Details

Time bar (total: 23.1s)

sample56.0ms

Algorithm
intervals
Results
40.0ms273×body80valid

simplify152.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
152.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize38.0ms

Local error

Found 3 expressions with local error:

24.7b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.7b
(- (* b c) (* a d))
0.0b
(+ (* c c) (* d d))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
3 → 67
Calls
3 calls:
Slowest
24.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
15.0ms
(+ (* c c) (* d d))
8.0ms
(- (* b c) (* a d))

series212.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
97.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
65.0ms
(- (* b c) (* a d))
50.0ms
(+ (* c c) (* d d))

simplify2.4s

Counts
43 → 76
Calls
43 calls:
Slowest
381.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
305.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
190.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
172.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
150.0ms
(/ (exp (* b c)) (exp (* a d)))

prune690.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.2b

localize31.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (+ (* c c) (* d d)))
29.0b
(sqrt (+ (* c c) (* d d)))
14.7b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.7b
(- (* b c) (* a d))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ hypot-def flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
Slowest
25.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
8.0ms
(sqrt (+ (* c c) (* d d)))
8.0ms
(- (* b c) (* a d))
6.0ms
(sqrt (+ (* c c) (* d d)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
56.0ms
(- (* b c) (* a d))
41.0ms
(sqrt (+ (* c c) (* d d)))
37.0ms
(sqrt (+ (* c c) (* d d)))

simplify4.1s

Counts
80 → 114
Calls
80 calls:
Slowest
320.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
298.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
279.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
276.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
275.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.8b

localize41.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (+ (* c c) (* d d)))
29.0b
(sqrt (+ (* c c) (* d d)))
14.8b
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
0.7b
(- (* b c) (* a d))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 add-cbrt-cube sqrt-div add-exp-log associate-/l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ hypot-def flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-exp prod-diff div-inv
Counts
4 → 101
Calls
4 calls:
Slowest
19.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
7.0ms
(- (* b c) (* a d))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
70.0ms
(sqrt (+ (* c c) (* d d)))
67.0ms
(- (* b c) (* a d))
39.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.9s

Counts
79 → 113
Calls
79 calls:
Slowest
283.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
281.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
271.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
270.0ms
(/ (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))) (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))))
255.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 22.8b

localize24.0ms

Local error

Found 4 expressions with local error:

24.7b
(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))
0.7b
(- (* b c) (* a d))
0.1b
(/ 1 (+ (* c c) (* d d)))
0.0b
(+ (* c c) (* d d))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×times-frac add-cube-cbrt
17×add-exp-log
15×associate-*r*
11×add-cbrt-cube
8×add-log-exp
7×pow1
4×expm1-log1p-u div-exp prod-exp associate-/r/ insert-posit16 log1p-expm1-u
3×associate-/r* flip3-+ flip3-- associate-*l* flip-+ flip-- associate-/l* unswap-sqr
2×frac-times cbrt-undiv rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×+-commutative clear-num sum-log sub-neg fma-def frac-2neg fma-neg diff-log prod-diff pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 113
Calls
4 calls:
Slowest
44.0ms
(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))
15.0ms
(/ 1 (+ (* c c) (* d d)))
13.0ms
(- (* b c) (* a d))
7.0ms
(+ (* c c) (* d d))

series263.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))
55.0ms
(/ 1 (+ (* c c) (* d d)))
54.0ms
(- (* b c) (* a d))
38.0ms
(+ (* c c) (* d d))

simplify5.0s

Counts
83 → 125
Calls
83 calls:
Slowest
668.0ms
(* (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (/ 1 (+ (* c c) (* d d))) (/ 1 (+ (* c c) (* d d)))) (/ 1 (+ (* c c) (* d d)))))
399.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
364.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
328.0ms
(* (- (* (* b c) (* b c)) (* (* a d) (* a d))) 1)
292.0ms
(* (- (* (* b c) (* b c)) (* (* a d) (* a d))) (/ 1 (+ (* c c) (* d d))))

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 22.8b

regimes304.0ms

Accuracy

0% (2.7b remaining)

Error of 25.4b against oracle of 22.8b and baseline of 25.4b

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.3s8456×body80valid