Details

Time bar (total: 6.4s)

sample29.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
7.0ms293×body80nan

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: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×*-un-lft-identity
8×add-log-exp
7×add-cube-cbrt
5×pow1 associate-*r*
4×associate-*r/
3×times-frac associate-*l* associate-/r* sum-log
2×cbrt-undiv distribute-rgt-in sub-neg flip3-- distribute-lft-in flip3-+ div-exp prod-exp associate-/r/ flip-- cbrt-unprod flip-+ associate-/l/
1×+-commutative associate-+l+ frac-2neg pow-prod-down clear-num *-commutative div-inv associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 64
Calls
3 calls:
28.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
20.0ms
(* 6.0 (- x 1.0))
46.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series153.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
44.0ms
(* 6.0 (- x 1.0))
74.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify43.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0377495
11642421
25001420

prune143.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite351.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
103×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×associate-/r/
10×add-exp-log add-cbrt-cube
8×add-log-exp
6×div-inv associate-/l*
5×flip3-- flip--
4×cbrt-undiv div-exp
3×pow1 sum-log
2×frac-2neg flip3-+ clear-num flip-+ associate-/l/
1×+-commutative associate-+l+
Counts
3 → 154
Calls
3 calls:
222.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
75.0ms
(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
45.0ms
(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

series188.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
69.0ms
(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
81.0ms
(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

simplify83.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06412084
129421986
250011984

prune359.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite553.0ms

Algorithm
rewrite-expression-head
Rules
875×times-frac
803×add-sqr-sqrt
612×*-un-lft-identity
579×sqrt-prod
364×add-cube-cbrt
196×difference-of-squares
185×associate-*r*
98×distribute-lft-out--
75×associate-/r*
36×associate-*l*
34×add-exp-log add-cbrt-cube
26×distribute-lft-out
22×associate-/r/
14×cbrt-undiv div-exp associate-/l*
12×div-inv unswap-sqr
8×flip3-- flip--
6×pow1 sqrt-div prod-exp cbrt-unprod
4×flip3-+ flip-+ associate-/l/ add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 657
Calls
4 calls:
62.0ms
(/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))
59.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
59.0ms
(/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0))))
315.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
474.0ms
(/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))
222.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
288.0ms
(/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0))))
407.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))))

simplify136.0ms

Algorithm
egg-herbie
Counts
669 → 669
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0193514196
1500113598

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ x 1.0) (* 4.0 (sqrt x)))
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)
11.3b
(/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

rewrite247.0ms

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
9×add-log-exp
7×prod-exp cbrt-unprod distribute-lft-out-- difference-of-squares
6×associate-*r*
5×associate-*l/ associate-/l*
4×flip3-- pow-prod-down associate-/r/ flip--
3×cbrt-undiv distribute-rgt-in sub-neg distribute-lft-in div-exp associate--l+ associate-/r*
2×frac-times flip3-+ diff-log associate-*r/ *-commutative flip-+ div-inv associate-/l/ unswap-sqr
1×frac-2neg div-sub clear-num sum-log
Counts
4 → 125
Calls
4 calls:
37.0ms
(- (+ x 1.0) (* 4.0 (sqrt x)))
127.0ms
(* (* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
55.0ms
(* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
24.0ms
(/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

series273.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (+ x 1.0) (* 4.0 (sqrt x)))
124.0ms
(* (* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
56.0ms
(* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
56.0ms
(/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

simplify98.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06842033
131131784
250021769

prune332.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02120
12120

end0.0ms

sample660.0ms

Algorithm
intervals
Results
231.0ms8000×body80valid
193.0ms7890×body80nan