Details

Time bar (total: 36.0s)

sample128.0ms

Algorithm
intervals
Results
104.0ms691×body80valid

simplify198.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
198.0ms
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1)

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (+ 3 a))
0.3b
(pow (+ (* a a) (* b b)) 2)
0.1b
(* (* a a) (- 1 a))
0.0b
(* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
17×add-sqr-sqrt pow1 add-exp-log
16×add-cbrt-cube
15×*-un-lft-identity
13×associate-*r*
10×add-cube-cbrt
7×pow-prod-down prod-exp cbrt-unprod
5×associate-*l*
4×distribute-rgt-in distribute-lft-in flip3-+ frac-add flip-+ insert-posit16 add-log-exp
3×pow-unpow unpow-prod-down flip3-- *-commutative flip-- unswap-sqr
2×sub-neg difference-of-squares
1×pow-to-exp pow-pow pow-exp distribute-lft-out distribute-lft-out-- unpow2 sqr-pow
Counts
4 → 100
Calls
4 calls:
Slowest
87.0ms
(* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))
41.0ms
(* (* a a) (- 1 a))
23.0ms
(* (* b b) (+ 3 a))
16.0ms
(pow (+ (* a a) (* b b)) 2)

series247.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
74.0ms
(* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))
61.0ms
(* (* a a) (- 1 a))
59.0ms
(* (* b b) (+ 3 a))
53.0ms
(pow (+ (* a a) (* b b)) 2)

simplify9.2s

Counts
73 → 112
Calls
73 calls:
Slowest
793.0ms
(* (* (* 4 4) 4) (* (* (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))) (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))) (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
603.0ms
(* (* (* (* a a) a) (* (* a a) a)) (* (* (- 1 a) (- 1 a)) (- 1 a)))
570.0ms
(* (* (* (* a a) (* a a)) (* a a)) (* (* (- 1 a) (- 1 a)) (- 1 a)))
428.0ms
(+ (* (* (* a a) (- 1 a)) (* (* a a) (- 1 a))) (- (* (* (* b b) (+ 3 a)) (* (* b b) (+ 3 a))) (* (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
359.0ms
(- (+ (* 12 (pow b 2)) (* 4 (* a (pow b 2)))) (* 4 (pow a 3)))

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

6.4b
(cbrt (+ (* a a) (* b b)))
6.4b
(cbrt (+ (* a a) (* b b)))
0.5b
(pow (cbrt (+ (* a a) (* b b))) 2)
0.5b
(* (* b b) (+ 3 a))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt
9×cbrt-prod add-cbrt-cube
6×unpow-prod-down
4×cbrt-div associate-*r* insert-posit16 add-log-exp
3×pow-unpow flip3-+ pow1/3 pow-prod-down prod-exp cbrt-unprod flip-+
2×pow-pow associate-*r/
1×distribute-rgt-in pow-to-exp distribute-lft-in associate-*l* pow-exp *-commutative distribute-lft-out unpow2 unswap-sqr sqr-pow
Counts
4 → 76
Calls
4 calls:
Slowest
44.0ms
(* (* b b) (+ 3 a))
15.0ms
(pow (cbrt (+ (* a a) (* b b))) 2)
9.0ms
(cbrt (+ (* a a) (* b b)))
7.0ms
(cbrt (+ (* a a) (* b b)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(cbrt (+ (* a a) (* b b)))
126.0ms
(pow (cbrt (+ (* a a) (* b b))) 2)
120.0ms
(cbrt (+ (* a a) (* b b)))
46.0ms
(* (* b b) (+ 3 a))

simplify3.3s

Counts
49 → 88
Calls
49 calls:
Slowest
324.0ms
(cbrt (+ (pow (* a a) 3) (pow (* b b) 3)))
277.0ms
(cbrt (+ (pow (* a a) 3) (pow (* b b) 3)))
271.0ms
(pow (* (cbrt (cbrt (+ (* a a) (* b b)))) (cbrt (cbrt (+ (* a a) (* b b))))) 2)
255.0ms
(cbrt (- (* (* a a) (* a a)) (* (* b b) (* b b))))
207.0ms
(+ (pow b 2/3) (* 1/3 (* (pow a 2) (pow (/ 1 (pow b 4)) 1/3))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

