Details

sample100.0ms

Algorithm

intervals

Results

52.0ms	283×	body	80	valid
27.0ms	87×	body	80	nan

simplify172.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

172.0ms

(if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize163.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (fma -4 (* c a) (* b b)))
21.1b	(sqrt (fma -4 (* c a) (* b b)))
1.6b	(fma -4 (* c a) (* b b))
1.6b	(fma -4 (* c a) (* b b))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

Slowest

5.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
0.0ms	(fma -4 (* c a) (* b b))
0.0ms	(fma -4 (* c a) (* b b))

series427.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

130.0ms	(sqrt (fma -4 (* c a) (* b b)))
122.0ms	(sqrt (fma -4 (* c a) (* b b)))
91.0ms	(fma -4 (* c a) (* b b))
84.0ms	(fma -4 (* c a) (* b b))

simplify840.0ms

Counts

22 → 66

Calls

22 calls:

Slowest

105.0ms	(- (pow b 2) (* 4 (* a c)))
96.0ms	(- (pow b 2) (* 4 (* a c)))
90.0ms	(- (pow b 2) (* 4 (* a c)))
81.0ms	(- (pow b 2) (* 4 (* a c)))
73.0ms	(- (pow b 2) (* 4 (* a c)))

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.9b

localize195.0ms

Local error

Found 4 expressions with local error:

21.8b	(cbrt (fma -4 (* c a) (* b b)))
21.8b	(cbrt (fma -4 (* c a) (* b b)))
21.8b	(cbrt (fma -4 (* c a) (* b b)))
21.1b	(sqrt (fma -4 (* c a) (* b b)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

Slowest

2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

721.0ms	(cbrt (fma -4 (* c a) (* b b)))
308.0ms	(cbrt (fma -4 (* c a) (* b b)))
247.0ms	(cbrt (fma -4 (* c a) (* b b)))
121.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.6s

Counts

26 → 70

Calls

26 calls:

Slowest

315.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
289.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
278.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
277.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
274.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.9b

localize204.0ms

Local error

Found 4 expressions with local error:

21.8b	(cbrt (fma -4 (* c a) (* b b)))
21.8b	(cbrt (fma -4 (* c a) (* b b)))
21.1b	(sqrt (fma -4 (* c a) (* b b)))
21.1b	(sqrt (fma -4 (* c a) (* b b)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 60

Calls

4 calls:

Slowest

2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))

series768.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

268.0ms	(cbrt (fma -4 (* c a) (* b b)))
235.0ms	(cbrt (fma -4 (* c a) (* b b)))
135.0ms	(sqrt (fma -4 (* c a) (* b b)))
129.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.2s

Counts

28 → 72

Calls

28 calls:

Slowest

402.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
386.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
262.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))
261.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
244.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.9b

localize165.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (fma -4 (* c a) (* b b)))
21.1b	(sqrt (fma -4 (* c a) (* b b)))
21.1b	(sqrt (fma -4 (* c a) (* b b)))
21.1b	(sqrt (fma -4 (* c a) (* b b)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

Slowest

2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

129.0ms	(sqrt (fma -4 (* c a) (* b b)))
114.0ms	(sqrt (fma -4 (* c a) (* b b)))
106.0ms	(sqrt (fma -4 (* c a) (* b b)))
86.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify521.0ms

Counts

32 → 76

Calls

32 calls:

Slowest

46.0ms	(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
45.0ms	(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
43.0ms	(sqrt (sqrt (fma -4 (* c a) (* b b))))
42.0ms	(sqrt (fma -4 (* c a) (* b b)))
40.0ms	(sqrt (fma -4 (* c a) (* b b)))

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.9b

regimes290.0ms

Accuracy

92.4% (0.6b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 19.9b

bsearch151.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.9s	8736×	body	80	valid
530.0ms	2799×	body	80	nan