Details

Time bar (total: 28.6s)

sample66.0ms

Algorithm
intervals
Results
47.0ms269×body80valid

simplify124.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
124.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize19.0ms

Local error

Found 3 expressions with local error:

26.0b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.8b
(- (* b c) (* a d))
0.0b
(+ (* c c) (* d d))

rewrite62.0ms

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
44.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
10.0ms
(- (* b c) (* a d))
7.0ms
(+ (* c c) (* d d))

series243.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
141.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
52.0ms
(- (* b c) (* a d))
50.0ms
(+ (* c c) (* d d))

simplify2.8s

Counts
43 → 76
Calls
43 calls:
Slowest
467.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
378.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
247.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
188.0ms
(/ (exp (* b c)) (exp (* a d)))
160.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))

prune886.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.7b

localize41.0ms

Local error

Found 4 expressions with local error:

30.3b
(sqrt (+ (* c c) (* d d)))
30.3b
(sqrt (+ (* c c) (* d d)))
14.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.8b
(- (* b c) (* a d))

rewrite77.0ms

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
44.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
16.0ms
(- (* b c) (* a d))
9.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
65.0ms
(- (* b c) (* a d))
57.0ms
(sqrt (+ (* c c) (* d d)))
45.0ms
(sqrt (+ (* c c) (* d d)))

simplify5.2s

Counts
80 → 114
Calls
80 calls:
Slowest
395.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
387.0ms
(/ (* (* (- (* 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)))))
348.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
325.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
317.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.8b

localize36.0ms

Local error

Found 4 expressions with local error:

30.3b
(sqrt (+ (* c c) (* d d)))
30.3b
(sqrt (+ (* c c) (* d d)))
14.5b
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
0.8b
(- (* b c) (* a d))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×sqrt-div add-log-exp
5×unswap-sqr
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u
3×flip3-+ flip3-- associate-*l* flip-+ flip--
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ associate-/r/ cbrt-unprod hypot-def
1×cbrt-undiv rec-exp sub-neg fma-neg diff-log 1-exp prod-diff pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 111
Calls
4 calls:
Slowest
75.0ms
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
7.0ms
(- (* b c) (* a d))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
59.0ms
(sqrt (+ (* c c) (* d d)))
57.0ms
(- (* b c) (* a d))
51.0ms
(sqrt (+ (* c c) (* d d)))

simplify6.7s

Counts
80 → 123
Calls
80 calls:
Slowest
822.0ms
(* (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ 1 (sqrt (+ (* c c) (* d d))))) (/ 1 (sqrt (+ (* c c) (* d d))))))
500.0ms
(* (- (* (* b c) (* b c)) (* (* a d) (* a d))) 1)
452.0ms
(+ (log (- (* b c) (* a d))) (- (log 1) (log (sqrt (+ (* c c) (* d d))))))
364.0ms
(* (+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d)))) (sqrt (+ (* c c) (* d d))))
346.0ms
(* (- (* (* b c) (* b c)) (* (* a d) (* a d))) (/ 1 (sqrt (+ (* c c) (* d d)))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.8b

localize50.0ms

Local error

Found 4 expressions with local error:

30.3b
(sqrt (+ (* c c) (* d d)))
30.3b
(sqrt (+ (* c c) (* d d)))
14.4b
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
0.8b
(- (* b c) (* a d))

rewrite73.0ms

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
40.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
12.0ms
(sqrt (+ (* c c) (* d d)))
12.0ms
(sqrt (+ (* c c) (* d d)))
7.0ms
(- (* b c) (* a d))

series270.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
60.0ms
(sqrt (+ (* c c) (* d d)))
52.0ms
(- (* b c) (* a d))
49.0ms
(sqrt (+ (* c c) (* d d)))

simplify4.6s

Counts
79 → 113
Calls
79 calls:
Slowest
425.0ms
(/ (* (* (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))))
343.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
330.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
301.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
300.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.8b

regimes463.0ms

Accuracy

0% (2.6b remaining)

Error of 25.5b against oracle of 22.9b and baseline of 25.5b

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s8477×body80valid