Details

Time bar (total: 2.7m)

sample36.0ms

Algorithm
intervals
Results
24.0ms271×body80valid

simplify9.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
9.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize37.0ms

Local error

Found 2 expressions with local error:

24.9b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.0b
(+ (* c c) (* d d))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* flip3-+ flip-+ associate-/l*
2×pow1 associate-/r/ insert-posit16 associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Counts
2 → 44
Calls
2 calls:
Slowest
26.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
9.0ms
(+ (* c c) (* d d))

series194.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
142.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
52.0ms
(+ (* c c) (* d d))

simplify2.3s

Counts
36 → 50
Calls
36 calls:
Slowest
753.0ms
(- (* (* a c) (* a c)) (* (* b d) (* b d)))
337.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
278.0ms
(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
262.0ms
(+ (pow (* a c) 3) (pow (* b d) 3))
156.0ms
(* (exp (* c c)) (exp (* d d)))

prune575.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.5b

localize33.0ms

Local error

Found 4 expressions with local error:

30.1b
(sqrt (+ (* c c) (* d d)))
30.1b
(sqrt (+ (* c c) (* d d)))
15.9b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.1b
(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r* flip3-+ flip-+
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
Counts
4 → 268
Calls
4 calls:
Slowest
72.0ms
(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
43.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
12.0ms
(sqrt (+ (* c c) (* d d)))
11.0ms
(sqrt (+ (* c c) (* d d)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
116.0ms
(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
44.0ms
(sqrt (+ (* c c) (* d d)))
42.0ms
(sqrt (+ (* c c) (* d d)))

simplify21.7s

Counts
400 → 280
Calls
400 calls:
Slowest
415.0ms
(/ (* (* (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
348.0ms
(- (* (* a c) (* a c)) (* (* b d) (* b d)))
326.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
326.0ms
(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
324.0ms
(/ (sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))) (sqrt (cbrt (+ (* c c) (* d d)))))

prune3.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.0b

localize34.0ms

Local error

Found 4 expressions with local error:

30.1b
(sqrt (+ (* c c) (* d d)))
30.1b
(sqrt (+ (* c c) (* d d)))
15.9b
(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
0.1b
(/ (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d))))) (sqrt (+ (* c c) (* d d))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
28×times-frac add-exp-log
26×*-un-lft-identity
24×associate-*r* add-cube-cbrt
23×sqrt-prod
18×add-cbrt-cube
9×div-exp
8×pow1 flip3-+ sqrt-div prod-exp flip-+
6×associate-/r* associate-/l/
5×cbrt-undiv unswap-sqr
4×frac-times associate-*l/ associate-/r/ cbrt-unprod insert-posit16 add-log-exp
3×associate-*l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ un-div-inv div-inv
1×clear-num frac-2neg pow-prod-down *-commutative associate-/l*
Counts
4 → 126
Calls
4 calls:
Slowest
41.0ms
(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
40.0ms
(/ (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d))))) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
92.0ms
(/ (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d))))) (sqrt (+ (* c c) (* d d))))
46.0ms
(sqrt (+ (* c c) (* d d)))
45.0ms
(sqrt (+ (* c c) (* d d)))

simplify8.7s

Counts
112 → 138
Calls
112 calls:
Slowest
483.0ms
(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (sqrt (+ (* c c) (* d d)))))
456.0ms
(* (sqrt (+ (* a c) (* b d))) (/ (sqrt 1) (sqrt (sqrt (+ (* c c) (* d d))))))
456.0ms
(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (sqrt (+ (* c c) (* d d)))))
366.0ms
(/ (* (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (/ (* (* 1 1) 1) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
351.0ms
(/ (* (* (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d))))) (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))) (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.0b

localize30.0ms

Local error

Found 4 expressions with local error:

30.1b
(sqrt (+ (* c c) (* d d)))
30.1b
(sqrt (+ (* c c) (* d d)))
15.9b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.4b
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
1473×times-frac
681×add-sqr-sqrt
679×*-un-lft-identity add-cube-cbrt
522×sqrt-prod
155×associate-/r*
55×associate-/r/
54×sqrt-div
30×div-inv
28×flip3-+ flip-+
27×add-exp-log
16×div-exp
15×add-cbrt-cube
7×pow1 cbrt-undiv
6×associate-/l*
4×insert-posit16 add-log-exp
3×rec-exp 1-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
1×pow-flip inv-pow
Counts
4 → 701
Calls
4 calls:
Slowest
29.0ms
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))))
26.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))))
107.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
46.0ms
(sqrt (+ (* c c) (* d d)))
37.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.9m

Counts
1132 → 713
Calls
1132 calls:
Slowest
532.0ms
(/ 1 (/ (sqrt (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d))))) (/ (+ (* a c) (* b d)) (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d)))))))
455.0ms
(/ (sqrt 1) (/ 1 (/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) (* (cbrt (sqrt (+ (* c c) (* d d)))) (cbrt (sqrt (+ (* c c) (* d d))))))))
450.0ms
(/ (cbrt 1) (/ (sqrt (cbrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (cbrt (sqrt (+ (* c c) (* d d)))))))
438.0ms
(/ (cbrt 1) (/ (sqrt (+ (* c c) (* d d))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))))
433.0ms
(/ (sqrt 1) (/ (sqrt (+ (* c c) (* d d))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))))

prune6.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.0b

regimes325.0ms

Accuracy

0% (2.5b remaining)

Error of 25.4b against oracle of 22.9b and baseline of 25.4b

bsearch2.0ms

end0.0ms

sample1.0s

Algorithm
intervals
Results
795.0ms8507×body80valid