Details

Time bar (total: 4.5s)

sample59.0ms

Algorithm
intervals
Results
14.0ms184×body80valid
12.0ms31×body2560valid
6.0ms19×body1280valid
6.0ms256×pre80true
2.0ms10×body320valid
2.0ms6×body640valid
1.0ms3×body5120valid
0.0ms3×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.9b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
22×add-sqr-sqrt
21×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×expm1-log1p-u fma-def flip3-+ sqrt-div flip-+ log1p-expm1-u
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv distribute-lft-out
Counts
4 → 91
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
13.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
27.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (* (* 4.0 p) p) (* x x))
52.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
74.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify151.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (141.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune297.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x)))))
0.0b
(+ (* (* 4.0 p) p) (* x x))
0.9b
(+ 1.0 (/ x (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))))
15.7b
(sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt
12×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
5×sqrt-prod
4×expm1-log1p-u fma-def flip3-+ sqrt-div associate-*r/ associate-/r* flip-+ log1p-expm1-u
3×associate-/l*
2×+-commutative sqrt-pow1 sum-log associate-/r/
1×cbrt-undiv frac-2neg pow1/2 div-exp pow-prod-down clear-num div-inv distribute-lft-out
Counts
4 → 81
Calls
4 calls:
9.0ms
(/ x (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(+ (* (* 4.0 p) p) (* x x))
13.0ms
(+ 1.0 (/ x (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))))
8.0ms
(sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))

series230.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ x (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x)))))
33.0ms
(+ (* (* 4.0 p) p) (* x x))
78.0ms
(+ 1.0 (/ x (sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))))
59.0ms
(sqrt (* 1 (+ (* (* 4.0 p) p) (* x x))))

simplify49.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0305787
11382724
25002700

prune293.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.9b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
40×times-frac
37×*-un-lft-identity
35×add-cube-cbrt
26×sqrt-prod
24×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×pow1
6×sqrt-div associate-/r* add-log-exp
5×unswap-sqr
4×expm1-log1p-u flip3-+ div-exp prod-exp associate-/r/ flip-+ log1p-expm1-u
3×pow-flip fma-def associate-*l* associate-/l*
2×cbrt-undiv rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 133
Calls
4 calls:
14.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
32.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
52.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify53.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03841256
117101134
250011063

prune353.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
1.9b
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
15.9b
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
10×add-exp-log pow-unpow
8×add-log-exp
7×unpow-prod-down associate-*r*
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u fma-def log1p-expm1-u
3×distribute-lft-neg-in pow-neg distribute-rgt-neg-in associate-*l* prod-exp unswap-sqr sqr-pow
2×+-commutative neg-sub0 pow-to-exp flip3-+ associate-*r/ pow-exp sum-log flip-+ pow-sub
1×neg-mul-1 pow-pow un-div-inv *-commutative cbrt-unprod
Counts
4 → 88
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
46.0ms
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
3.0ms
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
11.0ms
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

series297.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* (* 4.0 p) p) (* x x))
59.0ms
(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
77.0ms
(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
127.0ms
(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

simplify53.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0378755
11528704
25001695

prune286.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.1b

regimes100.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.8b and baseline of 13.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12610
22610

end0.0ms

sample1.5s

Algorithm
intervals
Results
472.0ms6075×body80valid
303.0ms739×body2560valid
199.0ms592×body1280valid
157.0ms8000×pre80true
85.0ms308×body640valid
34.0ms169×body320valid
27.0ms54×body5120valid
9.0ms63×body160valid