Details

Time bar (total: 33.3s)

sample174.0ms

Algorithm
intervals
Results
151.0ms431×body80valid

simplify856.0ms

Counts
1 → 1

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.1b
(* (/ 2 3) (* (* (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)))))
0.1b
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))

rewrite10.0s

Algorithm
rewrite-expression-head
Rules
181×add-exp-log
128×prod-exp
107×add-cbrt-cube
70×cbrt-unprod
51×pow1
48×associate-*l*
46×add-sqr-sqrt
40×times-frac
35×*-un-lft-identity pow-prod-down
33×add-cube-cbrt
19×div-exp
15×associate-*l/
14×sqrt-prod
12×frac-add
11×cbrt-undiv
8×rec-exp 1-exp
6×frac-times flip3-+ 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 → 195
Calls
4 calls:
Slowest
8.4s
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.6s
(* (/ 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)))))
66.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
11.0ms
(sqrt PI)

series509.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
361.0ms
(* (/ 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)))))
90.0ms
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
58.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.2s

Counts
216 → 205

prune3.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite728.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
39×add-exp-log
38×associate-*l*
32×add-cbrt-cube
31×*-un-lft-identity times-frac
29×add-cube-cbrt
19×prod-exp
16×pow1
15×cbrt-unprod
14×sqrt-prod
11×associate-*r*
8×unswap-sqr
7×pow-prod-down
5×div-exp
4×expm1-log1p-u cbrt-undiv unpow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×frac-times flip3-+ associate-*l/ associate-*r/ flip-+ div-inv sqr-pow
1×distribute-rgt-in pow-to-exp rem-sqrt-square rec-exp distribute-lft-in sqrt-pow1 pow1/2 1-exp pow-exp
Counts
4 → 140
Calls
4 calls:
Slowest
655.0ms
(* (/ 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 (pow (fabs x) 7))))
60.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
8.0ms
(* 1/21 (pow (fabs x) 7))
2.0ms
(sqrt PI)

series516.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
374.0ms
(* (/ 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 (pow (fabs x) 7))))
96.0ms
(* 1/21 (pow (fabs x) 7))
46.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify465.0ms

Counts
160 → 150

prune2.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt PI) (cbrt PI))
1.0b
(sqrt (* (cbrt PI) (cbrt PI)))
1.0b
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
1.0b
(cbrt PI)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
28×pow1
22×*-un-lft-identity add-cube-cbrt
19×cbrt-prod pow1/3
18×sqrt-pow1
12×times-frac
11×pow-flip
10×add-exp-log
6×add-cbrt-cube swap-sqr associate-*r* associate-*l* pow-prod-down pow-sqr pow-prod-up
5×sqrt-prod
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow2 pow-plus associate-/l*
2×pow1/2 div-exp
1×cbrt-undiv rem-sqrt-square rec-exp clear-num frac-2neg 1-exp prod-exp *-commutative cbrt-unprod div-inv inv-pow
Counts
4 → 127
Calls
4 calls:
Slowest
11.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
7.0ms
(* (cbrt PI) (cbrt PI))
5.0ms
(sqrt (* (cbrt PI) (cbrt PI)))
1.0ms
(cbrt PI)

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(* (cbrt PI) (cbrt PI))
0.0ms
(sqrt (* (cbrt PI) (cbrt PI)))
0.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
0.0ms
(cbrt PI)

simplify869.0ms

Counts
152 → 131

prune2.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.3b
(/ (fma (fabs x) (fma 2/3 (* (fabs x) (fabs x)) 2) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* (* (fabs x) (fabs x)) 1/21)))) (sqrt PI))
0.2b
(* (* (fabs x) (fabs x)) 1/21)
0.1b
(* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* (* (fabs x) (fabs x)) 1/21)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
40×add-cbrt-cube add-exp-log
39×pow1
25×pow-prod-down prod-exp cbrt-unprod
24×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
6×associate-/r* associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×associate-*l* associate-*r/ *-commutative
1×distribute-rgt-in cbrt-undiv rem-sqrt-square clear-num frac-2neg distribute-lft-in sqrt-pow1 flip3-+ pow1/2 div-exp flip-+ div-inv unswap-sqr
Counts
4 → 120
Calls
4 calls:
Slowest
165.0ms
(* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* (* (fabs x) (fabs x)) 1/21)))
38.0ms
(* (* (fabs x) (fabs x)) 1/21)
6.0ms
(/ (fma (fabs x) (fma 2/3 (* (fabs x) (fabs x)) 2) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* (* (fabs x) (fabs x)) 1/21)))) (sqrt PI))
1.0ms
(sqrt PI)

series454.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
307.0ms
(/ (fma (fabs x) (fma 2/3 (* (fabs x) (fabs x)) 2) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* (* (fabs x) (fabs x)) 1/21)))) (sqrt PI))
108.0ms
(* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (+ 1/5 (* (* (fabs x) (fabs x)) 1/21)))
39.0ms
(* (* (fabs x) (fabs x)) 1/21)
0.0ms
(sqrt PI)

simplify1.1s

Counts
151 → 130

prune1.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes117.0ms

Accuracy

0% (0.2b remaining)

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

bsearch7.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
5.0s14000×body80valid