Details

sample952.0ms

Algorithm

intervals

Results

500.0ms	64×	body	2560	valid
178.0ms	77×	body	1280	valid
68.0ms	61×	body	640	valid
57.0ms	33×	body	320	valid
4.0ms	15×	body	80	valid
4.0ms	6×	body	160	valid

simplify94.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

93.0ms

(/ (- x (sin x)) (- x (tan x)))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize28.0ms

Local error

Found 3 expressions with local error:

0.5b	(- x (sin x))
0.4b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 113

Calls

3 calls:

Slowest

31.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series562.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

237.0ms	(- x (tan x))
225.0ms	(/ (- x (sin x)) (- x (tan x)))
100.0ms	(- x (sin x))

simplify6.2s

Counts

122 → 122

Calls

122 calls:

Slowest

474.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
401.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
396.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
363.0ms	(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
284.0ms	(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune999.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

15.1b	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.1b	(* (* x x) (* x x))
0.0b	(fma -27/2800 (* (* x x) (* x x)) -1/2)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

114×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`prod-exp` `cbrt-unprod`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

3 → 88

Calls

3 calls:

Slowest

22.0ms	(* (* x x) (* x x))
0.0ms	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)

series213.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

97.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)
68.0ms	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
48.0ms	(* (* x x) (* x x))

simplify3.0s

Counts

76 → 97

Calls

76 calls:

Slowest

838.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
349.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
332.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
265.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
152.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune757.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

15.1b	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.1b	(* (* x x) (* x x))
0.0b	(log1p (expm1 (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
0.0b	(fma -27/2800 (* (* x x) (* x x)) -1/2)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

115×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
16×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`log1p-udef` `swap-sqr` `associate-r` `associate-l` `log1p-expm1` `*-commutative` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

Slowest

26.0ms	(* (* x x) (* x x))
0.0ms	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.0ms	(log1p (expm1 (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
0.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)

series419.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

179.0ms	(log1p (expm1 (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
139.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)
57.0ms	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
44.0ms	(* (* x x) (* x x))

simplify2.7s

Counts

80 → 112

Calls

80 calls:

Slowest

369.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
315.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
310.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
293.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
150.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune994.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

16.1b	(cbrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))
16.1b	(cbrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))
16.1b	(cbrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))
15.1b	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

Slowest

1.0ms	(cbrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))
1.0ms	(cbrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))
1.0ms	(cbrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))
0.0ms	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))

series580.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

183.0ms	(cbrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))
170.0ms	(cbrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))
156.0ms	(cbrt (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)))
70.0ms	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))

simplify4.7s

Counts

21 → 65

Calls

21 calls:

Slowest

435.0ms	(- (pow -1/2 1/3) (+ (* 3/20 (* (pow x 2) (pow -1/2 1/3))) (* 9/560 (* (pow x 4) (pow -1/2 1/3)))))
418.0ms	(- (pow -1/2 1/3) (+ (* 3/20 (* (pow x 2) (pow -1/2 1/3))) (* 9/560 (* (pow x 4) (pow -1/2 1/3)))))
396.0ms	(- (pow -1/2 1/3) (+ (* 3/20 (* (pow x 2) (pow -1/2 1/3))) (* 9/560 (* (pow x 4) (pow -1/2 1/3)))))
338.0ms	(- (exp (* 1/3 (- (log -27/2800) (* 4 (log (/ -1 x)))))) (+ (* 70/9 (/ (exp (* 1/3 (- (log -27/2800) (* 4 (log (/ -1 x)))))) (pow x 2))) (* 3500/81 (/ (exp (* 1/3 (- (log -27/2800) (* 4 (log (/ -1 x)))))) (pow x 4)))))
321.0ms	(- (exp (* 1/3 (- (log -27/2800) (* 4 (log (/ 1 x)))))) (+ (* 70/9 (/ (exp (* 1/3 (- (log -27/2800) (* 4 (log (/ 1 x)))))) (pow x 2))) (* 3500/81 (/ (exp (* 1/3 (- (log -27/2800) (* 4 (log (/ 1 x)))))) (pow x 4)))))

prune589.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes112.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch134.0ms

end0.0ms

sample17.4s

Algorithm

intervals

Results

7.1s	1539×	body	2560	valid
5.8s	2740×	body	1280	valid
2.8s	1931×	body	640	valid
785.0ms	946×	body	320	valid
565.0ms	375×	body	80	valid
230.0ms	469×	body	160	valid