Details

sample63.0ms

Algorithm

intervals

Results

43.0ms

273×

body

valid

simplify107.0ms

Counts: 1 → 1

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize31.0ms

Local error

Found 2 expressions with local error:

24.7b	(/ (- (* b c) (* a d)) (fma d d (* c c)))
0.3b	(- (* b c) (* a d))

rewrite32.0ms

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` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `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

2 → 50

Calls

2 calls:

Slowest

16.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
15.0ms	(- (* b c) (* a d))

series191.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

140.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
50.0ms	(- (* b c) (* a d))

simplify1.0s

Counts: 56 → 56

prune955.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.2b

localize68.0ms

Local error

Found 4 expressions with local error:

28.8b	(sqrt (fma d d (* c c)))
28.8b	(sqrt (fma d d (* c c)))
15.2b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.3b	(- (* b c) (* a d))

rewrite31.0ms

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` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `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 → 96

Calls

4 calls:

Slowest

18.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
8.0ms	(- (* b c) (* a d))
2.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

164.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
81.0ms	(sqrt (fma d d (* c c)))
73.0ms	(sqrt (fma d d (* c c)))
50.0ms	(- (* b c) (* a d))

simplify821.0ms

Counts: 108 → 108

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.5b

localize72.0ms

Local error

Found 4 expressions with local error:

28.8b	(sqrt (fma d d (* c c)))
15.2b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.3b	(- (* b c) (* a d))
0.0b	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Counts

4 → 189

Calls

4 calls:

Slowest

28.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
23.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
10.0ms	(- (* b c) (* a d))
3.0ms	(sqrt (fma d d (* c c)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

224.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
149.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
60.0ms	(sqrt (fma d d (* c c)))
47.0ms	(- (* b c) (* a d))

simplify613.0ms

Counts: 201 → 201

prune3.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize30.0ms

Local error

Found 4 expressions with local error:

15.3b	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))
0.3b	(- (* b c) (* a d))
0.0b	(/ (* (- (* b c) (* a d)) (/ 1 (hypot d c))) (hypot d c))
0.0b	(hypot d c)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
21×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
15×	`*-un-lft-identity`
14×	`times-frac` `add-cube-cbrt`
13×	`associate-r`
9×	`div-exp`
8×	`prod-exp`
6×	`pow1` `add-log-exp` `associate-/l/`
5×	`cbrt-undiv` `flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-l*` `unswap-sqr`
2×	`rec-exp` `1-exp` `associate-*r/` `un-div-inv` `div-inv`
1×	`hypot-udef` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `associate-/l`

Counts

4 → 105

Calls

4 calls:

Slowest

34.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot d c))) (hypot d c))
25.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))
11.0ms	(- (* b c) (* a d))
0.0ms	(hypot d c)

series430.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

159.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot d c))) (hypot d c))
145.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))
65.0ms	(- (* b c) (* a d))
61.0ms	(hypot d c)

simplify2.1s

Counts: 117 → 117

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

regimes466.0ms

Accuracy

36.5% (6.7b remaining)

Error of 12.6b against oracle of 5.9b and baseline of 16.4b

bsearch92.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

1.0s

8465×

body

valid