Details

Time bar (total: 55.3s)

sample189.0ms

Algorithm
intervals
Results
158.0ms443×body80valid

simplify4.4s

Counts
1 → 1

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize90.0ms

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 (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)))

rewrite10.9s

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
8.7s
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.1s
(* (/ 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)))))
96.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series534.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
402.0ms
(* (/ 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)))))
81.0ms
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
50.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.6s

Counts
205 → 205

prune3.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (fabs x) 2/3)
0.1b
(* (* (fabs x) (fabs x)) (* (fabs x) 2/3))
0.1b
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (fabs x) 2 (fma 1/21 (pow (fabs x) 7) (* (* (fabs x) (fabs x)) (* (fabs x) 2/3))))))
0.1b
(fma 1/21 (pow (fabs x) 7) (* (* (fabs x) (fabs x)) (* (fabs x) 2/3)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×pow1 add-cbrt-cube associate-*l* add-exp-log
16×*-un-lft-identity sqrt-prod
15×add-cube-cbrt
11×times-frac
10×pow-prod-down prod-exp cbrt-unprod
7×associate-*r*
5×unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div associate-*l/ div-inv
Counts
4 → 97
Calls
4 calls:
Slowest
26.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (fabs x) 2 (fma 1/21 (pow (fabs x) 7) (* (* (fabs x) (fabs x)) (* (fabs x) 2/3))))))
23.0ms
(* (* (fabs x) (fabs x)) (* (fabs x) 2/3))
6.0ms
(* (fabs x) 2/3)
0.0ms
(fma 1/21 (pow (fabs x) 7) (* (* (fabs x) (fabs x)) (* (fabs x) 2/3)))

series651.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
393.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (fabs x) 2 (fma 1/21 (pow (fabs x) 7) (* (* (fabs x) (fabs x)) (* (fabs x) 2/3))))))
157.0ms
(fma 1/21 (pow (fabs x) 7) (* (* (fabs x) (fabs x)) (* (fabs x) 2/3)))
71.0ms
(* (* (fabs x) (fabs x)) (* (fabs x) 2/3))
29.0ms
(* (fabs x) 2/3)

simplify2.3s

Counts
109 → 109

prune1.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize87.0ms

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 (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 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
0.1b
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))

rewrite4.5s

Algorithm
rewrite-expression-head
Rules
122×pow1
60×pow-plus pow-prod-up
48×add-exp-log
44×add-cbrt-cube
40×add-sqr-sqrt
38×associate-*l/
36×associate-*l* frac-add
31×times-frac
29×*-un-lft-identity
27×add-cube-cbrt
26×prod-exp
24×cbrt-unprod
22×frac-times associate-*r/
17×pow-prod-down
14×flip3-+ sqrt-prod flip-+
8×pow2 pow-sqr
7×associate-*r*
5×div-exp unswap-sqr
4×expm1-log1p-u cbrt-undiv pow3 insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×div-inv
1×distribute-rgt-in rem-sqrt-square rec-exp distribute-lft-in sqrt-pow1 pow1/2 1-exp
Counts
4 → 199
Calls
4 calls:
Slowest
4.2s
(* (/ 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 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
185.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))
54.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
11.0ms
(sqrt PI)

series619.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
490.0ms
(* (/ 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 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
72.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
57.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))
0.0ms
(sqrt PI)

simplify3.4s

Counts
209 → 209

prune4.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize104.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.0b
(sqrt PI)
0.4b
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (/ (/ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (sqrt 21)) (sqrt 21)) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) 1/5)))) (sqrt (sqrt PI))))
0.2b
(/ (+ (/ (/ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (sqrt 21)) (sqrt 21)) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) 1/5)))) (sqrt (sqrt PI)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
163×add-sqr-sqrt
159×sqrt-prod
144×times-frac
122×*-un-lft-identity
72×add-cube-cbrt
40×associate-*r*
31×associate-*l*
28×add-exp-log unswap-sqr
19×distribute-lft-out
18×add-cbrt-cube
9×associate-/r* div-exp
8×pow1 prod-exp
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×div-inv
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times clear-num frac-2neg flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+
Counts
4 → 224
Calls
4 calls:
Slowest
763.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (/ (/ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (sqrt 21)) (sqrt 21)) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) 1/5)))) (sqrt (sqrt PI))))
630.0ms
(/ (+ (/ (/ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (sqrt 21)) (sqrt 21)) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) 1/5)))) (sqrt (sqrt PI)))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series1.3s

Counts
4 → 8
Calls
4 calls:
Slowest
725.0ms
(/ (+ (/ (/ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (sqrt 21)) (sqrt 21)) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) 1/5)))) (sqrt (sqrt PI)))
531.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (/ (/ (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (sqrt 21)) (sqrt 21)) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) 1/5)))) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify2.1s

Counts
232 → 232

prune4.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes100.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
4.5s13902×body80valid