Details

Time bar (total: 1.2m)

sample194.0ms

Algorithm
intervals
Results
162.0ms427×body80valid

simplify563.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
563.0ms
(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))))))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize118.0ms

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)))))

rewrite2.5s

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)))))
636.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
89.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series510.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
385.0ms
(* (/ 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)))))
64.0ms
(* (/ 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)

simplify34.1s

Counts
151 → 191
Calls
151 calls:
Slowest
1.2s
(* 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))))))
1.1s
(* (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))
980.0ms
(* 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))))))
893.0ms
(* (+ (* (+ (* 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)
887.0ms
(* 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)))

prune3.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize71.0ms

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
(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))

rewrite114.0ms

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
87.0ms
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
14.0ms
(* (* (fabs x) (fabs x)) 2/3)
11.0ms
(* (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)))))
0.0ms
(fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))

series595.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
332.0ms
(* (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)))))
172.0ms
(fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))
50.0ms
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
40.0ms
(* (* (fabs x) (fabs x)) 2/3)

simplify8.9s

Counts
69 → 110
Calls
69 calls:
Slowest
551.0ms
(* (sqrt (/ (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) 2))))))
424.0ms
(* (sqrt (/ 1 PI)) (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))))
416.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))
415.0ms
(* (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))) (sqrt (/ 1 PI)))
407.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))

prune1.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.3b
(/ (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))) (sqrt PI))
0.1b
(fma 2/3 (* (fabs x) (fabs x)) 2)
0.1b
(fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×fma-udef
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 80
Calls
4 calls:
Slowest
9.0ms
(/ (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))) (sqrt PI))
2.0ms
(sqrt PI)
1.0ms
(fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))
0.0ms
(fma 2/3 (* (fabs x) (fabs x)) 2)

series581.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
367.0ms
(/ (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))) (sqrt PI))
166.0ms
(fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))
48.0ms
(fma 2/3 (* (fabs x) (fabs x)) 2)
0.0ms
(sqrt PI)

simplify12.0s

Counts
60 → 90
Calls
60 calls:
Slowest
414.0ms
(/ (* (cbrt (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x))))) (cbrt (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))))) (sqrt (sqrt PI)))
413.0ms
(/ (* (cbrt (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x))))) (cbrt (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))))) (sqrt (sqrt PI)))
396.0ms
(/ (sqrt (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x))))) (sqrt PI))
386.0ms
(/ (sqrt (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x))))) (sqrt 1))
375.0ms
(sqrt (fma 1/5 (pow (fabs x) 5) (fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))))

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize92.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt PI) (cbrt PI))
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
13.0ms
(* (cbrt PI) (cbrt PI))
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(* (cbrt PI) (cbrt PI))
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)

simplify319.0ms

Counts
55 → 89
Calls
55 calls:
Slowest
65.0ms
(* (* (cbrt (cbrt PI)) (cbrt (cbrt PI))) (* (cbrt (cbrt PI)) (cbrt (cbrt PI))))
19.0ms
(sqrt (/ 1 (* (cbrt PI) (cbrt PI))))
12.0ms
(* (cbrt 1) (cbrt 1))
12.0ms
(sqrt (/ 1 (* (cbrt PI) (cbrt PI))))
12.0ms
(sqrt (/ 1 (* (cbrt PI) (cbrt PI))))

prune2.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes65.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
4.3s14054×body80valid