Details

Time bar (total: 35.6s)

sample118.0ms

Algorithm
intervals
Results
91.0ms440×body80valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: done (2.8s)

IterNodesCost
028847
170742
2250692
31049677
done5001637

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (* (fabs x) (fma (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (* (* (fabs x) (fabs x)) (/ 1.0 21.0)))) (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0))))
0.2b
(* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (* (* (fabs x) (fabs x)) (/ 1.0 21.0))))
0.2b
(* (* (fabs x) (fabs x)) (/ 1.0 21.0))
1.0b
(sqrt PI)

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
33×add-cbrt-cube add-exp-log
31×add-sqr-sqrt
28×times-frac
26×*-un-lft-identity add-cube-cbrt
24×associate-*l*
20×pow1
17×associate-*r*
15×prod-exp cbrt-unprod
12×sqrt-prod
9×pow-prod-down
5×distribute-rgt-in distribute-lft-in associate-*r/
4×expm1-log1p-u cbrt-undiv div-exp fma-udef log1p-expm1-u add-log-exp
3×*-commutative unswap-sqr
2×div-inv
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*l/ frac-add flip-+
Counts
4 → 126
Calls
4 calls:
24.0ms
(* (/ 1.0 (sqrt PI)) (* (fabs x) (fma (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (* (* (fabs x) (fabs x)) (/ 1.0 21.0)))) (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0))))
53.0ms
(* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (* (* (fabs x) (fabs x)) (/ 1.0 21.0))))
33.0ms
(* (* (fabs x) (fabs x)) (/ 1.0 21.0))
2.0ms
(sqrt PI)

series522.0ms

Counts
4 → 10
Calls
4 calls:
408.0ms
(* (/ 1.0 (sqrt PI)) (* (fabs x) (fma (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (* (* (fabs x) (fabs x)) (/ 1.0 21.0)))) (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0))))
77.0ms
(* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (* (* (fabs x) (fabs x)) (/ 1.0 21.0))))
36.0ms
(* (* (fabs x) (fabs x)) (/ 1.0 21.0))
0.0ms
(sqrt PI)

simplify1.5s

Counts
136 → 136
Iterations

Useful iterations: done (1.5s)

IterNodesCost
024258812
175954598
done500151337

prune983.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (* (fabs x) (fma (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (/ (* (* (fabs x) (fabs x)) 1.0) 21.0))) (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0))))
0.1b
(/ (* (* (fabs x) (fabs x)) 1.0) 21.0)
0.2b
(* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (/ (* (* (fabs x) (fabs x)) 1.0) 21.0)))
1.0b
(sqrt PI)

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube add-exp-log
23×add-sqr-sqrt *-un-lft-identity associate-*l*
21×times-frac add-cube-cbrt
15×pow1
12×prod-exp sqrt-prod cbrt-unprod
6×pow-prod-down
5×distribute-rgt-in cbrt-undiv distribute-lft-in div-exp associate-*r*
4×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
3×associate-/r* associate-*r/
2×*-commutative div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*l/ frac-add flip-+ distribute-lft-out associate-/l* unswap-sqr
Counts
4 → 115
Calls
4 calls:
26.0ms
(* (/ 1.0 (sqrt PI)) (* (fabs x) (fma (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (/ (* (* (fabs x) (fabs x)) 1.0) 21.0))) (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0))))
16.0ms
(/ (* (* (fabs x) (fabs x)) 1.0) 21.0)
68.0ms
(* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (/ (* (* (fabs x) (fabs x)) 1.0) 21.0)))
1.0ms
(sqrt PI)

series505.0ms

Counts
4 → 10
Calls
4 calls:
372.0ms
(* (/ 1.0 (sqrt PI)) (* (fabs x) (fma (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (/ (* (* (fabs x) (fabs x)) 1.0) 21.0))) (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0))))
38.0ms
(/ (* (* (fabs x) (fabs x)) 1.0) 21.0)
95.0ms
(* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (/ (* (* (fabs x) (fabs x)) 1.0) 21.0)))
0.0ms
(sqrt PI)

simplify3.3s

Counts
125 → 125
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
022755205
169151182
2488950153
done500050153

prune792.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize102.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

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* 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 → 123
Calls
4 calls:
1.0ms
(cbrt PI)
26.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
10.0ms
(sqrt (* (cbrt PI) (cbrt PI)))
18.0ms
(* (cbrt PI) (cbrt PI))

series0.0ms

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

simplify1.7s

Counts
127 → 127
Iterations

Useful iterations: done (1.6s)

IterNodesCost
013429063
125922966
294522926
done500022466

prune923.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize94.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite12.7s

Algorithm
rewrite-expression-head
Rules
107×add-cbrt-cube add-exp-log
70×prod-exp cbrt-unprod
51×pow1
48×associate-*l*
42×add-sqr-sqrt
38×times-frac
35×pow-prod-down
33×*-un-lft-identity add-cube-cbrt
15×associate-*l/
13×sqrt-prod
12×frac-add
11×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 173
Calls
4 calls:
1.4s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
81.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
11.2s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series605.0ms

Counts
4 → 10
Calls
4 calls:
446.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
57.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
101.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.6s

Counts
183 → 183
Iterations

Useful iterations: done (3.5s)

IterNodesCost
0384108469
1139795605
done500187632

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes378.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
028878
136878
done36878

end0.0ms

sample3.3s

Algorithm
intervals
Results
3.0s14022×body80valid