Details

Time bar (total: 1.3m)

sample172.0ms

Algorithm
intervals
Results
143.0ms457×body80valid

simplify432.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
431.0ms
(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))))))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize125.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.1b
(* (* (fabs x) (fabs x)) (fabs x))
0.1b
(* (* (fabs x) (fabs x)) (fabs x))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
52×pow1
35×add-cbrt-cube add-exp-log
18×prod-exp cbrt-unprod
17×add-sqr-sqrt
15×associate-*l*
14×*-un-lft-identity add-cube-cbrt
12×pow-plus pow-prod-down pow-prod-up
9×times-frac
7×associate-*r*
4×pow2 pow-sqr insert-posit16 add-log-exp
3×cbrt-undiv div-exp *-commutative sqrt-prod
2×pow3 unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ div-inv
Counts
4 → 111
Calls
4 calls:
Slowest
87.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
18.0ms
(* (* (fabs x) (fabs x)) (fabs x))
15.0ms
(* (* (fabs x) (fabs x)) (fabs x))
2.0ms
(sqrt PI)

series147.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
74.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
42.0ms
(* (* (fabs x) (fabs x)) (fabs x))
31.0ms
(* (* (fabs x) (fabs x)) (fabs x))
0.0ms
(sqrt PI)

simplify6.4s

Counts
92 → 121
Calls
92 calls:
Slowest
490.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
486.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
394.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
372.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
351.0ms
(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))))))

prune2.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.1b
(* (* (fabs x) (fabs x)) (fabs x))
0.1b
(* (* (fabs x) (fabs x)) (fabs x))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
52×pow1
35×add-cbrt-cube add-exp-log
18×prod-exp cbrt-unprod
17×add-sqr-sqrt
15×associate-*l*
14×*-un-lft-identity add-cube-cbrt
12×pow-plus pow-prod-down pow-prod-up
9×times-frac
7×associate-*r*
4×pow2 pow-sqr insert-posit16 add-log-exp
3×cbrt-undiv div-exp *-commutative sqrt-prod
2×pow3 unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ div-inv
Counts
4 → 111
Calls
4 calls:
Slowest
88.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
32.0ms
(* (* (fabs x) (fabs x)) (fabs x))
30.0ms
(* (* (fabs x) (fabs x)) (fabs x))
2.0ms
(sqrt PI)

series147.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
60.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
44.0ms
(* (* (fabs x) (fabs x)) (fabs x))
42.0ms
(* (* (fabs x) (fabs x)) (fabs x))
0.0ms
(sqrt PI)

simplify6.5s

Counts
92 → 121
Calls
92 calls:
Slowest
519.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
515.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
454.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
385.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
377.0ms
(* (* (* (/ 2 3) (/ 2 3)) (/ 2 3)) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))))

prune2.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.3b
(/ (+ (* 2/3 (* (* (fabs x) (fabs x)) (fabs x))) (+ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* 1/21 (* (fabs x) (fabs x))))) (* (fabs x) 2))) (sqrt PI))
0.2b
(* 1/21 (* (fabs x) (fabs x)))
0.2b
(* 2/3 (* (* (fabs x) (fabs x)) (fabs x)))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube add-exp-log
19×pow1
18×times-frac
15×sqrt-prod
9×pow-prod-down prod-exp cbrt-unprod
6×associate-/r* associate-*l*
4×insert-posit16 add-log-exp
3×associate-/l*
2×associate-*r* *-commutative associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp flip-+ div-inv unswap-sqr
Counts
4 → 98
Calls
4 calls:
Slowest
1.8s
(/ (+ (* 2/3 (* (* (fabs x) (fabs x)) (fabs x))) (+ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* 1/21 (* (fabs x) (fabs x))))) (* (fabs x) 2))) (sqrt PI))
63.0ms
(* 2/3 (* (* (fabs x) (fabs x)) (fabs x)))
25.0ms
(* 1/21 (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series835.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
717.0ms
(/ (+ (* 2/3 (* (* (fabs x) (fabs x)) (fabs x))) (+ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* 1/21 (* (fabs x) (fabs x))))) (* (fabs x) 2))) (sqrt PI))
71.0ms
(* 2/3 (* (* (fabs x) (fabs x)) (fabs x)))
47.0ms
(* 1/21 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify18.8s

