Details

Time bar (total: 8.2s)

sample81.0ms

Algorithm
intervals
Results
16.0ms301×body80nan
10.0ms168×body80valid
7.0ms25×body1280valid
5.0ms19×body1280nan
5.0ms23×body640valid
4.0ms27×body320valid
4.0ms19×body640nan
2.0ms11×body320nan
1.0ms13×body160valid
0.0ms4×body160nan

simplify85.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.5b

localize21.0ms

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)
13.0b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.5b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite149.0ms

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:
56.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms
(* (sqrt 2.0) t)
34.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
45.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts
4 → 12
Calls
4 calls:
402.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
44.0ms
(* (sqrt 2.0) t)
203.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.1s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify61.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04171207
120511099
250021094

prune305.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.0b

localize23.0ms

Local error

Found 4 expressions with local error:

3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.3b
(/ (pow l 2) x)
10.9b
(/ (pow t 2) x)
28.9b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite60.0ms

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:
21.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
9.0ms
(/ (pow l 2) x)
9.0ms
(/ (pow t 2) x)
17.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series249.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
17.0ms
(/ (pow l 2) x)
22.0ms
(/ (pow t 2) x)
151.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05261093
12235984
25001978

prune459.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.1b

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
10.9b
(/ (pow t 2) x)
28.9b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

rewrite61.0ms

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) (/ (fabs l) x)))
18.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
11.0ms
(/ (pow t 2) x)
17.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

series224.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
46.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
17.0ms
(/ (pow t 2) x)
137.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

simplify66.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04931086
12067999
25002996

prune390.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.1b

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
10.9b
(/ (pow t 2) x)
28.9b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

rewrite63.0ms

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:
13.0ms
(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
18.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
11.0ms
(/ (pow t 2) x)
17.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
66.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
18.0ms
(/ (pow t 2) x)
152.0ms
(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

prune389.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.1b

regimes454.0ms

Accuracy

76.5% (5.7b remaining)

Error of 9.2b against oracle of 3.5b and baseline of 27.7b

bsearch466.0ms

Steps
ItersRangePoint
9
1.5857668524149876e+139
3.3871370366029876e+145
1.708019048851353e+139
10
1.933008287221681e-162
1.9608508377038696e-152
6.496548842579948e-161
5
2.6991616684855972e-269
8.390503247003019e-269
5.479403094569755e-269
9
-7.264661280073341e+84
-8.858485632047111e+76
-4.072364829113804e+83

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
085116
185116

end0.0ms

sample2.4s

Algorithm
intervals
Results
556.0ms10341×body80nan
291.0ms5175×body80valid
230.0ms845×body1280valid
223.0ms1013×body640valid
151.0ms585×body1280nan
121.0ms598×body640nan
98.0ms613×body320valid
52.0ms343×body320nan
40.0ms354×body160valid
18.0ms181×body160nan