Details

sample283.0ms

Algorithm

intervals

Results

34.0ms	5×	body	160	nan
34.0ms	311×	body	80	nan
19.0ms	161×	body	80	valid
17.0ms	30×	body	1280	valid
13.0ms	27×	body	640	valid
11.0ms	20×	body	1280	nan
8.0ms	19×	body	640	nan
6.0ms	19×	body	320	valid
5.0ms	8×	body	320	nan
4.0ms	19×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5010
7	2894
6	1606
5	890
4	445
3	209
2	98
1	41
0	18

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
16.0b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

79.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
15.0ms	(* (sqrt 2.0) t)
49.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
61.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.9s

Counts

4 → 12

Calls

4 calls:

611.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
75.0ms	(* (sqrt 2.0) t)
381.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.9s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1672
1	471
0	178

prune790.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.0b

localize57.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
6.7b	(/ (* l l) x)
8.1b	(/ (* t t) x)
29.1b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 71

Calls

4 calls:

0.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
13.0ms	(/ (* l l) x)
11.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
37.0ms	(/ (* l l) x)
37.0ms	(/ (* t t) x)
282.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

simplify1.4s

Counts

83 → 83

Iterations

Iter	Nodes
done	5002
2	1490
1	354
0	131

prune604.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.7b

localize91.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
3.8b	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
8.1b	(/ (* t t) x)
29.1b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `div-exp`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `fma-def` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `prod-exp` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 62

Calls

4 calls:

36.0ms	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
0.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
8.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))
97.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))
21.0ms	(/ (* t t) x)
284.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

simplify1.5s

Counts

74 → 74

Iterations

Iter	Nodes
done	5011
2	1416
1	348
0	123

prune649.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.7b

localize183.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (* (* (cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))) (cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))) (cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))))
29.9b	(cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
29.9b	(cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
29.9b	(cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 65

Calls

4 calls:

38.0ms	(sqrt (* (* (cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))) (cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))) (cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))))
1.0ms	(cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
1.0ms	(cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
1.0ms	(cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

241.0ms	(sqrt (* (* (cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t))))) (cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))) (cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))))
709.0ms	(cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
356.0ms	(cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))
319.0ms	(cbrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* t t)))))

simplify2.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
4	4443
3	1371
2	544
1	231
0	110

prune640.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.7b

regimes768.0ms

Accuracy

74.2% (6.2b remaining)

Error of 10.0b against oracle of 3.8b and baseline of 27.8b

bsearch1.4s

Steps

Iters	Range		Point
10	1.3717035908280058e+110	9.416773298407726e+123	4.3989158505625655e+111
9	7.880712048074117e-244	6.696361263611533e-237	3.5177750870459065e-239
9	-2.267750316242303e-307	5.4650818186550785e-304	8.79911984523004e-305
6	-1.644420621869611e-274	-1.9344149889410284e-275	-9.405973531316699e-275
8	-1.048914663983069e-155	-1.9657921853589755e-159	-1.9933494186781088e-159
10	-1.0150002838305954e+118	-7.086310576970351e+104	-3.715046482673699e+110

simplify53.0ms

Iterations

Iter	Nodes
done	80
1	80
0	66

end0.0ms

sample6.1s

Algorithm

intervals

Results

1.5s	9898×	body	80	nan
1.3s	5169×	body	80	valid
751.0ms	606×	body	640	nan
510.0ms	993×	body	640	valid
439.0ms	818×	body	1280	valid
341.0ms	575×	body	1280	nan
273.0ms	653×	body	320	valid
124.0ms	367×	body	160	valid
103.0ms	335×	body	320	nan
33.0ms	170×	body	160	nan