Details

Time bar (total: 1.3m)

sample115.0ms

Algorithm
intervals
Results
93.0ms438×body80valid

simplify546.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
546.0ms
(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))))))

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize110.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
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)))))
0.1b
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 2 3) (* (* (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)))))
690.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
73.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series804.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
680.0ms
(* (/ 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)))))
70.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
53.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify35.4s

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
(* 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)))
1.0s
(* 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))))))
983.0ms
(* (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))
892.0ms
(+ (log (/ 1 5)) (+ (+ (log (* (* (fabs x) (fabs x)) (fabs x))) (log (fabs x))) (log (fabs x))))

prune3.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize76.0ms

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))

rewrite120.0ms

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
88.0ms
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
18.0ms
(* (* (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)))

series630.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
340.0ms
(* (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)))))
175.0ms
(fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2)))
63.0ms
(* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))
53.0ms
(* (* (fabs x) (fabs x)) 2/3)

simplify8.8s

Counts
69 → 110
Calls
69 calls:
Slowest
410.0ms
(* (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))) (sqrt (/ 1 PI)))
387.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))
386.0ms
(* (sqrt (/ 1 PI)) (fma (pow (fabs x) 7) 1/21 (* (fabs x) (+ (* (* (fabs x) (fabs x)) 2/3) 2))))
377.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))
370.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* 2/3 2/3) 2/3))

prune1.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize72.0ms

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 (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))
0.0b
(* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* associate-/l*
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef div-inv unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
11.0ms
(* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x))
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)
0.0ms
(fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))

series572.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
333.0ms
(/ (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))
170.0ms
(fma (pow (fabs x) 7) 1/21 (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x)))
68.0ms
(* (fma 2/3 (* (fabs x) (fabs x)) 2) (fabs x))
0.0ms
(sqrt PI)

simplify14.1s

Counts
70 → 100
Calls
70 calls:
Slowest
579.0ms
(/ (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 (sqrt PI)))
467.0ms
(* (* (* (fma 2/3 (* (fabs x) (fabs x)) 2) (fma 2/3 (* (fabs x) (fabs x)) 2)) (fma 2/3 (* (fabs x) (fabs x)) 2)) (* (* (fabs x) (fabs x)) (fabs x)))
451.0ms
(/ (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 (* (cbrt PI) (cbrt PI))))
438.0ms
(/ (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 (sqrt PI)))
435.0ms
(* (+ 2 (* 2/3 (pow (fabs x) 2))) (fabs x))

prune1.6s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize64.0ms

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)

rewrite10.0ms

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
8.0ms
(* (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)

simplify354.0ms

Counts
55 → 89
Calls
55 calls:
Slowest
77.0ms
(* (* (cbrt (cbrt PI)) (cbrt (cbrt PI))) (* (cbrt (cbrt PI)) (cbrt (cbrt PI))))
20.0ms
(sqrt (/ 1 (* (cbrt PI) (cbrt PI))))
16.0ms
(sqrt (/ 1 (* (cbrt PI) (cbrt PI))))
13.0ms
(* (cbrt 1) (cbrt 1))
11.0ms
(sqrt (/ 1 (* (cbrt PI) (cbrt PI))))

prune1.7s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes289.0ms

Accuracy

0% (0.2b remaining)

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

bsearch9.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
4.6s13845×body80valid