Details

Time bar (total: 7.9s)

sample74.0ms

Algorithm
intervals
Results
14.0ms300×body80nan
8.0ms164×body80valid
7.0ms28×body1280valid
5.0ms23×body1280nan
5.0ms28×body640valid
4.0ms29×body320valid
2.0ms13×body640nan
2.0ms10×body320nan
1.0ms7×body160valid
0.0ms3×body160nan

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b
(* (sqrt 2.0) t)
15.6b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.9b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* add-log-exp
4×sqrt-div
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
53.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
9.0ms
(* (sqrt 2.0) t)
34.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
44.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts
4 → 12
Calls
4 calls:
432.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
40.0ms
(* (sqrt 2.0) t)
220.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify58.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04171207
120511099
250021094

prune295.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.7b

localize17.0ms

Local error

Found 4 expressions with local error:

4.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
9.4b
(/ (pow l 2) x)
10.7b
(/ (pow t 2) x)
27.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×associate-*r/ add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r* add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×sqrt-prod
2×cbrt-undiv pow-to-exp associate-+r+ frac-2neg pow-exp clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 130
Calls
4 calls:
17.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
8.0ms
(/ (pow l 2) x)
11.0ms
(/ (pow t 2) x)
17.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series273.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
166.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05261067
12113984
25001978

prune455.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
4.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
10.7b
(/ (pow t 2) x)
27.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity times-frac
23×add-sqr-sqrt
22×add-cube-cbrt
12×unpow-prod-down
9×add-exp-log
8×associate-*r/ associate-/l* add-log-exp
6×add-cbrt-cube
5×pow1 flip3-+ flip-+
4×sqrt-div frac-add unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×+-commutative associate-+r+ sum-log
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp clear-num div-inv distribute-lft-out
Counts
4 → 93
Calls
4 calls:
57.0ms
(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
19.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
8.0ms
(/ (pow t 2) x)
17.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
65.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
24.0ms
(/ (pow t 2) x)
161.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify56.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04561099
119411003
25003982

prune374.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
4.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
10.7b
(/ (pow t 2) x)
27.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
9×add-exp-log
8×associate-*r/ associate-/l* add-log-exp
6×add-cbrt-cube
5×pow1 flip3-+ flip-+
4×sqrt-div frac-add unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×+-commutative associate-+r+ sum-log
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 92
Calls
4 calls:
12.0ms
(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
17.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
8.0ms
(/ (pow t 2) x)
19.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
72.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
19.0ms
(/ (pow t 2) x)
165.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04991468
121151360
250021357

prune369.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.3b

regimes518.0ms

Accuracy

76.2% (5.7b remaining)

Error of 9.6b against oracle of 3.9b and baseline of 27.9b

bsearch213.0ms

Steps
ItersRangePoint
10
1.1309459419082891e+56
1.452376769013907e+67
9.991764826799716e+66
8
-1.470821775419402e+149
-4.770441291713145e+146
-4.834780474181416e+146

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06358
16458
26458

end0.0ms

sample2.1s

Algorithm
intervals
Results
478.0ms10148×body80nan
245.0ms5039×body80valid
223.0ms897×body1280valid
183.0ms963×body640valid
123.0ms550×body1280nan
115.0ms626×body640nan
91.0ms670×body320valid
45.0ms346×body320nan
42.0ms431×body160valid
17.0ms186×body160nan