Details

Time bar (total: 15.3s)

sample76.0ms

Algorithm
intervals
Results
15.0ms323×body80nan
8.0ms164×body80valid
8.0ms32×body1280valid
7.0ms40×body640valid
5.0ms20×body1280nan
2.0ms13×body640nan
2.0ms16×body320valid
2.0ms13×body320nan
0.0ms4×body160valid
0.0ms4×body160nan

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01827
13927
29327
318927
439727
566127
6112227
7262427
8413127
done500027

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

localize18.0ms

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)
12.4b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.1b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite148.0ms

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:
55.0ms
(/ (* (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)
29.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
50.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

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))))
45.0ms
(* (sqrt 2.0) t)
230.0ms
(- (* (/ (+ 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)))

simplify902.0ms

Counts
92 → 92
Iterations

Useful iterations: done (898.0ms)

IterNodesCost
01682472
14142283
215522077
done50002025

prune314.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.7b

localize18.0ms

Local error

Found 4 expressions with local error:

3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
7.1b
(/ (pow l 2) x)
7.6b
(/ (pow t 2) x)
24.8b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite58.0ms

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:
18.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
8.0ms
(/ (pow l 2) x)
8.0ms
(/ (pow t 2) x)
18.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series278.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
19.0ms
(/ (pow l 2) x)
23.0ms
(/ (pow t 2) x)
165.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify803.0ms

Counts
142 → 142
Iterations

Useful iterations: done (793.0ms)

IterNodesCost
02542317
15352084
217251868
done50011862

prune469.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
7.6b
(/ (pow t 2) x)
24.8b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
12×unpow-prod-down
11×add-exp-log
8×associate-*r/ add-cbrt-cube associate-/l*
7×pow1 sqrt-prod
6×associate-*l* add-log-exp
4×flip3-+ sqrt-div frac-add flip-+ unpow2 sqr-pow
3×div-exp associate-*r* associate-/r*
2×associate-+r+ unswap-sqr
1×cbrt-undiv +-commutative distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down pow-exp prod-exp clear-num sum-log *-commutative cbrt-unprod div-inv
Counts
4 → 103
Calls
4 calls:
9.0ms
(* (sqrt 2.0) t)
16.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
8.0ms
(/ (pow t 2) x)
18.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sqrt 2.0) t)
70.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
19.0ms
(/ (pow t 2) x)
165.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

simplify847.0ms

Counts
115 → 115
Iterations

Useful iterations: done (843.0ms)

IterNodesCost
02142195
14851872
216731601
done50001587

prune415.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
7.6b
(/ (pow t 2) x)
24.8b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
21×add-exp-log
17×pow1
12×unpow-prod-down add-cbrt-cube
8×associate-*r/ pow-prod-down prod-exp cbrt-unprod associate-/l*
6×add-log-exp
4×flip3-+ sqrt-div frac-add flip-+ unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×associate-+r+
1×cbrt-undiv +-commutative distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 associate-*r* associate-*l* pow-exp clear-num sum-log *-commutative div-inv
Counts
4 → 103
Calls
4 calls:
42.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
16.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
11.0ms
(/ (pow t 2) x)
18.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

series292.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
65.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
21.0ms
(/ (pow t 2) x)
158.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

simplify902.0ms

Counts
115 → 115
Iterations

Useful iterations: done (898.0ms)

IterNodesCost
02222438
15302106
218881660
done50011577

prune395.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.5b

regimes591.0ms

Accuracy

78% (5.2b remaining)

Error of 9.0b against oracle of 3.8b and baseline of 27.4b

bsearch467.0ms

Steps
ItersRangePoint
8
4.675023421196728e+36
4.923303098506139e+39
4.8698681991528654e+39
9
3.742612203784258e-160
2.9120561417431717e-154
5.832383717323897e-160
10
9.221801955237562e-239
2.899958115691549e-221
4.894745026611551e-226
8
-2.0068295615508747e+75
-1.897864979438576e+72
-1.6066236751871663e+75

simplify19.0ms

Iterations

Useful iterations: done (18.0ms)

IterNodesCost
059186
174158
277121
380121
done80120

end0.0ms

sample2.1s

Algorithm
intervals
Results
476.0ms10130×body80nan
255.0ms5168×body80valid
209.0ms861×body1280valid
187.0ms999×body640valid
132.0ms589×body1280nan
110.0ms600×body640nan
82.0ms602×body320valid
45.0ms340×body320nan
34.0ms370×body160valid
17.0ms195×body160nan