Details

Time bar (total: 5.1m)

sample1.3s

Algorithm
intervals
Results
1.2s3481×body80valid

simplify1.1s

Counts
1 → 1
Calls
1 calls:
Slowest
1.1s
(* (* (/ 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))))))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize105.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.5b
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.4b
(* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8)))
0.3b
(* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x)))

rewrite435.0ms

Algorithm
rewrite-expression-head
Rules
1278×add-exp-log
644×div-exp
538×prod-exp
337×times-frac
270×add-cbrt-cube
242×add-sqr-sqrt
174×*-un-lft-identity
157×add-cube-cbrt
142×rec-exp 1-exp
110×cbrt-undiv
106×cbrt-unprod
92×pow1
59×associate-*r*
49×swap-sqr
45×associate-*l*
40×pow-div
37×frac-times
33×div-inv
29×associate-*l/
28×unswap-sqr
26×pow-flip inv-pow
25×pow-prod-up
15×associate-*r/
12×pow-prod-down
9×flip3-+ flip-+
7×pow-sqr
4×un-div-inv insert-posit16 add-log-exp
3×*-commutative sqrt-prod
1×pow2 distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow-plus pow1/2
Counts
4 → 575
Calls
4 calls:
Slowest
287.0ms
(* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8)))
67.0ms
(* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x)))
45.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series241.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
123.0ms
(* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8)))
61.0ms
(* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x)))
57.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify2.6m

Counts
680 → 585
Calls
680 calls:
Slowest
1.3s
(* (* (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ (* (* 1 1) 1) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) (* (* (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8)) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8))) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8))))
1.1s
(* (* (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))) (/ (* (* 1 1) 1) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8)) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8))) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8))))
1.1s
(* (* (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x)))) (/ (* (* 1 1) 1) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8)) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8))) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8))))
1.1s
(* (* (* (/ (/ (* (* 1 1) 1) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))) (/ (* (* 1 1) 1) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8)) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8))) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8))))
1.1s
(* (* (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))) (/ (* (* 1 1) 1) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8)) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8))) (+ 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) 15/8))))

prune9.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize94.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
496×times-frac
265×*-un-lft-identity
250×add-sqr-sqrt
249×add-cube-cbrt
60×associate-/l*
33×add-exp-log
23×div-inv
20×add-cbrt-cube div-exp
15×unpow-prod-down
13×pow1 associate-/r*
10×cbrt-undiv
8×distribute-lft-out
6×pow-div
5×sqr-pow
4×insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg sqrt-prod
2×rec-exp 1-exp pow-flip inv-pow
1×pow-to-exp rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-exp flip-+
Counts
4 → 342
Calls
4 calls:
Slowest
48.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
13.0ms
(/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))
7.0ms
(/ (/ 1 (fabs x)) (fabs x))
2.0ms
(sqrt PI)

series210.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
131.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
55.0ms
(/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))
24.0ms
(/ (/ 1 (fabs x)) (fabs x))
0.0ms
(sqrt PI)

simplify45.3s

Counts
552 → 352
Calls
552 calls:
Slowest
790.0ms
(* (* (/ (+ 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)))) (pow (fabs x) 5)))
603.0ms
(/ (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (fabs x)) (cbrt (fabs x)))) 1) (sqrt (fabs x)))
535.0ms
(/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
527.0ms
(* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x)))
463.0ms
(/ (/ (/ (* (cbrt 1) (cbrt 1)) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (fabs x)) (cbrt (fabs x))))

prune5.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize103.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.5b
(* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x))))
0.4b
(/ (- (* 3/4 3/4) (* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x))))) (* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
0.4b
(* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
55×add-exp-log
47×add-cbrt-cube
36×add-sqr-sqrt
21×times-frac prod-exp
20×*-un-lft-identity
18×add-cube-cbrt
17×cbrt-unprod
16×div-exp
14×cbrt-undiv associate-*l*
13×associate-*r*
12×pow1
7×swap-sqr unswap-sqr
5×associate-*r/ div-inv
4×unpow-prod-down insert-posit16 associate-/l* add-log-exp difference-of-squares
3×flip3-- sqrt-prod flip--
2×distribute-rgt-in pow-to-exp sub-neg distribute-lft-in pow-exp associate-/r/ *-commutative sqr-pow associate-/l/
1×pow2 frac-times rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow-plus pow1/2 div-sub pow-prod-down associate-*l/ pow-sqr pow-prod-up distribute-lft-out--
Counts
4 → 140
Calls
4 calls:
Slowest
66.0ms
(* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x))))
63.0ms
(* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
52.0ms
(/ (- (* 3/4 3/4) (* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x))))) (* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
2.0ms
(sqrt PI)

