Details

sample91.0ms

Algorithm

intervals

Results

50.0ms	256×	body	80	valid
16.0ms	256×	pre	80	true

simplify338.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize35.0ms

Local error

Found 4 expressions with local error:

45.8b	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
39.8b	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))
0.1b	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
0.0b	(fma (+ (+ alpha beta) i) i (* beta alpha))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-cbrt-cube` `add-exp-log`
26×	`times-frac`
22×	`add-sqr-sqrt`
21×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
7×	`div-inv`
6×	`associate-/l*` `difference-of-squares`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `pow-prod-down` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-/r/` `flip-+`
1×	`flip3--` `associate-r` `*-commutative` `fma-udef` `flip--`

Counts

4 → 123

Calls

4 calls:

Slowest

72.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
63.0ms	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))
62.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
0.0ms	(fma (+ (+ alpha beta) i) i (* beta alpha))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

446.0ms	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))
351.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
164.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
41.0ms	(fma (+ (+ alpha beta) i) i (* beta alpha))

simplify341.0ms

Counts: 157 → 135

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.6b

localize41.0ms

Local error

Found 4 expressions with local error:

38.1b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
37.4b	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
0.1b	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
0.0b	(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

232×	`times-frac`
179×	`add-sqr-sqrt`
154×	`*-un-lft-identity`
98×	`add-cube-cbrt`
74×	`add-cbrt-cube` `add-exp-log`
58×	`associate-l`
48×	`associate-r`
35×	`cbrt-undiv` `div-exp`
30×	`difference-of-squares`
22×	`div-inv`
17×	`prod-exp` `cbrt-unprod`
15×	`sqrt-prod` `distribute-lft-out--`
13×	`distribute-lft-out`
12×	`associate-/r*`
11×	`associate-/l*`
6×	`pow1` `associate-/r/` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*l/` `associate-/l/`
2×	`flip3-+` `flip3--` `flip-+` `flip--`
1×	`frac-times` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 284

Calls

4 calls:

Slowest

131.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
38.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
34.0ms	(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
4.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series1.5s

Counts

4 → 12

Calls

4 calls:

Slowest

745.0ms	(* (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
462.0ms	(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
159.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
115.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify863.0ms

Counts: 359 → 296

prune4.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 36.6b

localize92.0ms

Local error

Found 4 expressions with local error:

38.1b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
38.1b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
37.4b	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
0.1b	(* (sqrt (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

179×	`times-frac`
139×	`add-sqr-sqrt`
125×	`*-un-lft-identity`
85×	`add-cube-cbrt`
71×	`sqrt-prod`
61×	`associate-l`
48×	`associate-r`
27×	`add-cbrt-cube` `add-exp-log`
15×	`div-inv`
14×	`difference-of-squares`
13×	`distribute-lft-out`
9×	`cbrt-undiv` `associate-/r*` `div-exp`
8×	`unswap-sqr`
7×	`associate-/l*` `distribute-lft-out--`
6×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*l/`
2×	`flip3-+` `sqrt-div` `flip-+` `associate-/l/`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 226

Calls

4 calls:

Slowest

108.0ms	(* (sqrt (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
31.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
18.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
9.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series2.0s

Counts

4 → 12

Calls

4 calls:

Slowest

1.5s	(* (sqrt (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
177.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
159.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
142.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify1.4s

Counts: 270 → 238

prune4.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.6b

localize118.0ms

Local error

Found 4 expressions with local error:

38.1b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
37.9b	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
37.9b	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
37.4b	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-/r*` `sqrt-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*l/` `div-inv` `associate-/l/`
1×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 88

Calls

4 calls:

Slowest

37.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
4.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
1.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
1.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

182.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
132.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
101.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
78.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

simplify493.0ms

Counts: 116 → 100

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 36.6b

regimes273.0ms

Accuracy

44.8% (1.6b remaining)

Error of 35.4b against oracle of 33.8b and baseline of 36.6b

bsearch131.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
371.0ms	8000×	pre	80	true