Counts
85 → 108
Calls
85 calls:
Slowest
1.1s
(/ (* (* (+ (* 2/3 (* (* (fabs x) (fabs x)) (fabs x))) (+ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* 1/21 (* (fabs x) (fabs x))))) (* (fabs x) 2))) (+ (* 2/3 (* (* (fabs x) (fabs x)) (fabs x))) (+ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* 1/21 (* (fabs x) (fabs x))))) (* (fabs x) 2)))) (+ (* 2/3 (* (* (fabs x) (fabs x)) (fabs x))) (+ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* 1/21 (* (fabs x) (fabs x))))) (* (fabs x) 2)))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))
604.0ms
(* (* (* 2/3 2/3) 2/3) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))))
533.0ms
(- (* (* 2/3 (* (* (fabs x) (fabs x)) (fabs x))) (* 2/3 (* (* (fabs x) (fabs x)) (fabs x)))) (* (+ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* 1/21 (* (fabs x) (fabs x))))) (* (fabs x) 2)) (+ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* 1/21 (* (fabs x) (fabs x))))) (* (fabs x) 2))))
522.0ms
(/ (sqrt (+ (* 2/3 (* (* (fabs x) (fabs x)) (fabs x))) (+ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* 1/21 (* (fabs x) (fabs x))))) (* (fabs x) 2)))) (sqrt 1))
503.0ms
(/ (cbrt (+ (* 2/3 (* (* (fabs x) (fabs x)) (fabs x))) (+ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* 1/21 (* (fabs x) (fabs x))))) (* (fabs x) 2)))) (sqrt (sqrt PI)))

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.0b
(sqrt PI)
0.3b
(* (/ 1 (sqrt (sqrt PI))) (/ (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (sqrt (sqrt PI))))
0.2b
(* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x)))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
48×add-exp-log sqrt-prod
42×times-frac
33×*-un-lft-identity
32×associate-*l*
30×add-cbrt-cube add-cube-cbrt
19×prod-exp
16×associate-*r*
14×div-exp
13×pow1
11×cbrt-unprod
8×unswap-sqr
7×cbrt-undiv
4×pow-prod-down insert-posit16 add-log-exp
3×rec-exp 1-exp associate-*r/
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
1×distribute-rgt-in frac-times distribute-lft-in flip3-+ associate-*l/ flip-+
Counts
4 → 134
Calls
4 calls:
Slowest
114.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (sqrt (sqrt PI))))
41.0ms
(* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x)))))
2.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series487.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
343.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (sqrt (sqrt PI))))
144.0ms
(* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x)))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify26.5s

Counts
111 → 142
Calls
111 calls:
Slowest
1.8s
(* (/ (* (* 1 1) 1) (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI)))) (/ (* (* (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2))) (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2))) (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI)))))
1.8s
(* (* (* (/ 1 (sqrt (sqrt PI))) (/ 1 (sqrt (sqrt PI)))) (/ 1 (sqrt (sqrt PI)))) (/ (* (* (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2))) (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2))) (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI)))))
979.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI)))) (* (* (/ (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (sqrt (sqrt PI))) (/ (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (sqrt (sqrt PI)))) (/ (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (sqrt (sqrt PI)))))
736.0ms
(* (sqrt (/ 1 (sqrt (sqrt PI)))) (sqrt (/ (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (sqrt (sqrt PI)))))
576.0ms
(* (* (* (/ 1 (sqrt (sqrt PI))) (/ 1 (sqrt (sqrt PI)))) (/ 1 (sqrt (sqrt PI)))) (* (* (/ (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (sqrt (sqrt PI))) (/ (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (sqrt (sqrt PI)))) (/ (* (fabs x) (+ (* (* (fabs x) (fabs x)) (+ 2/3 (* (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) (fabs x))))) 2)) (sqrt (sqrt PI)))))

prune2.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes93.0ms

Accuracy

0% (0.2b remaining)

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

bsearch16.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
5.1s13938×body80valid