series414.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
245.0ms
(/ (- (* 3/4 3/4) (* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x))))) (* (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)))))
36.0ms
(* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x))))
0.0ms
(sqrt PI)

simplify37.0s

Counts
173 → 150
Calls
173 calls:
Slowest
1.0s
(/ (* (* (- (* 3/4 3/4) (* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x))))) (- (* 3/4 3/4) (* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x)))))) (- (* 3/4 3/4) (* (/ 15/8 (* (fabs x) (fabs x))) (/ 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)))))) (* (pow (fabs x) 5) (- 3/4 (/ 15/8 (* (fabs x) (fabs x)))))))
935.0ms
(/ (* (* (- (* 3/4 3/4) (* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x))))) (- (* 3/4 3/4) (* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x)))))) (- (* 3/4 3/4) (* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x)))))) (* (* (* (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)))))))
686.0ms
(* (/ (* (* 15/8 15/8) 15/8) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (/ (* (* 15/8 15/8) 15/8) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))))
686.0ms
(* (/ (* (* 15/8 15/8) 15/8) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (/ (* (* 15/8 15/8) 15/8) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))))
590.0ms
(* (/ (* (* 15/8 15/8) 15/8) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (/ 15/8 (* (fabs x) (fabs x))) (/ 15/8 (* (fabs x) (fabs x)))) (/ 15/8 (* (fabs x) (fabs x)))))

prune2.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
83×times-frac
70×*-un-lft-identity
55×add-sqr-sqrt
54×add-cube-cbrt
23×add-exp-log
21×associate-/l*
20×add-cbrt-cube
18×sqrt-prod
15×unpow-prod-down distribute-lft-out
14×associate-/r*
12×div-inv
10×div-exp
8×cbrt-undiv associate-/l/
5×pow1 sqr-pow
4×frac-add insert-posit16 add-log-exp
3×clear-num frac-2neg flip3-+ associate-*r/ flip-+
2×prod-exp cbrt-unprod
1×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp
Counts
4 → 169
Calls
4 calls:
Slowest
259.0ms
(/ (+ (* (exp (* (fabs x) (fabs x))) (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5)))) (/ (exp (* (fabs x) (fabs x))) (fabs x))) (sqrt PI))
46.0ms
(/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5))
15.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series838.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
651.0ms
(/ (+ (* (exp (* (fabs x) (fabs x))) (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5)))) (/ (exp (* (fabs x) (fabs x))) (fabs x))) (sqrt PI))
138.0ms
(/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5))
48.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify41.4s

Counts
248 → 179
Calls
248 calls:
Slowest
876.0ms
(* (* (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5)) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5))) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5)))
841.0ms
(log (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5)))
732.0ms
(/ (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5))) (/ 1 (fabs x))) (sqrt PI))
551.0ms
(/ (* (* (+ (* (exp (* (fabs x) (fabs x))) (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5)))) (/ (exp (* (fabs x) (fabs x))) (fabs x))) (+ (* (exp (* (fabs x) (fabs x))) (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5)))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))) (+ (* (exp (* (fabs x) (fabs x))) (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5)))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))
463.0ms
(* (sqrt PI) (+ (* (* (exp (* (fabs x) (fabs x))) (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5)))) (* (exp (* (fabs x) (fabs x))) (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5))))) (- (* (/ (exp (* (fabs x) (fabs x))) (fabs x)) (/ (exp (* (fabs x) (fabs x))) (fabs x))) (* (* (exp (* (fabs x) (fabs x))) (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (pow (fabs x) 5)))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))

prune2.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes225.0ms

bsearch5.0ms

end0.0ms