Details

sample593.0ms

Algorithm

intervals

Results

261.0ms	66×	body	2560	valid
171.0ms	75×	body	1280	valid
44.0ms	60×	body	640	valid
16.0ms	34×	body	320	valid
6.0ms	15×	body	160	valid
1.0ms	6×	body	80	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize67.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.3b	(- x (tan x))
2.3b	(- x (sin x))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

48.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
22.0ms	(- x (sin x))

series292.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms	(/ (- x (sin x)) (- x (tan x)))
66.0ms	(- x (tan x))
84.0ms	(- x (sin x))

simplify824.0ms

Counts

89 → 89

Iterations

Useful iterations: done (820.0ms)

Iter	Nodes	Cost
0	157	1237
1	371	1200
2	1358	1149
done	5001	1147

prune364.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.3b	(* 27/2800 (pow x 4))
15.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

25.0ms	(* 9/40 (pow x 2))
24.0ms	(* 27/2800 (pow x 4))
51.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series190.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* 9/40 (pow x 2))
70.0ms	(* 27/2800 (pow x 4))
71.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify796.0ms

Counts

75 → 75

Iterations

Useful iterations: done (793.0ms)

Iter	Nodes	Cost
0	121	788
1	291	703
2	1076	645
done	5000	643

prune260.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.3b	(* 27/2800 (pow x 4))
0.8b	(log (exp (* 27/2800 (pow x 4))))
15.3b	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`pow1`
4×	`sqr-pow`
3×	`log-prod` `log-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `sum-log` `flip--` `associate--r+`

Counts

4 → 80

Calls

4 calls:

13.0ms	(* 9/40 (pow x 2))
12.0ms	(* 27/2800 (pow x 4))
4.0ms	(log (exp (* 27/2800 (pow x 4))))
55.0ms	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

series235.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 9/40 (pow x 2))
56.0ms	(* 27/2800 (pow x 4))
73.0ms	(log (exp (* 27/2800 (pow x 4))))
58.0ms	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

simplify886.0ms

Counts

92 → 92

Iterations

Useful iterations: done (883.0ms)

Iter	Nodes	Cost
0	140	987
1	321	825
2	1255	757
done	5000	755

prune304.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 27/2800 (pow x 4))
0.8b	(log (sqrt (exp (* 27/2800 (pow x 4)))))
0.8b	(log (sqrt (exp (* 27/2800 (pow x 4)))))
15.3b	(- (* 9/40 (pow x 2)) (+ (+ (log (sqrt (exp (* 27/2800 (pow x 4))))) (log (sqrt (exp (* 27/2800 (pow x 4)))))) 1/2))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`add-log-exp`
12×	`log-prod`
11×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
10×	`log-pow`
8×	`pow1`
7×	`associate-r`
6×	`sqrt-pow1` `sqrt-prod` `add-cbrt-cube`
4×	`unpow-prod-down`
3×	`diff-log` `associate-l` `prod-exp` `sum-log` `unswap-sqr`
2×	`exp-prod` `exp-to-pow` `pow1/2` `rem-log-exp` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

4 → 78

Calls

4 calls:

16.0ms	(* 27/2800 (pow x 4))
9.0ms	(log (sqrt (exp (* 27/2800 (pow x 4)))))
9.0ms	(log (sqrt (exp (* 27/2800 (pow x 4)))))
212.0ms	(- (* 9/40 (pow x 2)) (+ (+ (log (sqrt (exp (* 27/2800 (pow x 4))))) (log (sqrt (exp (* 27/2800 (pow x 4)))))) 1/2))

series1.8s

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 27/2800 (pow x 4))
726.0ms	(log (sqrt (exp (* 27/2800 (pow x 4)))))
775.0ms	(log (sqrt (exp (* 27/2800 (pow x 4)))))
228.0ms	(- (* 9/40 (pow x 2)) (+ (+ (log (sqrt (exp (* 27/2800 (pow x 4))))) (log (sqrt (exp (* 27/2800 (pow x 4)))))) 1/2))

simplify772.0ms

Counts

90 → 90

Iterations

Useful iterations: done (769.0ms)

Iter	Nodes	Cost
0	121	1353
1	269	1082
2	1121	896
done	5000	893

prune354.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch220.0ms

Steps

Iters	Range		Point
11	0.022891638200552334	5.118117448855024e+31	0.027540850594149503
10	-911936.9907706906	-4.3470241882695893e-07	-0.028532925378081175

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	51
1	33	43
done	33	43

end0.0ms

sample13.6s

Algorithm

intervals

Results

6.4s	1664×	body	2560	valid
4.0s	2736×	body	1280	valid
1.3s	949×	body	320	valid
1.3s	1835×	body	640	valid
208.0ms	482×	body	160	valid
55.0ms	334×	body	80	valid