Details

Time bar (total: 3.7m)

sample407.0ms

Algorithm
intervals
Results
104.0ms307×body80nan
38.0ms172×body80valid
25.0ms27×body640valid
22.0ms19×body1280valid
16.0ms19×body640nan
15.0ms14×body1280nan
11.0ms17×body320valid
9.0ms14×body320nan
9.0ms21×body160valid
3.0ms6×body160nan

simplify275.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
274.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize43.0ms

Local error

Found 4 expressions with local error:

22.0b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
12.4b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.5b
(* (sqrt 2) t)
0.1b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r* times-frac associate-*l* add-log-exp
4×sqrt-div insert-posit16
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in rem-sqrt-square clear-num sub-neg frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down *-commutative div-inv associate-/l*
Counts
4 → 84
Calls
4 calls:
Slowest
48.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
45.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
27.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
8.0ms
(* (sqrt 2) t)

series2.3s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
543.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
280.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
72.0ms
(* (sqrt 2) t)

simplify11.2s

Counts
61 → 96
Calls
61 calls:
Slowest
464.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
421.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
414.0ms
(sqrt (* (cbrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (cbrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
391.0ms
(- (log (* (sqrt 2) t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
382.0ms
(/ (sqrt 2) (* (cbrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (cbrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.0b

localize51.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.8b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.5b
(* (sqrt 2) t)
0.1b
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×*-un-lft-identity associate-*r/ add-cube-cbrt
11×add-cbrt-cube add-exp-log
8×sqrt-div
7×pow1
6×associate-/r* flip3-+ times-frac associate-*l* frac-add flip-+ add-log-exp
4×associate-/r/ insert-posit16
3×associate-*r*
2×cbrt-undiv associate-+l+ div-exp prod-exp cbrt-unprod unswap-sqr
1×distribute-rgt-in +-commutative rem-sqrt-square clear-num sum-log frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down *-commutative div-inv associate-/l*
Counts
4 → 89
Calls
4 calls:
Slowest
87.0ms
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))
68.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
29.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
14.0ms
(* (sqrt 2) t)

series641.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
298.0ms
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))
206.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
87.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
50.0ms
(* (sqrt 2) t)

simplify10.0s

Counts
69 → 101
Calls
69 calls:
Slowest
675.0ms
(* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) x)
490.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
444.0ms
(sqrt (+ (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (- (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x))) (* (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))
362.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
331.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x)))))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize51.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.8b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.4b
(/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t)
0.1b
(/ (sqrt 2) (/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t))

rewrite251.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
158×add-sqr-sqrt
157×*-un-lft-identity add-cube-cbrt
147×sqrt-prod
25×associate-/r*
12×associate-*r/ associate-/l*
11×add-cbrt-cube add-exp-log
9×div-inv
8×sqrt-div
6×flip3-+ frac-add flip-+ add-log-exp
5×pow1
4×cbrt-undiv div-exp insert-posit16 associate-/l/
2×associate-+l+ clear-num frac-2neg
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2 associate-/r/
Counts
4 → 254
Calls
4 calls:
Slowest
98.0ms
(/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t)
66.0ms
(/ (sqrt 2) (/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t))
51.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
27.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))

series865.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
300.0ms
(/ (sqrt 2) (/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t))
267.0ms
(/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t)
196.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
102.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))

simplify1.2m

Counts
372 → 266
Calls
372 calls:
Slowest
548.0ms
(/ (sqrt (* (cbrt 2) (cbrt 2))) (* (cbrt (/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t)) (cbrt (/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t))))
451.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
428.0ms
(/ 1 (/ (* (cbrt (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))) (cbrt (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))) (* (cbrt t) (cbrt t))))
409.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (* (cbrt (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))) (cbrt (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))) (sqrt t)))
399.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (* (cbrt (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))) (cbrt (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))) 1))

prune4.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

localize56.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.8b
(/ (cbrt (sqrt 2)) (/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t))
0.8b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.4b
(/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t)

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
396×times-frac
220×add-sqr-sqrt
219×*-un-lft-identity add-cube-cbrt
174×sqrt-prod
138×cbrt-prod
25×associate-/r*
15×associate-/l*
12×associate-*r/ div-inv
11×add-exp-log
9×add-cbrt-cube
8×sqrt-div
6×flip3-+ frac-add flip-+ add-log-exp
5×pow1
4×cbrt-undiv div-exp insert-posit16 associate-/l/
2×associate-+l+ clear-num frac-2neg
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2 associate-/r/
Counts
4 → 323
Calls
4 calls:
Slowest
96.0ms
(/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t)
46.0ms
(/ (cbrt (sqrt 2)) (/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t))
38.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
34.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
509.0ms
(/ (cbrt (sqrt 2)) (/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t))
304.0ms
(/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t)
211.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
96.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))

simplify1.7m

Counts
507 → 335
Calls
507 calls:
Slowest
631.0ms
(/ (cbrt (sqrt (sqrt 2))) (/ (sqrt (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))) t))
624.0ms
(/ 1 (/ (sqrt (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))) (* (cbrt t) (cbrt t))))
563.0ms
(/ (cbrt (sqrt (cbrt 2))) (cbrt (/ (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) t)))
476.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
445.0ms
(/ 1 (/ (* (cbrt (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))) (cbrt (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))) (* (cbrt t) (cbrt t))))

prune5.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.6b

regimes856.0ms

Accuracy

75.2% (6.1b remaining)

Error of 9.1b against oracle of 3.0b and baseline of 27.7b

bsearch2.0s

end0.0ms

sample8.7s

Algorithm
intervals
Results
2.5s9880×body80nan
1.7s5202×body80valid
996.0ms827×body1280valid
884.0ms985×body640valid
677.0ms579×body1280nan
544.0ms576×body640nan
396.0ms619×body320valid
238.0ms328×body320nan
171.0ms367×body160valid
66.0ms180×body160nan