Details

Time bar (total: 22.9s)

sample302.0ms

Algorithm
intervals
Results
98.0ms323×body80nan
21.0ms171×body80valid
17.0ms28×body1280valid
13.0ms28×body640valid
11.0ms20×body1280nan
10.0ms23×body640nan
9.0ms19×body320valid
3.0ms8×body320nan
2.0ms10×body160valid
1.0ms4×body160nan

simplify1.6s

Counts
1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (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)
12.2b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite244.0ms

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:
89.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
12.0ms
(* (sqrt 2.0) t)
52.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
86.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts
4 → 12
Calls
4 calls:
624.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
50.0ms
(* (sqrt 2.0) t)
356.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.1s

Counts
92 → 92

prune511.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.4b

localize25.0ms

Local error

Found 4 expressions with local error:

2.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.4b
(/ (pow l 2) x)
9.3b
(/ (pow t 2) x)
27.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite95.0ms

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:
20.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
27.0ms
(/ (pow l 2) x)
18.0ms
(/ (pow t 2) x)
24.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series367.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
24.0ms
(/ (pow l 2) x)
26.0ms
(/ (pow t 2) x)
229.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify1.1s

Counts
142 → 142

prune752.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
2.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
9.3b
(/ (pow t 2) x)
27.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

rewrite93.0ms

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:
15.0ms
(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
25.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
13.0ms
(/ (pow t 2) x)
30.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

series409.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
88.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
21.0ms
(/ (pow t 2) x)
241.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

simplify1.2s

Counts
104 → 104

prune705.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize89.0ms

Local error

Found 4 expressions with local error:

9.3b
(/ (pow t 2) x)
27.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))
27.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))
27.4b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity times-frac
12×unpow-prod-down sqrt-div associate-*r/
9×add-exp-log sqrt-prod
8×associate-/l*
7×pow1
6×flip3-+ frac-add add-cbrt-cube flip-+
4×unpow2 add-log-exp sqr-pow
3×rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r*
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 100
Calls
4 calls:
12.0ms
(/ (pow t 2) x)
37.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))
39.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))
38.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

series787.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (pow t 2) x)
240.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))
275.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))
237.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

simplify973.0ms

Counts
112 → 112

prune961.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.0b

regimes764.0ms

Accuracy

75.1% (5.9b remaining)

Error of 9.5b against oracle of 3.6b and baseline of 27.4b

bsearch1.3s

Steps
ItersRangePoint
9
6.310229186656893e+16
5.676664727499879e+25
5.564401068892686e+25
6
6.4318589732970825e-304
3.6233550902429726e-303
6.5024372382880295e-304
7
-9.456641075359029e-166
-1.4724282309499112e-167
-1.1004385006624384e-166
7
-4.647295446985087e+142
-1.4932325044728722e+141
-2.52679670936607e+142

simplify661.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
1.2s10068×body80nan
1.2s5178×body80valid
727.0ms552×body1280nan
573.0ms873×body1280valid
458.0ms991×body640valid
350.0ms619×body640nan
212.0ms620×body320valid
157.0ms338×body160valid
101.0ms364×body320nan
80.0ms178×body160nan