Details

Time bar (total: 4.4s)

sample25.0ms

Algorithm
intervals
Results
8.0ms245×body80nan
7.0ms256×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1397
2617
3807
41057
51147
61147

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.3b
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
7×add-exp-log add-cbrt-cube add-log-exp
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
3×times-frac associate-/r* sum-log
2×pow1 cbrt-undiv flip3-+ associate-*r/ div-exp associate-/r/ flip-+ associate-/l/
1×+-commutative associate-+l+ flip3-- frac-2neg prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l*
Counts
2 → 38
Calls
2 calls:
13.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
21.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series115.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
77.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify39.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0310397
11293333
25001328

prune94.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
0.1b
(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.2b
(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
0.2b
(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
108×times-frac
95×*-un-lft-identity
69×add-cube-cbrt
63×sqrt-prod
36×associate-*r*
24×associate-*l*
20×add-exp-log add-cbrt-cube
13×distribute-lft-out-- difference-of-squares
12×associate-/r*
10×sqrt-div
9×unswap-sqr
8×associate-/r/ associate-/l*
7×pow1
6×cbrt-undiv div-exp
5×flip3-+ flip-+
4×prod-exp cbrt-unprod div-inv add-log-exp
2×frac-2neg clear-num associate-/l/
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 203
Calls
4 calls:
16.0ms
(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
18.0ms
(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
105.0ms
(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
24.0ms
(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

series404.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
111.0ms
(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
79.0ms
(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
142.0ms
(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

simplify88.0ms

Algorithm
egg-herbie
Counts
215 → 215
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07723129
133692865
250012758

prune452.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
0.2b
(* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
0.2b
(+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
15.7b
(/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
39×*-un-lft-identity
31×times-frac
25×add-cube-cbrt
22×associate-*l*
20×add-exp-log add-cbrt-cube
11×pow1
7×prod-exp cbrt-unprod distribute-lft-out-- difference-of-squares
6×associate-*r* add-log-exp
5×associate-*l/ associate-/l*
4×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r/
3×cbrt-undiv flip3-- flip3-+ div-exp associate-/r* flip-- flip-+
2×frac-times sub-neg associate-+r+ associate-*r/ associate--l+ *-commutative div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg div-sub clear-num sum-log
Counts
4 → 124
Calls
4 calls:
56.0ms
(* (* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
27.0ms
(* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
4.0ms
(+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
10.0ms
(/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

series278.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(* (* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
68.0ms
(* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
22.0ms
(+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
57.0ms
(/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

simplify94.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
06792076
131091821
250011802

prune398.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (- x 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.0b
(* (/ (* 6.0 (sqrt (- x 1.0))) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (sqrt (- x 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
0.1b
(/ (* 6.0 (sqrt (- x 1.0))) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.2b
(* 6.0 (sqrt (- x 1.0)))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
135×sqrt-prod
121×add-sqr-sqrt
112×times-frac
103×*-un-lft-identity
75×add-cube-cbrt
62×associate-*r*
34×add-exp-log add-cbrt-cube
15×associate-*l*
14×sqrt-div distribute-lft-out-- difference-of-squares
12×associate-/r*
10×cbrt-undiv div-exp prod-exp cbrt-unprod
9×associate-/l*
8×pow1 associate-/r/
7×unswap-sqr
5×associate-*r/
4×flip3-+ flip-+ div-inv associate-/l/ add-log-exp
3×flip3-- flip--
2×frac-2neg pow-prod-down clear-num *-commutative
1×frac-times sqrt-undiv associate-*l/
Counts
4 → 231
Calls
4 calls:
25.0ms
(/ (sqrt (- x 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
113.0ms
(* (/ (* 6.0 (sqrt (- x 1.0))) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (sqrt (- x 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
24.0ms
(/ (* 6.0 (sqrt (- x 1.0))) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
11.0ms
(* 6.0 (sqrt (- x 1.0)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (sqrt (- x 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
95.0ms
(* (/ (* 6.0 (sqrt (- x 1.0))) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (sqrt (- x 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
164.0ms
(/ (* 6.0 (sqrt (- x 1.0))) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
58.0ms
(* 6.0 (sqrt (- x 1.0)))

simplify147.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
08703904
147223480
250013421

prune614.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01714
11714

end0.0ms

sample622.0ms

Algorithm
intervals
Results
233.0ms8000×body80valid
209.0ms8078×body80nan