6.4b
(cbrt (+ (* a a) (* b b)))
5.9b
(sqrt (+ (* a a) (* b b)))
5.9b
(sqrt (+ (* a a) (* b b)))
0.6b
(cbrt (sqrt (+ (* a a) (* b b))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×cbrt-prod *-un-lft-identity add-cube-cbrt sqrt-prod
6×pow1 sqrt-div
4×cbrt-div flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 63
Calls
4 calls:
Slowest
12.0ms
(sqrt (+ (* a a) (* b b)))
10.0ms
(sqrt (+ (* a a) (* b b)))
4.0ms
(cbrt (sqrt (+ (* a a) (* b b))))
4.0ms
(cbrt (+ (* a a) (* b b)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(cbrt (+ (* a a) (* b b)))
118.0ms
(cbrt (sqrt (+ (* a a) (* b b))))
56.0ms
(sqrt (+ (* a a) (* b b)))
53.0ms
(sqrt (+ (* a a) (* b b)))

simplify2.9s

Counts
39 → 75
Calls
39 calls:
Slowest
329.0ms
(cbrt (+ (pow (* a a) 3) (pow (* b b) 3)))
321.0ms
(sqrt (+ (pow (* a a) 3) (pow (* b b) 3)))
283.0ms
(cbrt (sqrt (- (* (* a a) (* a a)) (* (* b b) (* b b)))))
281.0ms
(sqrt (+ (pow (* a a) 3) (pow (* b b) 3)))
270.0ms
(cbrt (sqrt (+ (pow (* a a) 3) (pow (* b b) 3))))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

6.4b
(cbrt (+ (* a a) (* b b)))
6.4b
(cbrt (+ (* a a) (* b b)))
6.4b
(cbrt (+ (* a a) (* b b)))
0.5b
(* (sqrt (cbrt (+ (* a a) (* b b)))) (sqrt (cbrt (+ (* a a) (* b b)))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
38×sqrt-prod
27×cbrt-prod
19×pow1 *-un-lft-identity add-cube-cbrt
18×cbrt-div
14×sqrt-pow1
12×sqrt-div
11×swap-sqr
9×flip3-+ pow1/3 associate-*r* associate-*l* flip-+ unswap-sqr
8×pow1/2
6×add-cbrt-cube add-exp-log pow-prod-up
4×frac-times pow-prod-down pow-sqr insert-posit16 add-log-exp
2×associate-*l/ associate-*r/
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 117
Calls
4 calls:
Slowest
85.0ms
(* (sqrt (cbrt (+ (* a a) (* b b)))) (sqrt (cbrt (+ (* a a) (* b b)))))
8.0ms
(cbrt (+ (* a a) (* b b)))
8.0ms
(cbrt (+ (* a a) (* b b)))
8.0ms
(cbrt (+ (* a a) (* b b)))

series550.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(* (sqrt (cbrt (+ (* a a) (* b b)))) (sqrt (cbrt (+ (* a a) (* b b)))))
142.0ms
(cbrt (+ (* a a) (* b b)))
138.0ms
(cbrt (+ (* a a) (* b b)))
124.0ms
(cbrt (+ (* a a) (* b b)))

simplify7.3s

Counts
127 → 129
Calls
127 calls:
Slowest
695.0ms
(* (sqrt (cbrt (+ (pow (* a a) 3) (pow (* b b) 3)))) (sqrt (cbrt (+ (pow (* a a) 3) (pow (* b b) 3)))))
413.0ms
(* (sqrt (cbrt (- (* a a) (* b b)))) (sqrt (cbrt (+ (* (* a a) (* a a)) (- (* (* b b) (* b b)) (* (* a a) (* b b)))))))
346.0ms
(* (sqrt (cbrt (+ (* (* a a) (* a a)) (- (* (* b b) (* b b)) (* (* a a) (* b b)))))) (sqrt (cbrt (+ (* (* a a) (* a a)) (- (* (* b b) (* b b)) (* (* a a) (* b b)))))))
314.0ms
(* (sqrt (cbrt (+ (* (* a a) (* a a)) (- (* (* b b) (* b b)) (* (* a a) (* b b)))))) (sqrt (cbrt (- (* a a) (* b b)))))
295.0ms
(cbrt (+ (pow (* a a) 3) (pow (* b b) 3)))

prune1.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch7.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
3.8s20692×body80valid