8×cbrt-undiv associate-/r*
7×pow1 unswap-sqr
6×pow-to-exp rec-exp 1-exp pow-exp
5×div-inv
4×associate-*r* cbrt-unprod insert-posit16 add-log-exp
3×sqrt-prod
2×frac-times clear-num frac-2neg flip3-+ associate-*r/ flip-+
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative pow-flip distribute-lft-out inv-pow associate-/l/
Calls
4 calls:
Slowest
69.0ms
(* (/ 1 (pow (fabs x) 5)) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
19.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
11.0ms
(/ 1 (pow (fabs x) 5))
2.0ms
(sqrt PI)

series205.0ms

Calls
4 calls:
Slowest
116.0ms
(* (/ 1 (pow (fabs x) 5)) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
44.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
44.0ms
(/ 1 (pow (fabs x) 5))
0.0ms
(sqrt PI)

simplify20.9s

Calls
182 calls:
Slowest
713.0ms
(* (/ (* (* 1 1) 1) (* (* (pow (fabs x) 5) (pow (fabs x) 5)) (pow (fabs x) 5))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
577.0ms
(/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 5))
513.0ms
(/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 5))
480.0ms
(+ (- 0 (log (pow (fabs x) 5))) (log (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
472.0ms
(* (/ (sqrt 1) (pow (sqrt (fabs x)) 5)) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))

prune3.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize79.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
0.3b
(* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
0.3b
(/ (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log
32×add-cbrt-cube
24×add-sqr-sqrt
20×*-un-lft-identity
18×times-frac
14×div-exp add-cube-cbrt
12×cbrt-undiv
11×prod-exp associate-/l*
7×associate-*l* cbrt-unprod
6×associate-*r*
5×pow1
4×unpow-prod-down associate-*r/ insert-posit16 div-inv add-log-exp
3×sqrt-prod unswap-sqr associate-/l/
2×distribute-rgt-in pow-to-exp clear-num associate-/r* sub-neg frac-2neg distribute-lft-in flip3-- pow-exp associate-/r/ flip-- distribute-lft-out difference-of-squares sqr-pow
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 *-commutative flip-+ distribute-lft-out--
Calls
4 calls:
Slowest
134.0ms
(/ (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
43.0ms
(* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
27.0ms
(/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series484.0ms

Calls
4 calls:
Slowest
296.0ms
(/ (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
133.0ms
(* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
55.0ms
(/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify15.5s

Calls
95 calls:
Slowest
1.1s
(/ (* (* (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16)) (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16)) (* (* (* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))))
667.0ms
(+ (pow (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 3) (pow 9/16 3))
643.0ms
(/ (* (* (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16)) (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16)) (* (* (* (pow (fabs x) 5) (pow (fabs x) 5)) (pow (fabs x) 5)) (* (* (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))))
574.0ms
(* (- (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
539.0ms
(* (pow (fabs x) 5) (- (/ 15/8 (* (fabs x) (fabs x)))))

prune2.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

localize67.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
0.4b
(/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
0.3b
(/ (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (* (sqrt (pow (fabs x) 5)) (* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
36×add-cbrt-cube add-exp-log
27×add-sqr-sqrt
21×*-un-lft-identity
18×times-frac
15×add-cube-cbrt
13×cbrt-undiv div-exp sqrt-prod
11×associate-/l*
10×associate-*l*
9×prod-exp cbrt-unprod
7×pow1
6×associate-*r* associate-*r/
4×unpow-prod-down insert-posit16 div-inv add-log-exp unswap-sqr
3×associate-/l/
2×distribute-rgt-in clear-num associate-/r* sub-neg frac-2neg distribute-lft-in flip3-- associate-/r/ flip-- distribute-lft-out difference-of-squares sqr-pow
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down *-commutative flip-+ distribute-lft-out--
Calls
4 calls:
Slowest
178.0ms
(/ (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (* (sqrt (pow (fabs x) 5)) (* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))))
41.0ms
(* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
21.0ms
(/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
1.0ms
(sqrt PI)

series367.0ms

Calls
4 calls:
Slowest
210.0ms
(/ (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (* (sqrt (pow (fabs x) 5)) (* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))))
123.0ms
(* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
33.0ms
(/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify17.6s

Calls
99 calls:
Slowest
1.0s
(/ (* (* (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16)) (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16)) (* (* (* (sqrt (pow (fabs x) 5)) (sqrt (pow (fabs x) 5))) (sqrt (pow (fabs x) 5))) (* (* (* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))))))
880.0ms
(/ (* (* (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16)) (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16)) (* (* (* (sqrt (pow (fabs x) 5)) (sqrt (pow (fabs x) 5))) (sqrt (pow (fabs x) 5))) (* (* (* (sqrt (pow (fabs x) 5)) (sqrt (pow (fabs x) 5))) (sqrt (pow (fabs x) 5))) (* (* (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))))))
683.0ms
(/ (* (* (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16) (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16)) (+ (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 9/16)) (* (* (* (sqrt (pow (fabs x) 5)) (* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (* (sqrt (pow (fabs x) 5)) (* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))))) (* (sqrt (pow (fabs x) 5)) (* (sqrt (pow (fabs x) 5)) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))))))
680.0ms
(+ (pow (/ (/ -225/64 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 3) (pow 9/16 3))
451.0ms
(/ (- 9/16 (* 225/64 (/ 1 (pow (fabs x) 4)))) (* (- 3/4 (* 15/8 (/ 1 (pow (fabs x) 2)))) (pow (fabs x) 5)))

prune2.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

regimes408.0ms

Accuracy

0% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 0.7b

bsearch9.0ms

end0.0ms

sample44.0s

Algorithm
intervals
Results
41.6s107501×body80valid