Details

Time bar (total: 5.0s)

sample64.0ms

Algorithm
intervals
Results
19.0ms190×body80valid
12.0ms24×body2560valid
9.0ms22×body1280valid
6.0ms256×pre80true
3.0ms11×body320valid
2.0ms5×body640valid
1.0ms4×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize16.0ms

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))))
1.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×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×flip3-+ sqrt-div flip-+
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 → 79
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
25.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* (* 4.0 p) p) (* x x))
51.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify147.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune277.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.4b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×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×flip3-+ div-exp prod-exp associate-/r/ flip-+
3×pow-flip 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 → 122
Calls
4 calls:
13.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
36.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
59.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
69.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify50.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03671199
116421080
250011018

prune316.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.0b

localize15.0ms

Local error

Found 4 expressions with local error:

4.4b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
4.4b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
2×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 52
Calls
4 calls:
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
75.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify71.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
0175554
1566512
22177508
35001506

prune480.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.8b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
20×*-un-lft-identity
18×add-cube-cbrt pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 125
Calls
4 calls:
55.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
22.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
52.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify53.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
02901356
110841258
250011216

prune306.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.0b

regimes142.0ms

Accuracy

0% (0.5b remaining)

Error of 13.8b against oracle of 13.3b and baseline of 13.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02621
12621

end0.0ms

sample1.8s

Algorithm
intervals
Results
616.0ms5995×body80valid
416.0ms819×body2560valid
261.0ms614×body1280valid
177.0ms8000×pre80true
111.0ms326×body640valid
45.0ms166×body320valid
14.0ms80×body160valid